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Giant dipole resonance as a quantitative constraint on the symmetry energy

2008-06-16
Luca Trippa , G. Colò , E. Vigezzi
The possible constraints on the poorly determined symmetry part of the effective nuclear Hamiltonians or effective energy functionals, i.e., the so-called symmetry energy $S(\ensuremath{\rho})$, are very much under debate. In … The possible constraints on the poorly determined symmetry part of the effective nuclear Hamiltonians or effective energy functionals, i.e., the so-called symmetry energy $S(\ensuremath{\rho})$, are very much under debate. In the present work, we show that the value of the symmetry energy associated with Skyrme functionals, at densities \ensuremath{\rho} around 0.1 fm${}^{\ensuremath{-}3}$, is strongly correlated with the value of the centroid of the Giant Dipole Resonance (GDR) in spherical nuclei. Consequently, the experimental value of the GDR in, e.g., $^{208}\mathrm{Pb}$ can be used as a constraint on the symmetry energy, leading to $23.3 \mathrm{MeV}<S(\ensuremath{\rho}=0.1 {\mathrm{fm}}^{\ensuremath{-}3})<24.9$ MeV.

The halo of the exotic nucleus 11Li: a single Cooper pair

2001-10-01
F. Barranco , P. F. Bortignon , R.A. Broglia +2 more
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Many-body effects in nuclear structure

2004-07-01
F. Barranco , R.A. Broglia , G. Colò +3 more
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Linear response of light deformed nuclei investigated by self-consistent quasiparticle random-phase approximation

2010-06-08
Cristina Losa , A. Pastore , T. Døssing +2 more
We present a calculation of the properties of vibrational states in deformed, axially-symmetric even-even nuclei, within the framework of a fully self-consistent quasiparticle random phase approximation (QRPA). The same Skyrme … We present a calculation of the properties of vibrational states in deformed, axially-symmetric even-even nuclei, within the framework of a fully self-consistent quasiparticle random phase approximation (QRPA). The same Skyrme energy density and density-dependent pairing functionals are used to calculate the mean field and the residual interaction in the particle-hole and particle-particle channels. We have tested our software in the case of spherical nuclei against fully self-consistent calculations published in the literature, finding excellent agreement. We investigate the consequences of neglecting the spin-orbit and Coulomb residual interactions in QRPA. Furthermore we discuss the improvement obtained in the QRPA result associated with the removal of spurious modes. Isoscalar and isovector responses in the deformed $^{24--26}\mathrm{Mg}$, $^{34}\mathrm{Mg}$ isotopes are presented and compared to experimental findings.
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Quasiparticle random-phase approximation with quasiparticle-vibration coupling: Application to the Gamow-Teller response of the superfluid nucleus<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Sn</mml:mi><mml:mprescripts /><mml:none /><mml:mn>120</mml:mn></mml:mmultiscripts></mml:math>

2016-12-29
Y. Niu , G. Colò , E. Vigezzi +2 more
We propose a self-consistent quasiparticle random-phase approximation (QRPA) plus quasiparticle-vibration coupling (QPVC) model with Skyrme interactions to describe the width and the line shape of giant resonances in open-shell nuclei, … We propose a self-consistent quasiparticle random-phase approximation (QRPA) plus quasiparticle-vibration coupling (QPVC) model with Skyrme interactions to describe the width and the line shape of giant resonances in open-shell nuclei, in which the effect of superfluidity should be taken into account in both the ground state and the excited states. We apply the new model to the Gamow-Teller resonance in the superfluid nucleus $^{120}\mathrm{Sn}$, including both the isoscalar spin-triplet and the isovector spin-singlet pairing interactions. The strength distribution in $^{120}\mathrm{Sn}$ is well reproduced and the underlying microscopic mechanisms, related to QPVC and also to isoscalar pairing, are analyzed in detail.
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Continuum particle-vibration coupling method in coordinate-space representation for finite nuclei

2012-09-14
K. Mizuyama , G. Colò , E. Vigezzi
In this paper we present a new formalism to implement the nuclear particle-vibration coupling (PVC) model. The key issue is the proper treatment of the continuum, that is allowed by … In this paper we present a new formalism to implement the nuclear particle-vibration coupling (PVC) model. The key issue is the proper treatment of the continuum, that is allowed by the coordinate space representation. Our formalism, based on the use of zero-range interactions like the Skyrme forces, is microscopic and fully self-consistent. We apply it to the case of neutron single-particle states in $^{40}$Ca, $^{208}$Pb and $^{24}$O. The first two cases are meant to illustrate the comparison with the usual (i.e., discrete) PVC model. However, we stress that the present approach allows to calculate properly the effect of PVC on resonant states. We compare our results with those from experiments in which the particle transfer in the continuum region has been attempted. The latter case, namely $^{24}$O, is chosen as an example of a weakly-bound system. Such a nucleus, being double-magic and not displaying collective low-lying vibrational excitations, is characterized by quite pure neutron single-particle states around the Fermi surface.
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Pairing matrix elements and pairing gaps with bare, effective, and induced interactions

2005-11-21
F. Barranco , P. F. Bortignon , Ricardo A. Broglia +4 more
The dependence on the single-particle states of the pairing matrix elements of the Gogny force and of the bare low-momentum nucleon-nucleon potential ${v}_{\mathrm{low}\text{\ensuremath{-}}k}$---designed so as to reproduce the low-energy observables … The dependence on the single-particle states of the pairing matrix elements of the Gogny force and of the bare low-momentum nucleon-nucleon potential ${v}_{\mathrm{low}\text{\ensuremath{-}}k}$---designed so as to reproduce the low-energy observables avoiding the use of a repulsive core---is studied for a typical finite, superfluid nucleus ($^{120}\mathrm{Sn}$). It is found that the matrix elements of ${v}_{\mathrm{low}\text{\ensuremath{-}}k}$ follow closely those of ${v}_{\mathrm{Gogny}}$ on a wide range of energy values around the Fermi energy ${e}_{F}$, those associated with ${v}_{\mathrm{low}\text{\ensuremath{-}}k}$ being less attractive. This result explains the fact that around ${e}_{F}$ the pairing gap ${\ensuremath{\Delta}}_{\mathrm{Gogny}}$ associated with the Gogny interaction (and with a density of single-particle levels corresponding to an effective k mass ${m}_{k}\ensuremath{\approx}0.7 m$) is a factor of about 2 larger than ${\ensuremath{\Delta}}_{\mathrm{low}\text{\ensuremath{-}}k}$, being in agreement with ${\ensuremath{\Delta}}_{\mathrm{exp}}=1.4$ MeV. The exchange of low-lying collective surface vibrations among pairs of nucleons moving in time-reversal states gives rise to an induced pairing interaction ${v}_{\mathrm{ind}}$ peaked at ${e}_{F}$. The interaction $({v}_{\mathrm{low}\text{\ensuremath{-}}k}+{v}_{\mathrm{ind}}) {Z}_{\ensuremath{\omega}}$ arising from the renormalization of the bare nucleon-nucleon potential and of the single-particle motion (\ensuremath{\omega}-mass and quasiparticle strength ${Z}_{\ensuremath{\omega}}$) associated with the particle-vibration coupling mechanism, leads to a value of the pairing gap at the Fermi energy ${\ensuremath{\Delta}}_{\mathrm{ren}}$ that accounts for the experimental value. An important question that remains to be studied quantitatively is to what extent ${\ensuremath{\Delta}}_{\mathrm{Gogny}}$, which depends on average parameters, and ${\ensuremath{\Delta}}_{\mathrm{ren}}$, which explicitly depends on the parameters describing the (low-energy) nuclear structure, display or not a similar isotopic dependence and whether this dependence is borne out by the data.
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Attractive and repulsive contributions of medium fluctuations to nuclear superfluidity

2005-07-18
G. Gori , Fabio Ramponi , F. Barranco +4 more
Oscillations of mainly surface character ($S=0$ modes) give rise, in atomic nuclei, to an attractive (induced) pairing interaction, while spin ($S=1$) modes of mainly volume character generate a repulsive interaction, … Oscillations of mainly surface character ($S=0$ modes) give rise, in atomic nuclei, to an attractive (induced) pairing interaction, while spin ($S=1$) modes of mainly volume character generate a repulsive interaction, the net effect being an attraction which accounts for a sizeable fraction of the experimental pairing gap. Suppressing the particle-vibration coupling mediated by the proton degrees of freedom, i.e., mimicking neutron matter, the total surface plus spin-induced pairing interaction becomes repulsive.
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Interweaving of elementary modes of excitation in superfluid nuclei through particle-vibration coupling: Quantitative account of the variety of nuclear structure observables

2015-09-18
A. Idini , G. Potel , F. Barranco +2 more
A complete characterization of the structure of nuclei can be obtained by combining information arising from inelastic scattering, Coulomb excitation and $\gamma-$decay, together with one- and two-particle transfer reactions. In … A complete characterization of the structure of nuclei can be obtained by combining information arising from inelastic scattering, Coulomb excitation and $\gamma-$decay, together with one- and two-particle transfer reactions. In this way it is possible to probe the single-particle and collective components of the nuclear many-body wavefunction resulting from their mutual coupling and diagonalising the low-energy Hamiltonian. We address the question of how accurately such a description can account for experimental observations. It is concluded that renormalizing empirically and on equal footing bare single-particle and collective motion in terms of self-energy (mass) and vertex corrections (screening), as well as particle-hole and pairing interactions through particle-vibration coupling allows theory to provide an overall, quantitative account of the data.
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Electron–phonon coupling in charged buckminsterfullerene

1998-04-01
N. Breda , Ricardo A. Broglia , G. Colò +5 more
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Quantum entanglement in nuclear Cooper-pair tunneling with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>γ</mml:mi></mml:math> rays

2021-02-25
G. Potel , F. Barranco , E. Vigezzi +1 more
A new analysis of heavy-ion collision experiments uncovers evidence that two colliding nuclei behave like a Josephson junction---a device in which Cooper pairs tunnel through a barrier between two superfluids. A new analysis of heavy-ion collision experiments uncovers evidence that two colliding nuclei behave like a Josephson junction---a device in which Cooper pairs tunnel through a barrier between two superfluids.
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Nuclear energy density functionals grounded in <i>ab initio</i> calculations

2021-08-09
F. Marino , C. Barbieri , Arianna Carbone +5 more
We discuss the construction of a nuclear energy density functional (EDF) from ab initio computations and advocate the need for a methodical approach that is free from ad hoc assumptions. … We discuss the construction of a nuclear energy density functional (EDF) from ab initio computations and advocate the need for a methodical approach that is free from ad hoc assumptions. The equations of state (EoSs) of symmetric nuclear and pure neutron matter are computed using the chiral ${\mathrm{NNLO}}_{\mathrm{sat}}$ and the phenomenological ${\mathrm{AV4}}^{\ensuremath{'}}+{\mathrm{UIX}}_{c}$ Hamiltonians as inputs to self-consistent Green's function (SCGF) and auxiliary field diffusion Monte Carlo (AFDMC) methods. We propose a convenient parametrization of the EoS as a function of the Fermi momentum and fit it on the SCGF and AFDMC calculations. We apply the ab initio based EDF to carry out an analysis of the binding energies and charge radii of different nuclei in the local density approximation. The ${\mathrm{NNLO}}_{\mathrm{sat}}$-based EDF produces encouraging results, whereas the ${\mathrm{AV4}}^{\ensuremath{'}}+{\mathrm{UIX}}_{c}$-based one is farther from experiment. Possible explanations of these different behaviors are suggested, and the importance of gradient and spin-orbit terms is analyzed. Our paper paves the way for a practical and systematic way to merge ab initio nuclear theory and density functional theory, while shedding light on some critical aspects of this procedure.
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Spectral line shape of exotic nuclei

1996-11-01
Francesco Ghielmetti , G. Colò , E. Vigezzi +2 more
The quadrupole strength function of $^{28}O$ is calculated making use of the SIII interaction, within the framework of continuum-RPA and taking into account collisions among the nucleons (doorway coupling). The … The quadrupole strength function of $^{28}O$ is calculated making use of the SIII interaction, within the framework of continuum-RPA and taking into account collisions among the nucleons (doorway coupling). The centroid of the giant resonance is predicted at $\approx 14$ MeV, that is much below the energy expected for both isoscalar and isovector quadrupole resonances in nuclei along the stability valley. About half of this width arises from the coupling of the resonance to the continuum and about half is due to doorway coupling. This result is similar to that obtained in the study of giant resonances in light, $\beta$-stable nuclei, and shows the lack of basis for the expectation, entertained until now in the literature, that continuum decay was the main damping mechanism of giant resonances in halo nuclei.
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Probing the Order-to-Chaos Region in Superdeformed<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi>Tb</mml:mi><mml:mprescripts /><mml:none /><mml:mn>151</mml:mn></mml:mmultiscripts></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi>Pb</mml:mi><mml:mprescripts /><mml:none /><mml:mn>196</mml:mn></mml:mmultiscripts></mml:math>Nuclei with Continuum<mml:math xmlns:mml="http://www.w3.…

2008-09-30
S. Leoni , G. Benzoni , N. Blasi +7 more
The γ decay associated with the warm rotation of the superdeformed nuclei Tb151 and Pb196 has been measured with the EUROBALL IV array. Several independent quantities provide a stringent test … The γ decay associated with the warm rotation of the superdeformed nuclei Tb151 and Pb196 has been measured with the EUROBALL IV array. Several independent quantities provide a stringent test of the population and decay dynamics in the superdeformed well. A Monte Carlo simulation of the γ decay based on microscopic calculations gives remarkable agreement with the data only assuming a large enhancement of the B(E1) strength for 1–2 MeV γ rays, which may be related to the evidence for octupole vibrations in both mass regions.Received 27 June 2008DOI:https://doi.org/10.1103/PhysRevLett.101.142502©2008 American Physical Society
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Correlation energy contribution to nuclear masses

2004-08-21
Simone Baroni , M Armati , F. Barranco +4 more
The ground-state correlation energies associated with collective surface and pairing vibrations are calculated for Pb and Ca isotopes. It is shown that this contribution, when added to those predicted by … The ground-state correlation energies associated with collective surface and pairing vibrations are calculated for Pb and Ca isotopes. It is shown that this contribution, when added to those predicted by one of the most accurate modern nuclear mass formulae (HFBCS MSk7 mass formula), reduces the associated rms error by an important factor, making mean-field theory, once its time dependence is taken into account, a quantitative predictive tool for nuclear masses.
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Medium polarization isotopic effects on nuclear binding energies

2006-08-16
Simone Baroni , F. Barranco , P. F. Bortignon +3 more
There exist several effective interactions whose parameters are fitted to force mean field predictions to reproduce experimental findings of finite nuclei and calculated properties of infinite nuclear matter. Exploiting this … There exist several effective interactions whose parameters are fitted to force mean field predictions to reproduce experimental findings of finite nuclei and calculated properties of infinite nuclear matter. Exploiting this tecnique one can give a good description of nuclear binding energies. We present evidence that further progress can be made by taking into account medium polarization effects associated with surface and pairing vibrations.
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First step in the nuclear inverse Kohn-Sham problem: From densities to potentials

2020-02-28
Giacomo Accorto , P. Brandolini , F. Marino +5 more
Nuclear density functional theory (DFT) plays a prominent role in the understanding of nuclear structure, being the approach with the widest range of applications. Hohenberg and Kohn theorems warrant the … Nuclear density functional theory (DFT) plays a prominent role in the understanding of nuclear structure, being the approach with the widest range of applications. Hohenberg and Kohn theorems warrant the existence of a nuclear energy density functional (EDF), yet its form is unknown. Current efforts to build a nuclear EDF are hindered by the lack of a strategy for systematic improvement. In this context, alternative approaches should be pursued and, so far, an unexplored avenue is that related to the inverse DFT problem. DFT is based on the one-to-one correspondence between Kohn-Sham (KS) potentials and densities. The exact EDF produces the exact density, so that from the knowledge of experimental or ab initio densities one may deduce useful information through reverse engineering. The idea has already been proved to be useful in the case of electronic systems. The general problem should be dealt with in steps, and the objective of the present work is to focus on testing algorithms to extract the Kohn-Sham potential within the simplest ansatz from the knowledge of the experimental neutron and proton densities. We conclude that, while robust algorithms exist, the experimental densities present some critical aspects. Finally, we provide some perspectives for future works.
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Microscopic structure of rotational damping

1999-03-01
Masayuki Matsuo , Kōji Yoshida , T. Døssing +2 more
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From bare to renormalized order parameter in gauge space: Structure and reactions

2017-09-12
G. Potel , A. Idini , F. Barranco +2 more
It is not physically obvious why one can calculate with similar accuracy, as compared to the experimental data, the absolute cross section associated with two-nucleon transfer processes between members of … It is not physically obvious why one can calculate with similar accuracy, as compared to the experimental data, the absolute cross section associated with two-nucleon transfer processes between members of pairing rotational bands, making use of simple BCS (constant matrix elements) or of many-body [Nambu-Gorkov (NG), nuclear field theory (NFT)] spectroscopic amplitudes. Restoration of spontaneous symmetry breaking and associated emergent generalized rigidity in gauge space provides the answer and points to a new emergence: A physical sum rule resulting from the intertwining of structure and reaction processes, closely connected with the central role induced pairing interaction plays in structure, together with the fact that successive transfer dominates Cooper pair tunneling.
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Single Cooper pair transfer in stable and in exotic nuclei

2009-01-01
G. Potel , B. F. Bayman , F. Barranco +3 more
We discuss in this paper both the past and the present of two-nucleon transfer reactions, as well as try to foresee the near future of such studies in nuclei, induced … We discuss in this paper both the past and the present of two-nucleon transfer reactions, as well as try to foresee the near future of such studies in nuclei, induced by light as well as by heavy ion reactions.

Exact restoration of Galilei invariance in density functional calculations with quantum Monte Carlo

2019-11-18
P. Massella , F. Barranco , Diego Lonardoni +3 more
Galilean invariance is usually violated in self-consistent mean-field calculations that employ effective density-dependent nuclear forces. We present a novel approach, based on variational quantum Monte Carlo techniques, suitable to preserve … Galilean invariance is usually violated in self-consistent mean-field calculations that employ effective density-dependent nuclear forces. We present a novel approach, based on variational quantum Monte Carlo techniques, suitable to preserve this symmetry and assess the effect of its violation, seldom attempted in the past. To this aim, we generalize the linear optimization method to encompass the density-dependence of effective Hamiltonians, and study $^4$He, $^{16}$O, and $^{40}$Ca ground-state properties employing the Gogny interaction.
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Rotational Damping And Compound Formation In Warm Rotating Nuclei

2003-01-01
Masayuki Matsuo , S. Leoni , Camila Grassi +5 more
The rotational damping width \Gamma_{rot} and the compound damping width \Gamma_{comp} are two fundamental quantities that characterize rapidly rotating compound nuclei having finite thermal excitation energy. A two-component structure in … The rotational damping width \Gamma_{rot} and the compound damping width \Gamma_{comp} are two fundamental quantities that characterize rapidly rotating compound nuclei having finite thermal excitation energy. A two-component structure in the strength function of consecutive E2 transitions reflects the two widths, and it causes characteristic features in the double and triple gamma-ray spectra. We discuss a new method to extract experimentally values of \Gamma_{rot} and \Gamma_{comp}. The first preliminary result of this method is presented.
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Dual origin of pairing in nuclei

2016-11-01
A. Idini , G. Potel , F. Barranco +2 more
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Radioactive beams and inverse kinematics: Probing the quantal texture of the nuclear vacuum

2019-06-29
F. Barranco , G. Potel , E. Vigezzi +1 more
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Complete solution to the inverse Kohn-Sham problem: From the density to the energy

2022-03-07
Alberto Liardi , F. Marino , G. Colò +2 more
A complete solution to the inverse problem of Kohn-Sham (KS) density functional theory is proposed. Our method consists of two steps. First, the effective KS potential is determined from the … A complete solution to the inverse problem of Kohn-Sham (KS) density functional theory is proposed. Our method consists of two steps. First, the effective KS potential is determined from the ground-state density of a given system. Then, the knowledge of the potentials along a path in the space of densities is exploited in a line integration formula to determine numerically the KS energy of that system. A possible choice for the density path is proposed. A benchmark in the case of a simplified yet realistic nuclear system is shown to be successful, so the method seems promising for future applications.
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Perturbed nuclear matter studied within density functional theory with a finite number of particles

2023-04-17
F. Marino , G. Colò , X. Roca-Maza +1 more
Nuclear matter is studied within the density functional theory framework. Our method employs a finite number of nucleons in a box subject to periodic boundary conditions, in order to simulate … Nuclear matter is studied within the density functional theory framework. Our method employs a finite number of nucleons in a box subject to periodic boundary conditions, in order to simulate infinite matter and study its response to an external static potential. We detail both the theoretical formalism and its computational implementation for pure neutron matter and symmetric nuclear matter with Skyrme-like energy density functionals (EDFs). The implementation of spin-orbit, in particular, is carefully discussed. Our method is applied to the problem of the static response of nuclear matter and the impact of the perturbation on the energies, densities, and level structure of the system is investigated. Our work is a crucial step in our program of ab initio based nuclear EDFs [Phys. Rev. C 104, 024315 (2021)] as it paves the way towards the goal of constraining the EDF surface terms on ab initio calculations.
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The complete inverse Kohn-Sham problem: from the density to the energy

2021-10-21
Alberto Liardi , F. Marino , G. Colò +2 more
A complete solution to the inverse problem of Kohn-Sham (KS) density functional theory is proposed. Our method consists of two steps. First, the effective KS potential is determined from the … A complete solution to the inverse problem of Kohn-Sham (KS) density functional theory is proposed. Our method consists of two steps. First, the effective KS potential is determined from the ground state density of a given system. Then, the knowledge of the potentials along a path in the space of densities is exploited in a line integration formula to determine numerically the KS energy of that system. A possible choice for the density path is proposed. A benchmark in the case of a simplified yet realistic nuclear system is shown to be successful, so that the method seems promising for future applications.

Transient Joule- and (ac) Josephson-like photon emission in one- and two- nucleon tunneling processes between superfluid nuclei: Blackbody and coherent spectral functions

2022-06-28
Ricardo A. Broglia , F. Barranco , G. Potel +1 more
Effective charged neutrons involved in one- and two- nucleon tunneling processes in heavy ion collisions between superfluid nuclei are expected to emit photons. Although the centroid, width and integrated energy … Effective charged neutrons involved in one- and two- nucleon tunneling processes in heavy ion collisions between superfluid nuclei are expected to emit photons. Although the centroid, width and integrated energy area characterizing the associated gamma-strength functions are rather similar, the corresponding line shapes reflect the thermal equilibrated-like character of the quasiparticle transfer (1n-channel, blackbody spectral functional dependence), and the quantal coherent character of the Cooper pair transfer (2n-channel, Gaussian functional dependence) respectively. The predicted angular distributions, polarizations and analyzing power provide further insight into the profoundly different physics to be found at the basis of what can be considered a transient Joule-like and a (ac) Josephson-like nuclear processes
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On the Origin of Nuclear Superfluidity

1998-01-01
F. Barranco , P. F. Bortignon , G. Gori +3 more
The induced pairing interaction arising from the exchange of collective surface vibrations among nucleons moving in time reversal states close to the Fermi energy is found to lead to values … The induced pairing interaction arising from the exchange of collective surface vibrations among nucleons moving in time reversal states close to the Fermi energy is found to lead to values of the pairing gap which are similar to those experimentally observed.

Correlation energy contribution to nuclear masses

2007-01-21
Simone Baroni , F. Barranco , P. F. Bortignon +3 more
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Quasi-particle properties and Cooper pairing in trapped Fermi gases

2004-01-01
Luca Giorgetti , L. Viverit , G. Gori +3 more
The possibility for the particles in a Fermi gas to emit and reabsorb density and spin fluctuations gives rise to an effective mass and to a lifetime of the quasi-particles, … The possibility for the particles in a Fermi gas to emit and reabsorb density and spin fluctuations gives rise to an effective mass and to a lifetime of the quasi-particles, as well as to an effective pairing interaction which affect in an important way the BCS critical temperature. We calculate these effects for a spherically symmetric trapped Fermi gas of $\sim$ 1000 particles. The calculation provides insight on the many-body physics of finite Fermi gases and is closely related to similar problems recently considered in the case of atomic nuclei and neutron stars.
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Exploring density-dependent effective interactions with quantum Monte Carlo

2018-08-01
P. Massella , F. Barranco , Diego Lonardoni +3 more
We investigate some aspects of the connection between mean-field and ab-initio calculations for many-nucleon systems employing the Gogny effective interaction. In particular, we present variational Monte Carlo calculations of $^4$He … We investigate some aspects of the connection between mean-field and ab-initio calculations for many-nucleon systems employing the Gogny effective interaction. In particular, we present variational Monte Carlo calculations of $^4$He and $^{16}$O, for which we extended the formalism of the linear method to the case of a density-dependent Hamiltonian. Monte Carlo calculations using an uncorrelated basis reduce to Hartree-Fock ones, but Galilean invariance can be preserved, contrary to the usual treatment. An analysis of the results obtained with the Gogny force when used in conjunction with correlated wave functions has also been performed. Calculations show the collapse of the deuteron, leading to a set of unphysical predictions for the structure of heavier nuclei. This behavior remarks the different role of the Gogny effective interaction as compared to bare interactions typically used in fully microscopic calculations.

Dual Origin of Pairing in Nuclei

2014-01-01
A. Idini , G. Potel , F. Barranco +2 more
An essentially "complete" description of the low-energy nuclear structure of the superfluid nucleus $^{120}$Sn and of its odd-$A$ neighbors is provided by the observations carried out with the help of … An essentially "complete" description of the low-energy nuclear structure of the superfluid nucleus $^{120}$Sn and of its odd-$A$ neighbors is provided by the observations carried out with the help of Coulomb excitation and of one-- and of two-- particle transfer reactions, specific probes of vibrations, quasiparticle and pairing degrees of freedom respectively, and of their mutual couplings. These experimental findings are used to stringently test the predictions of a similarly "complete" description of $^{119,120,121}$Sn carried out in terms of elementary modes of excitation which, through their interweaving, melt together into effective fields, each displaying properties reflecting that of all others, there individuality resulting from the actual relative importance of each one. Its implementation is done by solving the Nambu-Gor'kov equations including, for the first time, all medium polarization effects resulting from the interweaving of quasiparticles, spin and surface vibrations, taking into account, within the framework of nuclear field theory (NFT), the variety of processes leading to self-energy, vertex and Pauli principle corrections, and to the induced pairing interaction. Theory provides an overall quantitative account of the experimental findings. From these results one can, not only obtain strong circumstantial evidence for the inevitability for the dual origin of pairing in nuclei but also, extract information which can be used at profit to quantitatively disentangle the contributions to pairing correlations in general and to the pairing gap in particular, arising from the bare and from the induced pairing interactions.

Radioactive beams and inverse kinematics: probing the quantal texture of the nuclear vacuum

2019-01-01
F. Barranco , G. Potel , E. Vigezzi +1 more
The properties of the quantum electrodynamic (QED) vacuum in general, and of the nuclear vacuum (ground) state in particular are determined by virtual processes implying the excitation of a photon … The properties of the quantum electrodynamic (QED) vacuum in general, and of the nuclear vacuum (ground) state in particular are determined by virtual processes implying the excitation of a photon and of an electron--positron pair in the first case and of, for example, the excitation of a collective quadrupole surface vibration and a particle--hole pair in the nuclear case. Signals of these processes can be detected in the laboratory in terms of what can be considered a nuclear analogue of Hawking radiation. An analogy which extends to other physical processes involving QED vacuum fluctuations like the Lamb shift, pair creation by $γ-$rays, van der Waals forces and the Casimir effect, to the extent that one concentrates on the eventual outcome resulting by forcing a virtual process to become real, and not on the role of the black hole role in defining the event horizon. In the nuclear case, the role of this event is taken over at a microscopic, fully quantum mechanical level, by nuclear probes (reactions) acting on a virtual particle of the zero point fluctuation (ZPF) of the nuclear vacuum in a similar irreversible, no--return, fashion as the event horizon does, letting the other particle, entangled with the first one, escape to infinity, and eventually be detected. With this proviso in mind one can posit that the reactions $^1$H($^{11}$Be,$^{10}$Be$(2^+$;3.37 ${\rm MeV}$))$^2$H and $^{1}$H($^{11}$Li,$^9$Li($1/2^-$; 2.69 ${\rm MeV}$))$^3$H together with the associated $γ-$decay processes indicate a possible nuclear analogy of Hawking radiation.
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Probable observation of the nuclear Cooper pair mean square radius in superfluid nuclei

2021-01-01
Ricardo A. Broglia , F. Barranco , G. Potel +1 more
The phenomenon of low-temperature superconductivity is intimately associated with the condensation of weakly bound, very extended, strongly overlapping Cooper pairs, and systematic experimental studies of the associated mean square radius … The phenomenon of low-temperature superconductivity is intimately associated with the condensation of weakly bound, very extended, strongly overlapping Cooper pairs, and systematic experimental studies of the associated mean square radius (coherence length) have been made. While the extension of BCS theory to the atomic nucleus has been successful beyond expectation, to our knowledge, no measurement of the nuclear coherence length (expected to be much larger than nuclear dimensions) has been reported in the literature. Recent studies of Cooper pair transfer across a Josephson-like junction, transiently established in a heavy ion collision between superfluid nuclei, have likely changed the situation, providing the experimental input for a quantitative estimate of the nuclear coherence length, as well as the basis for a nuclear analogue of the (ac) Josephson effect.
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Nuclear Field Theory predictions for 11Li and 12Be: shedding light on the origin of pairing in nuclei

2012-01-01
G. Potel , A. Idini , F. Barranco +2 more
Recent data resulting from studies of two-nucleon transfer reaction on 11Li, analyzed through a unified nuclear-structure-direct-reaction theory have provided strong direct as well as indirect confirmation, through the population of … Recent data resulting from studies of two-nucleon transfer reaction on 11Li, analyzed through a unified nuclear-structure-direct-reaction theory have provided strong direct as well as indirect confirmation, through the population of the first excited state of 9Li and of the observation of a strongly quenched ground state transition, of the prediction that phonon mediated pairing interaction is the main mechanism binding the neutron halo of the 8.5 ms-lived 11Li nucleus. In other words, the ground state of 11Li can be viewed as a neutron Cooper pair bound to the 9Li core, mainly through the exchange of collective vibration of the core and of the pigmy resonance arizing from the sloshing back and forth of the neutron halo against the protons of the core, the mean field leading to unbound two particle states, a situation essentially not altered by the bare nucleon-nucleon interaction acting between the halo neutrons. Two-neutron pick-up data, together with (t,p) data on 7Li, suggest the existence of a pairing vibrational band based on 9Li, whose members can be excited with the help of inverse kinematic experiments as was done in the case of 11Li(p,t)9Li reaction. The deviation from harmonicity can provide insight into the workings of medium polarization effects on Cooper pair nuclear pairing, let alone specific information concering the "rigidity" of the N=6 shell closure. Further information concerning these questions is provided by the predicted absolute differential cross sections associated with the reactions 12Be(p,t)10Be(gs) and 12Be(p,t)10Be(pv)(~10Be(p,t)8Be(gs)). In particular, concerning this last reaction, predictions of \sigma_{abs} can change by an order of magnitude depending on whether the halo properties associated with the d_{5/2} orbital are treated selfconsistently in calculating the ground state correlations of the (pair removal) mode, or not.
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The ASIMOV Prize for scientific publishing - HEP researchers trigger young people toward science

2022-10-14
A. Ventura , W.M. Alberico , Roberta Antolini +7 more
This work presents the ASIMOV Prize for scientific publishing, which was launched in Italy in 2016. The prize aims to bring the young generations closer to scientific culture, through the … This work presents the ASIMOV Prize for scientific publishing, which was launched in Italy in 2016. The prize aims to bring the young generations closer to scientific culture, through the critical reading of popular science books. The books are selected by a committee that includes scientists, professors, Ph.D. and Ph.D. students, writers, journalists and friends of culture, and most importantly, over 800 school teachers. Students are actively involved in the prize, according to the best practices of public engagement: they read, review the books and vote for them, choosing the winner. The experience is quite successful: 12,000 students from 270 schools all over Italy participated in the last edition. The possibility of replicating this experience in other countries is indicated, as was done in Brazil in 2020 with more than encouraging results.
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Perturbed nuclear matter studied within Density Functional Theory with a finite number of particles

2022-01-01
Francesco Marino , G. Colò , X. Roca-Maza +1 more
Nuclear matter is studied within the Density Functional Theory (DFT) framework. Our method employs a finite number of nucleons in a box subject to periodic boundary conditions, in order to … Nuclear matter is studied within the Density Functional Theory (DFT) framework. Our method employs a finite number of nucleons in a box subject to periodic boundary conditions, in order to simulate infinite matter and study its response to an external static potential. We detail both the theoretical formalism and its computational implementation for pure neutron matter and symmetric nuclear matter with Skyrme-like Energy Density Functionals (EDFs). The implementation of spin-orbit, in particular, is carefully discussed. Our method is applied to the problem of the static response of nuclear matter and the impact of the perturbation on the energies, densities and level structure of the system is investigated. Our work is a crucial step in our program of ab initio-based nuclear EDFs [Phys. Rev. C 104, 024315 (2021)] as it paves the way towards the goal of constraining the EDF surface terms on ab initio calculations.
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Microscopic calculation of the pinning energy of a vortex in the inner crust of a neutron star

2023-01-01
Pietro Klausner , F. Barranco , P. M. Pizzochero +2 more
The structure of a vortex in the inner crust of a pulsar is calculated microscopically in the Wigner-Seitz cell approximation, simulating the conditions of the inner crust of a cold, … The structure of a vortex in the inner crust of a pulsar is calculated microscopically in the Wigner-Seitz cell approximation, simulating the conditions of the inner crust of a cold, non-accreting neutron star, in which a lattice of nuclei coexists with a sea of superfluid neutrons. The calculation is based on the axially deformed Hartree-Fock-Bogolyubov framework, using effective interactions. The present work extends and improves previous studies in four ways: i) it allows for the axial deformation of protons induced by the large deformation of neutrons due to the appearance of vortices; ii) it includes the effect of Coulomb exchange; iii) considers the possible effects of the screening of the pairing interaction; and iv) it improves the numerical treatment. We also demonstrate that the binding energy of the nucleus-vortex system can be used as a proxy to the pinning energy of a vortex and discuss in which conditions this applies. From our results, we can estimate the mesoscopic pinning forces per unit length acting on vortices. We obtain values ranging between $10^{14}$ to $10^{16}$ dyn/cm, consistent with previous findings.
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Expansion of one-, two- and three-body matrix elements on a generic spherical basis for nuclear ab initio calculations

2023-01-01
A. Scalesi , C. Barbieri , E. Vigezzi
Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a … Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a Harmonic Oscillator single-particle basis, which allows for a simple separation of the center-of-mass motion from the intrinsic one. A few recent investigations have showed that the use of different single-particle bases can bring significant advantages to numerical nuclear structure computations. In this work, the complete analytical expression of the Hamiltonian matrix elements expanded on a generic spherical basis is presented for the first time. This will allow systematic studies aimed at the determination of optimal nuclear bases.
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Expansion of One-, Two- and Three-Body Matrix Elements on a Generic Spherical Basis for Nuclear Ab Initio Calculations

2024-01-01
A. Scalesi , C. Barbieri , E. Vigezzi
Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a … Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a Harmonic Oscillator single-particle basis, which allows for a simple separation of the center-of-mass motion from the intrinsic one. A few recent investigations have showed that the use of different single-particle bases can bring significant advantages to numerical nuclear structure computations. In this work, the complete analytical expression of the Hamiltonian matrix elements expanded on a generic spherical basis is presented for the first time. This will allow systematic studies aimed at the determination of optimal nuclear bases.
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Fragmentation of the Giant Pairing Vibration in 14C induced by many-body processes

2024-02-21
F. Barranco , G. Potel , E. Vigezzi
We present a theoretical framework for treating the full excitation spectrum of J{\pi} = 0+ pair addition modes, including the well-known low-lying and bound Pairing Vibration on par with the … We present a theoretical framework for treating the full excitation spectrum of J{\pi} = 0+ pair addition modes, including the well-known low-lying and bound Pairing Vibration on par with the predicted Giant Pairing Vibration lying in the continuum. Our formalism includes the coupling to low-energy collective quadrupole modes of the core, in such a way that both single-particle self-energy effects and the pairing interaction induced by phonon exchange are accounted for. The theory is applied to the case of the excitation spectrum of 14C, recently populated by two-neutron transfer reactions.
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Expansion of one-, two- and three-body matrix elements on a generic spherical basis for nuclear ab initio calculations

2024-05-15
A. Scalesi , C. Barbieri , E. Vigezzi
Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a … Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a Harmonic Oscillator single-particle basis, which allows for a simple separation of the center-of-mass motion from the intrinsic one. A few recent investigations have showed that the use of different single-particle bases can bring significant advantages to numerical nuclear structure computations. In this work, the complete analytical expression of the Hamiltonian matrix elements expanded on a generic spherical basis is presented for the first time. This will allow systematic studies aimed at the determination of optimal nuclear bases.
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Impact of ground-state properties and collective excitations on the Skyrme ansatz: a Bayesian study

2024-10-24
Pietro Klausner , G. Colò , X. Roca-Maza +1 more
State-of-the-art models based on nuclear Density Functional Theory are successful in the description of nuclei throughout the whole nuclear chart. Among them, some differences arise regarding their accuracy. For a … State-of-the-art models based on nuclear Density Functional Theory are successful in the description of nuclei throughout the whole nuclear chart. Among them, some differences arise regarding their accuracy. For a given nuclear model, this depends on the procedure adopted to determine the parameters, and, at the same time, new experimental findings constantly challenge theory. In the present work, we present a Bayesian inference study aimed at assessing the performance of the Skyrme Energy Density Functional. For the sake of simplicity and clarity, we restrict to spherical, double-magic nuclei, giving equal emphasis to ground-state and dynamical properties. Our basic constraints are: i) masses and charge radii, which are known to be very sensitive to the saturation energy and density; ii) spin-orbit splittings, which are associated with the spin-orbit parameter(s); iii) the electric dipole polarizability and parity-violating asymmetry, which are associated with the density dependence of the symmetry energy; iv) the excitation energy of the Isoscalar Giant Monopole Resonance, to constrain the nuclear matter incompressibility; v) the energy-weighted sum rule of the Isovector Giant Dipole Resonance, to account for the isovector effective mass; and vi) the excitation energy of the Isoscalar Quadrupole Resonance, that is related to the isoscalar effective mass. In this way, we test the Skyrme ansatz in a statistically meaningful way, by determining the posterior distributions of the parameters as well as their correlation, and discussing a possible strategy for future developments.
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Diagrammatic Monte Carlo for finite systems at zero temperature

2025-01-05
Stefano Brolli , C. Barbieri , E. Vigezzi
High-order virtual excitations play an important role in microscopic models of nuclear reactions at intermediate energies. However, the factorial growth of their complexity has prevented their consistent inclusion in ab … High-order virtual excitations play an important role in microscopic models of nuclear reactions at intermediate energies. However, the factorial growth of their complexity has prevented their consistent inclusion in ab initio many-body calculations. For infinite systems at finite temperature, such drawbacks can be overcome using diagrammatic Monte Carlo (DiagMC) techniques to resum entire series of Feynman diagrams. We present a DiagMC algorithm that can be applied to self-bound systems with discrete energy levels at zero temperature, and demonstrate its potential for the Richardson model of nuclear pairing. We show that sampling the topological space of diagrams allows the inclusion of high-order excitations that are neglected in state-of-the-art approximations used in nuclear physics and quantum chemistry. We propose that sampling the diagrammatic space can overcome the long-standing gap between our microscopic understanding of structure and reactions in nuclear physics.
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Impact of ground-state properties and collective excitations on the Skyrme ansatz: A Bayesian study

2025-01-09
Pietro Klausner , G. Colò , X. Roca-Maza +1 more
State-of-the-art models based on nuclear density functional theory are successful in the description of nuclei throughout the whole nuclear chart. Among them, some differences arise regarding their accuracy. For a … State-of-the-art models based on nuclear density functional theory are successful in the description of nuclei throughout the whole nuclear chart. Among them, some differences arise regarding their accuracy. For a given nuclear model, this depends on the procedure adopted to determine the parameters, and, at the same time, new experimental findings constantly challenge theory. In the present work, we present a Bayesian inference study aimed at assessing the performance of the Skyrme energy density functionals. For the sake of simplicity and clarity, we restrict our study to spherical, double-magic nuclei, giving equal emphasis to ground-state and dynamical properties. Our basic constraints are (i) masses and charge radii, which are known to be very sensitive to the saturation energy and density; (ii) spin-orbit splittings, which are associated with the spin-orbit parameter(s); (iii) the electric dipole polarizability and parity-violating asymmetry, which are associated with the density dependence of the symmetry energy; (iv) the excitation energy of the isoscalar giant monopole resonance, to constrain the nuclear matter incompressibility; (v) the energy-weighted sum rule of the isovector giant dipole resonance, to account for the isovector effective mass; and (vi) the excitation energy of the isoscalar quadrupole resonance, which is related to the isoscalar effective mass. We are then able to test the Skyrme ansatz in a statistically meaningful way, by determining the posterior distributions of the parameters. In particular, we have found probability distributions in line with published results, with the only exceptions of the symmetry energy at saturation 𝐽 and its slope 𝐿, whose distributions favor lower values than commonly reported. Using our method, we have also been able to discuss the correlations among parameters and observables. Finally, we discuss a few possible future developments. locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon Physics Subject Headings (PhySH)Binding energy & massesEquations of state of nuclear matterGiant resonancesNuclear structure & decaysSymmetry energyBayesian methodsNuclear density functional theory
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Diagrammatic Monte Carlo for Finite Systems at Zero Temperature

2025-05-09
Stefano Brolli , C. Barbieri , E. Vigezzi
High-order virtual excitations play an important role in microscopic models of nuclear reactions at intermediate energies. However, the factorial growth of their complexity has prevented their consistent inclusion in ab … High-order virtual excitations play an important role in microscopic models of nuclear reactions at intermediate energies. However, the factorial growth of their complexity has prevented their consistent inclusion in ab initio many-body calculations. For infinite systems at finite temperature, such drawbacks can be overcome using diagrammatic Monte Carlo techniques to resum entire series of Feynman diagrams. We present a diagrammatic Monte Carlo algorithm that can be applied to self-bound systems with discrete energy levels at zero temperature, and demonstrate its potential for the Richardson model of nuclear pairing. We show that sampling the topological space of diagrams allows the inclusion of high-order excitations that are neglected in state-of-the-art approximations used in nuclear physics and quantum chemistry. We propose that sampling the diagrammatic space can overcome the long-standing gap between our microscopic understanding of structure and reactions in nuclear physics.
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Diagrammatic Monte Carlo for Finite Systems at Zero Temperature

2025-05-09
Stefano Brolli , C. Barbieri , E. Vigezzi
High-order virtual excitations play an important role in microscopic models of nuclear reactions at intermediate energies. However, the factorial growth of their complexity has prevented their consistent inclusion in ab … High-order virtual excitations play an important role in microscopic models of nuclear reactions at intermediate energies. However, the factorial growth of their complexity has prevented their consistent inclusion in ab initio many-body calculations. For infinite systems at finite temperature, such drawbacks can be overcome using diagrammatic Monte Carlo techniques to resum entire series of Feynman diagrams. We present a diagrammatic Monte Carlo algorithm that can be applied to self-bound systems with discrete energy levels at zero temperature, and demonstrate its potential for the Richardson model of nuclear pairing. We show that sampling the topological space of diagrams allows the inclusion of high-order excitations that are neglected in state-of-the-art approximations used in nuclear physics and quantum chemistry. We propose that sampling the diagrammatic space can overcome the long-standing gap between our microscopic understanding of structure and reactions in nuclear physics.
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Impact of ground-state properties and collective excitations on the Skyrme ansatz: A Bayesian study

2025-01-09
Pietro Klausner , G. Colò , X. Roca-Maza +1 more
State-of-the-art models based on nuclear density functional theory are successful in the description of nuclei throughout the whole nuclear chart. Among them, some differences arise regarding their accuracy. For a … State-of-the-art models based on nuclear density functional theory are successful in the description of nuclei throughout the whole nuclear chart. Among them, some differences arise regarding their accuracy. For a given nuclear model, this depends on the procedure adopted to determine the parameters, and, at the same time, new experimental findings constantly challenge theory. In the present work, we present a Bayesian inference study aimed at assessing the performance of the Skyrme energy density functionals. For the sake of simplicity and clarity, we restrict our study to spherical, double-magic nuclei, giving equal emphasis to ground-state and dynamical properties. Our basic constraints are (i) masses and charge radii, which are known to be very sensitive to the saturation energy and density; (ii) spin-orbit splittings, which are associated with the spin-orbit parameter(s); (iii) the electric dipole polarizability and parity-violating asymmetry, which are associated with the density dependence of the symmetry energy; (iv) the excitation energy of the isoscalar giant monopole resonance, to constrain the nuclear matter incompressibility; (v) the energy-weighted sum rule of the isovector giant dipole resonance, to account for the isovector effective mass; and (vi) the excitation energy of the isoscalar quadrupole resonance, which is related to the isoscalar effective mass. We are then able to test the Skyrme ansatz in a statistically meaningful way, by determining the posterior distributions of the parameters. In particular, we have found probability distributions in line with published results, with the only exceptions of the symmetry energy at saturation 𝐽 and its slope 𝐿, whose distributions favor lower values than commonly reported. Using our method, we have also been able to discuss the correlations among parameters and observables. Finally, we discuss a few possible future developments. locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon Physics Subject Headings (PhySH)Binding energy & massesEquations of state of nuclear matterGiant resonancesNuclear structure & decaysSymmetry energyBayesian methodsNuclear density functional theory
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Diagrammatic Monte Carlo for finite systems at zero temperature

2025-01-05
Stefano Brolli , C. Barbieri , E. Vigezzi
High-order virtual excitations play an important role in microscopic models of nuclear reactions at intermediate energies. However, the factorial growth of their complexity has prevented their consistent inclusion in ab … High-order virtual excitations play an important role in microscopic models of nuclear reactions at intermediate energies. However, the factorial growth of their complexity has prevented their consistent inclusion in ab initio many-body calculations. For infinite systems at finite temperature, such drawbacks can be overcome using diagrammatic Monte Carlo (DiagMC) techniques to resum entire series of Feynman diagrams. We present a DiagMC algorithm that can be applied to self-bound systems with discrete energy levels at zero temperature, and demonstrate its potential for the Richardson model of nuclear pairing. We show that sampling the topological space of diagrams allows the inclusion of high-order excitations that are neglected in state-of-the-art approximations used in nuclear physics and quantum chemistry. We propose that sampling the diagrammatic space can overcome the long-standing gap between our microscopic understanding of structure and reactions in nuclear physics.
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Impact of ground-state properties and collective excitations on the Skyrme ansatz: a Bayesian study

2024-10-24
Pietro Klausner , G. Colò , X. Roca-Maza +1 more
State-of-the-art models based on nuclear Density Functional Theory are successful in the description of nuclei throughout the whole nuclear chart. Among them, some differences arise regarding their accuracy. For a … State-of-the-art models based on nuclear Density Functional Theory are successful in the description of nuclei throughout the whole nuclear chart. Among them, some differences arise regarding their accuracy. For a given nuclear model, this depends on the procedure adopted to determine the parameters, and, at the same time, new experimental findings constantly challenge theory. In the present work, we present a Bayesian inference study aimed at assessing the performance of the Skyrme Energy Density Functional. For the sake of simplicity and clarity, we restrict to spherical, double-magic nuclei, giving equal emphasis to ground-state and dynamical properties. Our basic constraints are: i) masses and charge radii, which are known to be very sensitive to the saturation energy and density; ii) spin-orbit splittings, which are associated with the spin-orbit parameter(s); iii) the electric dipole polarizability and parity-violating asymmetry, which are associated with the density dependence of the symmetry energy; iv) the excitation energy of the Isoscalar Giant Monopole Resonance, to constrain the nuclear matter incompressibility; v) the energy-weighted sum rule of the Isovector Giant Dipole Resonance, to account for the isovector effective mass; and vi) the excitation energy of the Isoscalar Quadrupole Resonance, that is related to the isoscalar effective mass. In this way, we test the Skyrme ansatz in a statistically meaningful way, by determining the posterior distributions of the parameters as well as their correlation, and discussing a possible strategy for future developments.
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Expansion of one-, two- and three-body matrix elements on a generic spherical basis for nuclear ab initio calculations

2024-05-15
A. Scalesi , C. Barbieri , E. Vigezzi
Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a … Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a Harmonic Oscillator single-particle basis, which allows for a simple separation of the center-of-mass motion from the intrinsic one. A few recent investigations have showed that the use of different single-particle bases can bring significant advantages to numerical nuclear structure computations. In this work, the complete analytical expression of the Hamiltonian matrix elements expanded on a generic spherical basis is presented for the first time. This will allow systematic studies aimed at the determination of optimal nuclear bases.
View PDF Chat

Fragmentation of the Giant Pairing Vibration in 14C induced by many-body processes

2024-02-21
F. Barranco , G. Potel , E. Vigezzi
We present a theoretical framework for treating the full excitation spectrum of J{\pi} = 0+ pair addition modes, including the well-known low-lying and bound Pairing Vibration on par with the … We present a theoretical framework for treating the full excitation spectrum of J{\pi} = 0+ pair addition modes, including the well-known low-lying and bound Pairing Vibration on par with the predicted Giant Pairing Vibration lying in the continuum. Our formalism includes the coupling to low-energy collective quadrupole modes of the core, in such a way that both single-particle self-energy effects and the pairing interaction induced by phonon exchange are accounted for. The theory is applied to the case of the excitation spectrum of 14C, recently populated by two-neutron transfer reactions.
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Expansion of One-, Two- and Three-Body Matrix Elements on a Generic Spherical Basis for Nuclear Ab Initio Calculations

2024-01-01
A. Scalesi , C. Barbieri , E. Vigezzi
Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a … Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a Harmonic Oscillator single-particle basis, which allows for a simple separation of the center-of-mass motion from the intrinsic one. A few recent investigations have showed that the use of different single-particle bases can bring significant advantages to numerical nuclear structure computations. In this work, the complete analytical expression of the Hamiltonian matrix elements expanded on a generic spherical basis is presented for the first time. This will allow systematic studies aimed at the determination of optimal nuclear bases.
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Perturbed nuclear matter studied within density functional theory with a finite number of particles

2023-04-17
F. Marino , G. Colò , X. Roca-Maza +1 more
Nuclear matter is studied within the density functional theory framework. Our method employs a finite number of nucleons in a box subject to periodic boundary conditions, in order to simulate … Nuclear matter is studied within the density functional theory framework. Our method employs a finite number of nucleons in a box subject to periodic boundary conditions, in order to simulate infinite matter and study its response to an external static potential. We detail both the theoretical formalism and its computational implementation for pure neutron matter and symmetric nuclear matter with Skyrme-like energy density functionals (EDFs). The implementation of spin-orbit, in particular, is carefully discussed. Our method is applied to the problem of the static response of nuclear matter and the impact of the perturbation on the energies, densities, and level structure of the system is investigated. Our work is a crucial step in our program of ab initio based nuclear EDFs [Phys. Rev. C 104, 024315 (2021)] as it paves the way towards the goal of constraining the EDF surface terms on ab initio calculations.
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Microscopic calculation of the pinning energy of a vortex in the inner crust of a neutron star

2023-01-01
Pietro Klausner , F. Barranco , P. M. Pizzochero +2 more
The structure of a vortex in the inner crust of a pulsar is calculated microscopically in the Wigner-Seitz cell approximation, simulating the conditions of the inner crust of a cold, … The structure of a vortex in the inner crust of a pulsar is calculated microscopically in the Wigner-Seitz cell approximation, simulating the conditions of the inner crust of a cold, non-accreting neutron star, in which a lattice of nuclei coexists with a sea of superfluid neutrons. The calculation is based on the axially deformed Hartree-Fock-Bogolyubov framework, using effective interactions. The present work extends and improves previous studies in four ways: i) it allows for the axial deformation of protons induced by the large deformation of neutrons due to the appearance of vortices; ii) it includes the effect of Coulomb exchange; iii) considers the possible effects of the screening of the pairing interaction; and iv) it improves the numerical treatment. We also demonstrate that the binding energy of the nucleus-vortex system can be used as a proxy to the pinning energy of a vortex and discuss in which conditions this applies. From our results, we can estimate the mesoscopic pinning forces per unit length acting on vortices. We obtain values ranging between $10^{14}$ to $10^{16}$ dyn/cm, consistent with previous findings.
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Expansion of one-, two- and three-body matrix elements on a generic spherical basis for nuclear ab initio calculations

2023-01-01
A. Scalesi , C. Barbieri , E. Vigezzi
Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a … Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a Harmonic Oscillator single-particle basis, which allows for a simple separation of the center-of-mass motion from the intrinsic one. A few recent investigations have showed that the use of different single-particle bases can bring significant advantages to numerical nuclear structure computations. In this work, the complete analytical expression of the Hamiltonian matrix elements expanded on a generic spherical basis is presented for the first time. This will allow systematic studies aimed at the determination of optimal nuclear bases.
View PDF Chat

The ASIMOV Prize for scientific publishing - HEP researchers trigger young people toward science

2022-10-14
A. Ventura , W.M. Alberico , Roberta Antolini +7 more
This work presents the ASIMOV Prize for scientific publishing, which was launched in Italy in 2016. The prize aims to bring the young generations closer to scientific culture, through the … This work presents the ASIMOV Prize for scientific publishing, which was launched in Italy in 2016. The prize aims to bring the young generations closer to scientific culture, through the critical reading of popular science books. The books are selected by a committee that includes scientists, professors, Ph.D. and Ph.D. students, writers, journalists and friends of culture, and most importantly, over 800 school teachers. Students are actively involved in the prize, according to the best practices of public engagement: they read, review the books and vote for them, choosing the winner. The experience is quite successful: 12,000 students from 270 schools all over Italy participated in the last edition. The possibility of replicating this experience in other countries is indicated, as was done in Brazil in 2020 with more than encouraging results.
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Transient Joule- and (ac) Josephson-like photon emission in one- and two- nucleon tunneling processes between superfluid nuclei: Blackbody and coherent spectral functions

2022-06-28
Ricardo A. Broglia , F. Barranco , G. Potel +1 more
Effective charged neutrons involved in one- and two- nucleon tunneling processes in heavy ion collisions between superfluid nuclei are expected to emit photons. Although the centroid, width and integrated energy … Effective charged neutrons involved in one- and two- nucleon tunneling processes in heavy ion collisions between superfluid nuclei are expected to emit photons. Although the centroid, width and integrated energy area characterizing the associated gamma-strength functions are rather similar, the corresponding line shapes reflect the thermal equilibrated-like character of the quasiparticle transfer (1n-channel, blackbody spectral functional dependence), and the quantal coherent character of the Cooper pair transfer (2n-channel, Gaussian functional dependence) respectively. The predicted angular distributions, polarizations and analyzing power provide further insight into the profoundly different physics to be found at the basis of what can be considered a transient Joule-like and a (ac) Josephson-like nuclear processes
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Complete solution to the inverse Kohn-Sham problem: From the density to the energy

2022-03-07
Alberto Liardi , F. Marino , G. Colò +2 more
A complete solution to the inverse problem of Kohn-Sham (KS) density functional theory is proposed. Our method consists of two steps. First, the effective KS potential is determined from the … A complete solution to the inverse problem of Kohn-Sham (KS) density functional theory is proposed. Our method consists of two steps. First, the effective KS potential is determined from the ground-state density of a given system. Then, the knowledge of the potentials along a path in the space of densities is exploited in a line integration formula to determine numerically the KS energy of that system. A possible choice for the density path is proposed. A benchmark in the case of a simplified yet realistic nuclear system is shown to be successful, so the method seems promising for future applications.
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Perturbed nuclear matter studied within Density Functional Theory with a finite number of particles

2022-01-01
Francesco Marino , G. Colò , X. Roca-Maza +1 more
Nuclear matter is studied within the Density Functional Theory (DFT) framework. Our method employs a finite number of nucleons in a box subject to periodic boundary conditions, in order to … Nuclear matter is studied within the Density Functional Theory (DFT) framework. Our method employs a finite number of nucleons in a box subject to periodic boundary conditions, in order to simulate infinite matter and study its response to an external static potential. We detail both the theoretical formalism and its computational implementation for pure neutron matter and symmetric nuclear matter with Skyrme-like Energy Density Functionals (EDFs). The implementation of spin-orbit, in particular, is carefully discussed. Our method is applied to the problem of the static response of nuclear matter and the impact of the perturbation on the energies, densities and level structure of the system is investigated. Our work is a crucial step in our program of ab initio-based nuclear EDFs [Phys. Rev. C 104, 024315 (2021)] as it paves the way towards the goal of constraining the EDF surface terms on ab initio calculations.
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The complete inverse Kohn-Sham problem: from the density to the energy

2021-10-21
Alberto Liardi , F. Marino , G. Colò +2 more
A complete solution to the inverse problem of Kohn-Sham (KS) density functional theory is proposed. Our method consists of two steps. First, the effective KS potential is determined from the … A complete solution to the inverse problem of Kohn-Sham (KS) density functional theory is proposed. Our method consists of two steps. First, the effective KS potential is determined from the ground state density of a given system. Then, the knowledge of the potentials along a path in the space of densities is exploited in a line integration formula to determine numerically the KS energy of that system. A possible choice for the density path is proposed. A benchmark in the case of a simplified yet realistic nuclear system is shown to be successful, so that the method seems promising for future applications.

Nuclear energy density functionals grounded in <i>ab initio</i> calculations

2021-08-09
F. Marino , C. Barbieri , Arianna Carbone +5 more
We discuss the construction of a nuclear energy density functional (EDF) from ab initio computations and advocate the need for a methodical approach that is free from ad hoc assumptions. … We discuss the construction of a nuclear energy density functional (EDF) from ab initio computations and advocate the need for a methodical approach that is free from ad hoc assumptions. The equations of state (EoSs) of symmetric nuclear and pure neutron matter are computed using the chiral ${\mathrm{NNLO}}_{\mathrm{sat}}$ and the phenomenological ${\mathrm{AV4}}^{\ensuremath{'}}+{\mathrm{UIX}}_{c}$ Hamiltonians as inputs to self-consistent Green's function (SCGF) and auxiliary field diffusion Monte Carlo (AFDMC) methods. We propose a convenient parametrization of the EoS as a function of the Fermi momentum and fit it on the SCGF and AFDMC calculations. We apply the ab initio based EDF to carry out an analysis of the binding energies and charge radii of different nuclei in the local density approximation. The ${\mathrm{NNLO}}_{\mathrm{sat}}$-based EDF produces encouraging results, whereas the ${\mathrm{AV4}}^{\ensuremath{'}}+{\mathrm{UIX}}_{c}$-based one is farther from experiment. Possible explanations of these different behaviors are suggested, and the importance of gradient and spin-orbit terms is analyzed. Our paper paves the way for a practical and systematic way to merge ab initio nuclear theory and density functional theory, while shedding light on some critical aspects of this procedure.
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Quantum entanglement in nuclear Cooper-pair tunneling with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>γ</mml:mi></mml:math> rays

2021-02-25
G. Potel , F. Barranco , E. Vigezzi +1 more
A new analysis of heavy-ion collision experiments uncovers evidence that two colliding nuclei behave like a Josephson junction---a device in which Cooper pairs tunnel through a barrier between two superfluids. A new analysis of heavy-ion collision experiments uncovers evidence that two colliding nuclei behave like a Josephson junction---a device in which Cooper pairs tunnel through a barrier between two superfluids.
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Probable observation of the nuclear Cooper pair mean square radius in superfluid nuclei

2021-01-01
Ricardo A. Broglia , F. Barranco , G. Potel +1 more
The phenomenon of low-temperature superconductivity is intimately associated with the condensation of weakly bound, very extended, strongly overlapping Cooper pairs, and systematic experimental studies of the associated mean square radius … The phenomenon of low-temperature superconductivity is intimately associated with the condensation of weakly bound, very extended, strongly overlapping Cooper pairs, and systematic experimental studies of the associated mean square radius (coherence length) have been made. While the extension of BCS theory to the atomic nucleus has been successful beyond expectation, to our knowledge, no measurement of the nuclear coherence length (expected to be much larger than nuclear dimensions) has been reported in the literature. Recent studies of Cooper pair transfer across a Josephson-like junction, transiently established in a heavy ion collision between superfluid nuclei, have likely changed the situation, providing the experimental input for a quantitative estimate of the nuclear coherence length, as well as the basis for a nuclear analogue of the (ac) Josephson effect.
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First step in the nuclear inverse Kohn-Sham problem: From densities to potentials

2020-02-28
Giacomo Accorto , P. Brandolini , F. Marino +5 more
Nuclear density functional theory (DFT) plays a prominent role in the understanding of nuclear structure, being the approach with the widest range of applications. Hohenberg and Kohn theorems warrant the … Nuclear density functional theory (DFT) plays a prominent role in the understanding of nuclear structure, being the approach with the widest range of applications. Hohenberg and Kohn theorems warrant the existence of a nuclear energy density functional (EDF), yet its form is unknown. Current efforts to build a nuclear EDF are hindered by the lack of a strategy for systematic improvement. In this context, alternative approaches should be pursued and, so far, an unexplored avenue is that related to the inverse DFT problem. DFT is based on the one-to-one correspondence between Kohn-Sham (KS) potentials and densities. The exact EDF produces the exact density, so that from the knowledge of experimental or ab initio densities one may deduce useful information through reverse engineering. The idea has already been proved to be useful in the case of electronic systems. The general problem should be dealt with in steps, and the objective of the present work is to focus on testing algorithms to extract the Kohn-Sham potential within the simplest ansatz from the knowledge of the experimental neutron and proton densities. We conclude that, while robust algorithms exist, the experimental densities present some critical aspects. Finally, we provide some perspectives for future works.
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Exact restoration of Galilei invariance in density functional calculations with quantum Monte Carlo

2019-11-18
P. Massella , F. Barranco , Diego Lonardoni +3 more
Galilean invariance is usually violated in self-consistent mean-field calculations that employ effective density-dependent nuclear forces. We present a novel approach, based on variational quantum Monte Carlo techniques, suitable to preserve … Galilean invariance is usually violated in self-consistent mean-field calculations that employ effective density-dependent nuclear forces. We present a novel approach, based on variational quantum Monte Carlo techniques, suitable to preserve this symmetry and assess the effect of its violation, seldom attempted in the past. To this aim, we generalize the linear optimization method to encompass the density-dependence of effective Hamiltonians, and study $^4$He, $^{16}$O, and $^{40}$Ca ground-state properties employing the Gogny interaction.
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Radioactive beams and inverse kinematics: Probing the quantal texture of the nuclear vacuum

2019-06-29
F. Barranco , G. Potel , E. Vigezzi +1 more
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Radioactive beams and inverse kinematics: probing the quantal texture of the nuclear vacuum

2019-01-01
F. Barranco , G. Potel , E. Vigezzi +1 more
The properties of the quantum electrodynamic (QED) vacuum in general, and of the nuclear vacuum (ground) state in particular are determined by virtual processes implying the excitation of a photon … The properties of the quantum electrodynamic (QED) vacuum in general, and of the nuclear vacuum (ground) state in particular are determined by virtual processes implying the excitation of a photon and of an electron--positron pair in the first case and of, for example, the excitation of a collective quadrupole surface vibration and a particle--hole pair in the nuclear case. Signals of these processes can be detected in the laboratory in terms of what can be considered a nuclear analogue of Hawking radiation. An analogy which extends to other physical processes involving QED vacuum fluctuations like the Lamb shift, pair creation by $γ-$rays, van der Waals forces and the Casimir effect, to the extent that one concentrates on the eventual outcome resulting by forcing a virtual process to become real, and not on the role of the black hole role in defining the event horizon. In the nuclear case, the role of this event is taken over at a microscopic, fully quantum mechanical level, by nuclear probes (reactions) acting on a virtual particle of the zero point fluctuation (ZPF) of the nuclear vacuum in a similar irreversible, no--return, fashion as the event horizon does, letting the other particle, entangled with the first one, escape to infinity, and eventually be detected. With this proviso in mind one can posit that the reactions $^1$H($^{11}$Be,$^{10}$Be$(2^+$;3.37 ${\rm MeV}$))$^2$H and $^{1}$H($^{11}$Li,$^9$Li($1/2^-$; 2.69 ${\rm MeV}$))$^3$H together with the associated $γ-$decay processes indicate a possible nuclear analogy of Hawking radiation.
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Exploring density-dependent effective interactions with quantum Monte Carlo

2018-08-01
P. Massella , F. Barranco , Diego Lonardoni +3 more
We investigate some aspects of the connection between mean-field and ab-initio calculations for many-nucleon systems employing the Gogny effective interaction. In particular, we present variational Monte Carlo calculations of $^4$He … We investigate some aspects of the connection between mean-field and ab-initio calculations for many-nucleon systems employing the Gogny effective interaction. In particular, we present variational Monte Carlo calculations of $^4$He and $^{16}$O, for which we extended the formalism of the linear method to the case of a density-dependent Hamiltonian. Monte Carlo calculations using an uncorrelated basis reduce to Hartree-Fock ones, but Galilean invariance can be preserved, contrary to the usual treatment. An analysis of the results obtained with the Gogny force when used in conjunction with correlated wave functions has also been performed. Calculations show the collapse of the deuteron, leading to a set of unphysical predictions for the structure of heavier nuclei. This behavior remarks the different role of the Gogny effective interaction as compared to bare interactions typically used in fully microscopic calculations.

From bare to renormalized order parameter in gauge space: Structure and reactions

2017-09-12
G. Potel , A. Idini , F. Barranco +2 more
It is not physically obvious why one can calculate with similar accuracy, as compared to the experimental data, the absolute cross section associated with two-nucleon transfer processes between members of … It is not physically obvious why one can calculate with similar accuracy, as compared to the experimental data, the absolute cross section associated with two-nucleon transfer processes between members of pairing rotational bands, making use of simple BCS (constant matrix elements) or of many-body [Nambu-Gorkov (NG), nuclear field theory (NFT)] spectroscopic amplitudes. Restoration of spontaneous symmetry breaking and associated emergent generalized rigidity in gauge space provides the answer and points to a new emergence: A physical sum rule resulting from the intertwining of structure and reaction processes, closely connected with the central role induced pairing interaction plays in structure, together with the fact that successive transfer dominates Cooper pair tunneling.
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Quasiparticle random-phase approximation with quasiparticle-vibration coupling: Application to the Gamow-Teller response of the superfluid nucleus<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Sn</mml:mi><mml:mprescripts /><mml:none /><mml:mn>120</mml:mn></mml:mmultiscripts></mml:math>

2016-12-29
Y. Niu , G. Colò , E. Vigezzi +2 more
We propose a self-consistent quasiparticle random-phase approximation (QRPA) plus quasiparticle-vibration coupling (QPVC) model with Skyrme interactions to describe the width and the line shape of giant resonances in open-shell nuclei, … We propose a self-consistent quasiparticle random-phase approximation (QRPA) plus quasiparticle-vibration coupling (QPVC) model with Skyrme interactions to describe the width and the line shape of giant resonances in open-shell nuclei, in which the effect of superfluidity should be taken into account in both the ground state and the excited states. We apply the new model to the Gamow-Teller resonance in the superfluid nucleus $^{120}\mathrm{Sn}$, including both the isoscalar spin-triplet and the isovector spin-singlet pairing interactions. The strength distribution in $^{120}\mathrm{Sn}$ is well reproduced and the underlying microscopic mechanisms, related to QPVC and also to isoscalar pairing, are analyzed in detail.
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Dual origin of pairing in nuclei

2016-11-01
A. Idini , G. Potel , F. Barranco +2 more
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Interweaving of elementary modes of excitation in superfluid nuclei through particle-vibration coupling: Quantitative account of the variety of nuclear structure observables

2015-09-18
A. Idini , G. Potel , F. Barranco +2 more
A complete characterization of the structure of nuclei can be obtained by combining information arising from inelastic scattering, Coulomb excitation and $\gamma-$decay, together with one- and two-particle transfer reactions. In … A complete characterization of the structure of nuclei can be obtained by combining information arising from inelastic scattering, Coulomb excitation and $\gamma-$decay, together with one- and two-particle transfer reactions. In this way it is possible to probe the single-particle and collective components of the nuclear many-body wavefunction resulting from their mutual coupling and diagonalising the low-energy Hamiltonian. We address the question of how accurately such a description can account for experimental observations. It is concluded that renormalizing empirically and on equal footing bare single-particle and collective motion in terms of self-energy (mass) and vertex corrections (screening), as well as particle-hole and pairing interactions through particle-vibration coupling allows theory to provide an overall, quantitative account of the data.
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Dual Origin of Pairing in Nuclei

2014-01-01
A. Idini , G. Potel , F. Barranco +2 more
An essentially "complete" description of the low-energy nuclear structure of the superfluid nucleus $^{120}$Sn and of its odd-$A$ neighbors is provided by the observations carried out with the help of … An essentially "complete" description of the low-energy nuclear structure of the superfluid nucleus $^{120}$Sn and of its odd-$A$ neighbors is provided by the observations carried out with the help of Coulomb excitation and of one-- and of two-- particle transfer reactions, specific probes of vibrations, quasiparticle and pairing degrees of freedom respectively, and of their mutual couplings. These experimental findings are used to stringently test the predictions of a similarly "complete" description of $^{119,120,121}$Sn carried out in terms of elementary modes of excitation which, through their interweaving, melt together into effective fields, each displaying properties reflecting that of all others, there individuality resulting from the actual relative importance of each one. Its implementation is done by solving the Nambu-Gor'kov equations including, for the first time, all medium polarization effects resulting from the interweaving of quasiparticles, spin and surface vibrations, taking into account, within the framework of nuclear field theory (NFT), the variety of processes leading to self-energy, vertex and Pauli principle corrections, and to the induced pairing interaction. Theory provides an overall quantitative account of the experimental findings. From these results one can, not only obtain strong circumstantial evidence for the inevitability for the dual origin of pairing in nuclei but also, extract information which can be used at profit to quantitatively disentangle the contributions to pairing correlations in general and to the pairing gap in particular, arising from the bare and from the induced pairing interactions.

Continuum particle-vibration coupling method in coordinate-space representation for finite nuclei

2012-09-14
K. Mizuyama , G. Colò , E. Vigezzi
In this paper we present a new formalism to implement the nuclear particle-vibration coupling (PVC) model. The key issue is the proper treatment of the continuum, that is allowed by … In this paper we present a new formalism to implement the nuclear particle-vibration coupling (PVC) model. The key issue is the proper treatment of the continuum, that is allowed by the coordinate space representation. Our formalism, based on the use of zero-range interactions like the Skyrme forces, is microscopic and fully self-consistent. We apply it to the case of neutron single-particle states in $^{40}$Ca, $^{208}$Pb and $^{24}$O. The first two cases are meant to illustrate the comparison with the usual (i.e., discrete) PVC model. However, we stress that the present approach allows to calculate properly the effect of PVC on resonant states. We compare our results with those from experiments in which the particle transfer in the continuum region has been attempted. The latter case, namely $^{24}$O, is chosen as an example of a weakly-bound system. Such a nucleus, being double-magic and not displaying collective low-lying vibrational excitations, is characterized by quite pure neutron single-particle states around the Fermi surface.
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Nuclear Field Theory predictions for 11Li and 12Be: shedding light on the origin of pairing in nuclei

2012-01-01
G. Potel , A. Idini , F. Barranco +2 more
Recent data resulting from studies of two-nucleon transfer reaction on 11Li, analyzed through a unified nuclear-structure-direct-reaction theory have provided strong direct as well as indirect confirmation, through the population of … Recent data resulting from studies of two-nucleon transfer reaction on 11Li, analyzed through a unified nuclear-structure-direct-reaction theory have provided strong direct as well as indirect confirmation, through the population of the first excited state of 9Li and of the observation of a strongly quenched ground state transition, of the prediction that phonon mediated pairing interaction is the main mechanism binding the neutron halo of the 8.5 ms-lived 11Li nucleus. In other words, the ground state of 11Li can be viewed as a neutron Cooper pair bound to the 9Li core, mainly through the exchange of collective vibration of the core and of the pigmy resonance arizing from the sloshing back and forth of the neutron halo against the protons of the core, the mean field leading to unbound two particle states, a situation essentially not altered by the bare nucleon-nucleon interaction acting between the halo neutrons. Two-neutron pick-up data, together with (t,p) data on 7Li, suggest the existence of a pairing vibrational band based on 9Li, whose members can be excited with the help of inverse kinematic experiments as was done in the case of 11Li(p,t)9Li reaction. The deviation from harmonicity can provide insight into the workings of medium polarization effects on Cooper pair nuclear pairing, let alone specific information concering the "rigidity" of the N=6 shell closure. Further information concerning these questions is provided by the predicted absolute differential cross sections associated with the reactions 12Be(p,t)10Be(gs) and 12Be(p,t)10Be(pv)(~10Be(p,t)8Be(gs)). In particular, concerning this last reaction, predictions of \sigma_{abs} can change by an order of magnitude depending on whether the halo properties associated with the d_{5/2} orbital are treated selfconsistently in calculating the ground state correlations of the (pair removal) mode, or not.
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Linear response of light deformed nuclei investigated by self-consistent quasiparticle random-phase approximation

2010-06-08
Cristina Losa , A. Pastore , T. Døssing +2 more
We present a calculation of the properties of vibrational states in deformed, axially-symmetric even-even nuclei, within the framework of a fully self-consistent quasiparticle random phase approximation (QRPA). The same Skyrme … We present a calculation of the properties of vibrational states in deformed, axially-symmetric even-even nuclei, within the framework of a fully self-consistent quasiparticle random phase approximation (QRPA). The same Skyrme energy density and density-dependent pairing functionals are used to calculate the mean field and the residual interaction in the particle-hole and particle-particle channels. We have tested our software in the case of spherical nuclei against fully self-consistent calculations published in the literature, finding excellent agreement. We investigate the consequences of neglecting the spin-orbit and Coulomb residual interactions in QRPA. Furthermore we discuss the improvement obtained in the QRPA result associated with the removal of spurious modes. Isoscalar and isovector responses in the deformed $^{24--26}\mathrm{Mg}$, $^{34}\mathrm{Mg}$ isotopes are presented and compared to experimental findings.
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Single Cooper pair transfer in stable and in exotic nuclei

2009-01-01
G. Potel , B. F. Bayman , F. Barranco +3 more
We discuss in this paper both the past and the present of two-nucleon transfer reactions, as well as try to foresee the near future of such studies in nuclei, induced … We discuss in this paper both the past and the present of two-nucleon transfer reactions, as well as try to foresee the near future of such studies in nuclei, induced by light as well as by heavy ion reactions.

Probing the Order-to-Chaos Region in Superdeformed<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi>Tb</mml:mi><mml:mprescripts /><mml:none /><mml:mn>151</mml:mn></mml:mmultiscripts></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi>Pb</mml:mi><mml:mprescripts /><mml:none /><mml:mn>196</mml:mn></mml:mmultiscripts></mml:math>Nuclei with Continuum<mml:math xmlns:mml="http://www.w3.…

2008-09-30
S. Leoni , G. Benzoni , N. Blasi +7 more
The γ decay associated with the warm rotation of the superdeformed nuclei Tb151 and Pb196 has been measured with the EUROBALL IV array. Several independent quantities provide a stringent test … The γ decay associated with the warm rotation of the superdeformed nuclei Tb151 and Pb196 has been measured with the EUROBALL IV array. Several independent quantities provide a stringent test of the population and decay dynamics in the superdeformed well. A Monte Carlo simulation of the γ decay based on microscopic calculations gives remarkable agreement with the data only assuming a large enhancement of the B(E1) strength for 1–2 MeV γ rays, which may be related to the evidence for octupole vibrations in both mass regions.Received 27 June 2008DOI:https://doi.org/10.1103/PhysRevLett.101.142502©2008 American Physical Society
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Giant dipole resonance as a quantitative constraint on the symmetry energy

2008-06-16
Luca Trippa , G. Colò , E. Vigezzi
The possible constraints on the poorly determined symmetry part of the effective nuclear Hamiltonians or effective energy functionals, i.e., the so-called symmetry energy $S(\ensuremath{\rho})$, are very much under debate. In … The possible constraints on the poorly determined symmetry part of the effective nuclear Hamiltonians or effective energy functionals, i.e., the so-called symmetry energy $S(\ensuremath{\rho})$, are very much under debate. In the present work, we show that the value of the symmetry energy associated with Skyrme functionals, at densities \ensuremath{\rho} around 0.1 fm${}^{\ensuremath{-}3}$, is strongly correlated with the value of the centroid of the Giant Dipole Resonance (GDR) in spherical nuclei. Consequently, the experimental value of the GDR in, e.g., $^{208}\mathrm{Pb}$ can be used as a constraint on the symmetry energy, leading to $23.3 \mathrm{MeV}<S(\ensuremath{\rho}=0.1 {\mathrm{fm}}^{\ensuremath{-}3})<24.9$ MeV.

Correlation energy contribution to nuclear masses

2007-01-21
Simone Baroni , F. Barranco , P. F. Bortignon +3 more
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Medium polarization isotopic effects on nuclear binding energies

2006-08-16
Simone Baroni , F. Barranco , P. F. Bortignon +3 more
There exist several effective interactions whose parameters are fitted to force mean field predictions to reproduce experimental findings of finite nuclei and calculated properties of infinite nuclear matter. Exploiting this … There exist several effective interactions whose parameters are fitted to force mean field predictions to reproduce experimental findings of finite nuclei and calculated properties of infinite nuclear matter. Exploiting this tecnique one can give a good description of nuclear binding energies. We present evidence that further progress can be made by taking into account medium polarization effects associated with surface and pairing vibrations.
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Pairing matrix elements and pairing gaps with bare, effective, and induced interactions

2005-11-21
F. Barranco , P. F. Bortignon , Ricardo A. Broglia +4 more
The dependence on the single-particle states of the pairing matrix elements of the Gogny force and of the bare low-momentum nucleon-nucleon potential ${v}_{\mathrm{low}\text{\ensuremath{-}}k}$---designed so as to reproduce the low-energy observables … The dependence on the single-particle states of the pairing matrix elements of the Gogny force and of the bare low-momentum nucleon-nucleon potential ${v}_{\mathrm{low}\text{\ensuremath{-}}k}$---designed so as to reproduce the low-energy observables avoiding the use of a repulsive core---is studied for a typical finite, superfluid nucleus ($^{120}\mathrm{Sn}$). It is found that the matrix elements of ${v}_{\mathrm{low}\text{\ensuremath{-}}k}$ follow closely those of ${v}_{\mathrm{Gogny}}$ on a wide range of energy values around the Fermi energy ${e}_{F}$, those associated with ${v}_{\mathrm{low}\text{\ensuremath{-}}k}$ being less attractive. This result explains the fact that around ${e}_{F}$ the pairing gap ${\ensuremath{\Delta}}_{\mathrm{Gogny}}$ associated with the Gogny interaction (and with a density of single-particle levels corresponding to an effective k mass ${m}_{k}\ensuremath{\approx}0.7 m$) is a factor of about 2 larger than ${\ensuremath{\Delta}}_{\mathrm{low}\text{\ensuremath{-}}k}$, being in agreement with ${\ensuremath{\Delta}}_{\mathrm{exp}}=1.4$ MeV. The exchange of low-lying collective surface vibrations among pairs of nucleons moving in time-reversal states gives rise to an induced pairing interaction ${v}_{\mathrm{ind}}$ peaked at ${e}_{F}$. The interaction $({v}_{\mathrm{low}\text{\ensuremath{-}}k}+{v}_{\mathrm{ind}}) {Z}_{\ensuremath{\omega}}$ arising from the renormalization of the bare nucleon-nucleon potential and of the single-particle motion (\ensuremath{\omega}-mass and quasiparticle strength ${Z}_{\ensuremath{\omega}}$) associated with the particle-vibration coupling mechanism, leads to a value of the pairing gap at the Fermi energy ${\ensuremath{\Delta}}_{\mathrm{ren}}$ that accounts for the experimental value. An important question that remains to be studied quantitatively is to what extent ${\ensuremath{\Delta}}_{\mathrm{Gogny}}$, which depends on average parameters, and ${\ensuremath{\Delta}}_{\mathrm{ren}}$, which explicitly depends on the parameters describing the (low-energy) nuclear structure, display or not a similar isotopic dependence and whether this dependence is borne out by the data.
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Attractive and repulsive contributions of medium fluctuations to nuclear superfluidity

2005-07-18
G. Gori , Fabio Ramponi , F. Barranco +4 more
Oscillations of mainly surface character ($S=0$ modes) give rise, in atomic nuclei, to an attractive (induced) pairing interaction, while spin ($S=1$) modes of mainly volume character generate a repulsive interaction, … Oscillations of mainly surface character ($S=0$ modes) give rise, in atomic nuclei, to an attractive (induced) pairing interaction, while spin ($S=1$) modes of mainly volume character generate a repulsive interaction, the net effect being an attraction which accounts for a sizeable fraction of the experimental pairing gap. Suppressing the particle-vibration coupling mediated by the proton degrees of freedom, i.e., mimicking neutron matter, the total surface plus spin-induced pairing interaction becomes repulsive.
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Correlation energy contribution to nuclear masses

2004-08-21
Simone Baroni , M Armati , F. Barranco +4 more
The ground-state correlation energies associated with collective surface and pairing vibrations are calculated for Pb and Ca isotopes. It is shown that this contribution, when added to those predicted by … The ground-state correlation energies associated with collective surface and pairing vibrations are calculated for Pb and Ca isotopes. It is shown that this contribution, when added to those predicted by one of the most accurate modern nuclear mass formulae (HFBCS MSk7 mass formula), reduces the associated rms error by an important factor, making mean-field theory, once its time dependence is taken into account, a quantitative predictive tool for nuclear masses.
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Many-body effects in nuclear structure

2004-07-01
F. Barranco , R.A. Broglia , G. Colò +3 more
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Quasi-particle properties and Cooper pairing in trapped Fermi gases

2004-01-01
Luca Giorgetti , L. Viverit , G. Gori +3 more
The possibility for the particles in a Fermi gas to emit and reabsorb density and spin fluctuations gives rise to an effective mass and to a lifetime of the quasi-particles, … The possibility for the particles in a Fermi gas to emit and reabsorb density and spin fluctuations gives rise to an effective mass and to a lifetime of the quasi-particles, as well as to an effective pairing interaction which affect in an important way the BCS critical temperature. We calculate these effects for a spherically symmetric trapped Fermi gas of $\sim$ 1000 particles. The calculation provides insight on the many-body physics of finite Fermi gases and is closely related to similar problems recently considered in the case of atomic nuclei and neutron stars.
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Rotational Damping And Compound Formation In Warm Rotating Nuclei

2003-01-01
Masayuki Matsuo , S. Leoni , Camila Grassi +5 more
The rotational damping width \Gamma_{rot} and the compound damping width \Gamma_{comp} are two fundamental quantities that characterize rapidly rotating compound nuclei having finite thermal excitation energy. A two-component structure in … The rotational damping width \Gamma_{rot} and the compound damping width \Gamma_{comp} are two fundamental quantities that characterize rapidly rotating compound nuclei having finite thermal excitation energy. A two-component structure in the strength function of consecutive E2 transitions reflects the two widths, and it causes characteristic features in the double and triple gamma-ray spectra. We discuss a new method to extract experimentally values of \Gamma_{rot} and \Gamma_{comp}. The first preliminary result of this method is presented.
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The halo of the exotic nucleus 11Li: a single Cooper pair

2001-10-01
F. Barranco , P. F. Bortignon , R.A. Broglia +2 more
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Microscopic structure of rotational damping

1999-03-01
Masayuki Matsuo , Kōji Yoshida , T. Døssing +2 more
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Electron–phonon coupling in charged buckminsterfullerene

1998-04-01
N. Breda , Ricardo A. Broglia , G. Colò +5 more
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On the Origin of Nuclear Superfluidity

1998-01-01
F. Barranco , P. F. Bortignon , G. Gori +3 more
The induced pairing interaction arising from the exchange of collective surface vibrations among nucleons moving in time reversal states close to the Fermi energy is found to lead to values … The induced pairing interaction arising from the exchange of collective surface vibrations among nucleons moving in time reversal states close to the Fermi energy is found to lead to values of the pairing gap which are similar to those experimentally observed.

Spectral line shape of exotic nuclei

1996-11-01
Francesco Ghielmetti , G. Colò , E. Vigezzi +2 more
The quadrupole strength function of $^{28}O$ is calculated making use of the SIII interaction, within the framework of continuum-RPA and taking into account collisions among the nucleons (doorway coupling). The … The quadrupole strength function of $^{28}O$ is calculated making use of the SIII interaction, within the framework of continuum-RPA and taking into account collisions among the nucleons (doorway coupling). The centroid of the giant resonance is predicted at $\approx 14$ MeV, that is much below the energy expected for both isoscalar and isovector quadrupole resonances in nuclei along the stability valley. About half of this width arises from the coupling of the resonance to the continuum and about half is due to doorway coupling. This result is similar to that obtained in the study of giant resonances in light, $\beta$-stable nuclei, and shows the lack of basis for the expectation, entertained until now in the literature, that continuum decay was the main damping mechanism of giant resonances in halo nuclei.
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Coauthor Papers Together
F. Barranco 24
G. Colò 20
Ricardo A. Broglia 18
G. Potel 12
X. Roca-Maza 9
C. Barbieri 6
G. Gori 5
A. Idini 5
R.A. Broglia 5
F. Marino 5
A. Scalesi 4
P. F. Bortignon 4
P. F. Bortignon 4
Simone Baroni 3
Pietro Klausner 3
Francesco Pederiva 3
Alessandro Lovato 3
Stefano Brolli 2
B. Herskind 2
Masayuki Matsuo 2
Diego Lonardoni 2
Alberto Liardi 2
S. Leoni 2
P. Massella 2
A. Bracco 2
D. Montanari 1
N. Blasi 1
Cristina Losa 1
B. F. Bayman 1
W. Mȩczyński 1
Marco Radici 1
N. Breda 1
Luca Giorgetti 1
Luca Trippa 1
F. Alasia 1
K. Zuber 1
M. Kmiecik 1
Silvano Fuso 1
F. C. L. Crespi 1
Francesco Marino 1
Francesco Vissani 1
T. Døssing 1
Alessandro Papa 1
C. Distefano 1
H. Sagawa 1
J. Styczeń 1
P. Brandolini 1
Fabrizio Ursini 1
Kōji Yoshida 1
C. Puggioni 1

Many-body effects in nuclear structure

2004-07-01
F. Barranco , R.A. Broglia , G. Colò +3 more
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Solution of the Dyson equation for nucleons in the superfluid phase

2002-01-01
J. Terasaki , F. Barranco , Ricardo A. Broglia +2 more
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Cooper pair transfer in nuclei

2013-10-01
G. Potel , A. Idini , F. Barranco +2 more
The second-order distorted wave Born approximation implementation of two-particle transfer direct reactions which includes simultaneous and successive transfer, properly corrected by non-orthogonality effects, is tested with the help of controlled … The second-order distorted wave Born approximation implementation of two-particle transfer direct reactions which includes simultaneous and successive transfer, properly corrected by non-orthogonality effects, is tested with the help of controlled nuclear structure and reaction inputs against data spanning the whole mass table, and showed to constitute a quantitative probe of nuclear pairing correlations.
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Correlation energy contribution to nuclear masses

2004-08-21
Simone Baroni , M Armati , F. Barranco +4 more
The ground-state correlation energies associated with collective surface and pairing vibrations are calculated for Pb and Ca isotopes. It is shown that this contribution, when added to those predicted by … The ground-state correlation energies associated with collective surface and pairing vibrations are calculated for Pb and Ca isotopes. It is shown that this contribution, when added to those predicted by one of the most accurate modern nuclear mass formulae (HFBCS MSk7 mass formula), reduces the associated rms error by an important factor, making mean-field theory, once its time dependence is taken into account, a quantitative predictive tool for nuclear masses.
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Quasiparticle renormalization and pairing correlations in spherical superfluid nuclei

2012-01-31
A. Idini , F. Barranco , E. Vigezzi
We present a detailed discussion of the solution of Nambu-Gor'kov equations in superfluid nuclei, which provide a consistent framework to deal with the interplay between particle-hole and particle- particle channel, … We present a detailed discussion of the solution of Nambu-Gor'kov equations in superfluid nuclei, which provide a consistent framework to deal with the interplay between particle-hole and particle- particle channel, including the effects of the fragmentation of the quasiparticle strength and of the pairing interaction induced by the exchange of collective vibrations. The coupling between quasiparticle and vibrations is determined from the experimental polarizability of the low-lying collective surface vibrations. This coupling is used to renormalize the properties of quasiparticles obtained from a BCS calculation using the bare nucleon-nucleon interaction. We apply the formalism to the case of the nucleus 120Sn, showing results for the low-energy spectrum and the quasiparticle strength distribution in neighbouring odd nuclei and for the neutron pairing gap.
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The halo of the exotic nucleus 11Li: a single Cooper pair

2001-10-01
F. Barranco , P. F. Bortignon , R.A. Broglia +2 more
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A Guided Tour of ab initio Nuclear Many-Body Theory

2020-10-07
H. Hergert
Over the last decade, new developments in Similarity Renormalization Group techniques and nuclear many-body methods have dramatically increased the capabilities of ab initio nuclear structure and reaction theory. Ground and … Over the last decade, new developments in Similarity Renormalization Group techniques and nuclear many-body methods have dramatically increased the capabilities of ab initio nuclear structure and reaction theory. Ground and excited-state properties can be computed up to the tin region, and from the proton to the presumptive neutron drip lines, providing unprecedented opportunities to confront two- plus three-nucleon interactions from chiral Effective Field Theory with experimental data. In this contribution, I will give a broad survey of the current status of nuclear many-body approaches, and I will use selected results to discuss both achievements and open issues that need to be addressed in the coming decade.
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Interweaving of elementary modes of excitation in superfluid nuclei through particle-vibration coupling: Quantitative account of the variety of nuclear structure observables

2015-09-18
A. Idini , G. Potel , F. Barranco +2 more
A complete characterization of the structure of nuclei can be obtained by combining information arising from inelastic scattering, Coulomb excitation and $\gamma-$decay, together with one- and two-particle transfer reactions. In … A complete characterization of the structure of nuclei can be obtained by combining information arising from inelastic scattering, Coulomb excitation and $\gamma-$decay, together with one- and two-particle transfer reactions. In this way it is possible to probe the single-particle and collective components of the nuclear many-body wavefunction resulting from their mutual coupling and diagonalising the low-energy Hamiltonian. We address the question of how accurately such a description can account for experimental observations. It is concluded that renormalizing empirically and on equal footing bare single-particle and collective motion in terms of self-energy (mass) and vertex corrections (screening), as well as particle-hole and pairing interactions through particle-vibration coupling allows theory to provide an overall, quantitative account of the data.
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Accurate nucleon-nucleon potential with charge-independence breaking

1995-01-01
R. B. Wiringa , V. G. J. Stoks , R. Schiavilla
We present a new high-quality nucleon-nucleon potential with explicit charge dependence and charge asymmetry, which we designate Argonne ${\mathit{v}}_{18}$. The model has a charge-independent part with 14 operator components that … We present a new high-quality nucleon-nucleon potential with explicit charge dependence and charge asymmetry, which we designate Argonne ${\mathit{v}}_{18}$. The model has a charge-independent part with 14 operator components that is an updated version of the Argonne ${\mathit{v}}_{14}$ potential. Three additional charge-dependent and one charge-asymmetric operators are added, along with a complete electromagnetic interaction. The potential has been fit directly to the Nijmegen pp and np scattering database, low-energy nn scattering parameters, and deuteron binding energy. With 40 adjustable parameters it gives a ${\mathrm{\ensuremath{\chi}}}^{2}$ per datum of 1.09 for 4301 pp and np data in the range 0--350 MeV.
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Quantum Monte Carlo methods for nuclear physics

2015-09-09
J. Carlson , Stefano Gandolfi , Francesco Pederiva +4 more
Quantum Monte Carlo techniques aim at providing a description of complex quantum systems such as nuclei and nucleonic matter from first principles, i.e., realistic nuclear interactions and currents. The methods … Quantum Monte Carlo techniques aim at providing a description of complex quantum systems such as nuclei and nucleonic matter from first principles, i.e., realistic nuclear interactions and currents. The methods are similar to those used for many-electron systems in quantum chemistry and condensed matter physics, but are extended to include spin-isospin, tensor, spin-orbit, and three-body interactions. This review shows how to build the atomic nucleus from the ground up. Examples include the structure of light nuclei, electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter.
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The compression-mode giant resonances and nuclear incompressibility

2018-05-07
U. Garg , G. Colò
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Gamow-Teller strength and the spin-isospin coupling constants of the Skyrme energy functional

2002-05-13
M. Bender , J. Dobaczewski , J. Engel +1 more
We investigate the effects of the spin-isospin channel of the Skyrme energy functional on predictions for Gamow-Teller distributions and superdeformed rotational bands. We use the generalized Skyrme interaction ${\mathrm{SkO}}^{\ensuremath{'}}$ to … We investigate the effects of the spin-isospin channel of the Skyrme energy functional on predictions for Gamow-Teller distributions and superdeformed rotational bands. We use the generalized Skyrme interaction ${\mathrm{SkO}}^{\ensuremath{'}}$ to describe even-even ground states and then analyze the effects of time-odd spin-isospin couplings, first term by term and then together via linear regression. Some terms affect the strength and energy of the Gamow-Teller resonance in finite nuclei without altering the Landau parameter ${g}_{0}^{\ensuremath{'}}$ that to leading order determines spin-isospin properties of nuclear matter. Though the existing data are not sufficient to uniquely determine all the spin-isospin couplings, we are able to fit them locally. Altering these coupling constants does not change the quality with which the Skyrme functional describes rotational bands.
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Nuclear energy density optimization: Shell structure

2014-05-15
M. Kortelainen , Jordan McDonnell , W. Nazarewicz +7 more
Background: Nuclear density functional theory is the only microscopical theory that can be applied throughout the entire nuclear landscape. Its key ingredient is the energy density functional.Purpose: In this work, … Background: Nuclear density functional theory is the only microscopical theory that can be applied throughout the entire nuclear landscape. Its key ingredient is the energy density functional.Purpose: In this work, we propose a new parametrization unedf2 of the Skyrme energy density functional.Methods: The functional optimization is carried out using the pounders optimization algorithm within the framework of the Skyrme Hartree-Fock-Bogoliubov theory. Compared to the previous parametrization unedf1, restrictions on the tensor term of the energy density have been lifted, yielding a very general form of the energy density functional up to second order in derivatives of the one-body density matrix. In order to impose constraints on all the parameters of the functional, selected data on single-particle splittings in spherical doubly-magic nuclei have been included into the experimental dataset.Results: The agreement with both bulk and spectroscopic nuclear properties achieved by the resulting unedf2 parametrization is comparable with unedf1. While there is a small improvement on single-particle spectra and binding energies of closed shell nuclei, the reproduction of fission barriers and fission isomer excitation energies has degraded. As compared to previous unedf parametrizations, the parameter confidence interval for unedf2 is narrower. In particular, our results overlap well with those obtained in previous systematic studies of the spin-orbit and tensor terms.Conclusions: unedf2 can be viewed as an all-around Skyrme EDF that performs reasonably well for both global nuclear properties and shell structure. However, after adding new data aiming to better constrain the nuclear functional, its quality has improved only marginally. These results suggest that the standard Skyrme energy density has reached its limits, and significant changes to the form of the functional are needed.
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Structure and Reactions of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Be</mml:mi></mml:mrow><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>11</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math> : Many-Body Basis for Single-Neutron Halo

2017-08-24
F. Barranco , G. Potel , Ricardo A. Broglia +1 more
The exotic nucleus 11Be has been extensively studied and much experimental information is available on the structure of this system. Treating, within the framework of empirically renormalised nuclear field theory … The exotic nucleus 11Be has been extensively studied and much experimental information is available on the structure of this system. Treating, within the framework of empirically renormalised nuclear field theory in both configuration and 3D-space, the mixing of bound and continuum single-particle states through the coupling to collective particle-hole (p,h) and pairing vibrations of the 10Be core, as well as Pauli principle acting not only between the particles explicitly considered and those participating in the collective states, but also between fermions involved in two-phonon virtual states it is possible, for the first time, to simultaneously and quantitatively account for the energies of the 1/2+,1/2- low-lying states, the centroid and line shape of the 5/2+ resonance, the one-nucleon stripping and pickup absolute differential cross sections involving 11Be as either target or residual nucleus, and the dipole transitions connecting the 1/2+ and 1/2- parity inverted levels as well as the charge radius, thus providing a unified and exhaustive characterisation of the many-body effects which are at the basis of this paradigmatic one-neutron halo system.
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On the Self-Energy of a Bound Electron

1949-02-01
N. Kroll , Willis E. Lamb
The electromagnetic shift of the energy levels of a bound electron has been calculated on the basis of the usual formulation of relativistic quantum electrodynamics and positron theory. The theory … The electromagnetic shift of the energy levels of a bound electron has been calculated on the basis of the usual formulation of relativistic quantum electrodynamics and positron theory. The theory gives a finite result of 1052 megacycles per second for the shift $2^{2}S_{\frac{1}{2}}\ensuremath{-}2^{2}P_{\frac{1}{2}}$ in hydrogen, in close agreement with the non-relativistic calculation by Bethe.

Mean-field description of ground-state properties of drip-line nuclei: Pairing and continuum effects

1996-06-01
J. Dobaczewski , W. Nazarewicz , T. R. Werner +3 more
Ground-state properties of exotic even-even nuclei with extreme neutron-to-proton ratios are described in the framework of self-consistent mean-field theory with pairing formulated in coordinate space. This theory properly accounts for … Ground-state properties of exotic even-even nuclei with extreme neutron-to-proton ratios are described in the framework of self-consistent mean-field theory with pairing formulated in coordinate space. This theory properly accounts for the influence of the particle continuum, which is particularly important for weakly bound systems. The pairing properties of nuclei far from stability are studied with several interactions emphasizing different aspects, such as the range and density dependence of the effective interaction. Measurable consequences of spatially extended pairing fields are presented, and the sensitivity of the theoretical predictions to model details is discussed. \textcopyright{} 1996 The American Physical Society.
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Evidence for Phonon Mediated Pairing Interaction in the Halo of the Nucleus<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi>Li</mml:mi><mml:mprescripts /><mml:none /><mml:mn>11</mml:mn></mml:mmultiscripts></mml:math>

2010-10-19
G. Potel , F. Barranco , E. Vigezzi +1 more
With the help of a unified nuclear-structure-direct-reaction theory we analyze the reaction ¹H(¹¹Li,⁹Li)³H. The two halo neutrons are correlated through the bare and the induced (medium polarization) pairing interaction. By … With the help of a unified nuclear-structure-direct-reaction theory we analyze the reaction ¹H(¹¹Li,⁹Li)³H. The two halo neutrons are correlated through the bare and the induced (medium polarization) pairing interaction. By considering all dominant reaction channels leading to the population of the 1/2⁻ (2.69 MeV) first excited state of ⁹Li, namely, multistep transfer (successive, simultaneous, and nonorthogonality), breakup, and inelastic channels, it is possible to show that the experiment provides direct evidence of phonon mediated pairing.
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Unified description of structure and reactions: implementing the nuclear field theory program

2016-05-26
Ricardo A. Broglia , P. F. Bortignon , F. Barranco +3 more
The modern theory of the atomic nucleus results from the merging of the liquid drop (Niels Bohr and Fritz Kalckar) and of the shell model (Marie Goeppert Meyer and Axel … The modern theory of the atomic nucleus results from the merging of the liquid drop (Niels Bohr and Fritz Kalckar) and of the shell model (Marie Goeppert Meyer and Axel Jensen), which contributed the concepts of collective excitations and of independent-particle motion respectively.The unification of these apparently contradictory views in terms of the particle-vibration (rotation) coupling (Aage Bohr and Ben Mottelson) has allowed for an ever increasingly complete, accurate and detailed description of the nuclear structure, Nuclear Field Theory (NFT, developed by the Copenhagen-Buenos Aires collaboration) providing a powerful quantal embodiment.In keeping with the fact that reactions are not only at the basis of quantum mechanics (statistical interpretation, Max Born) , but also the specific tools to probe the atomic nucleus, NFT is being extended to deal with processes which involve the continuum in an intrinsic fashion, so as to be able to treat them on an equal footing with those associated with discrete states (nuclear structure).As a result, spectroscopic studies of transfer to continuum states could eventually use at profit the NFT rules, extended to take care of recoil effects.In the present contribution we review the implementation of the NFT program of structure and reactions, setting special emphasis on open problems and outstanding predictions.
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Fine Structure of the Hydrogen Atom by a Microwave Method

1947-08-01
Willis E. Lamb , Robert C. Retherford
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Measurement of the Two-Halo Neutron Transfer Reaction<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">H</mml:mi><mml:mprescripts /><mml:none /><mml:mn>1</mml:mn></mml:mmultiscripts><mml:mo stretchy="false">(</mml:mo><mml:mmultiscripts><mml:mi>Li</mml:mi><mml:mprescripts /><mml:none /><mml:mn>11</mml:mn></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mmultiscripts><mml:mi>Li</mml:mi><mml:mprescripts /><mml:none /><mml:mn>9</mml:…

2008-05-14
Isao Tanihata , M. Alcorta , Debades Bandyopadhyay +7 more
The p((11)Li, (9)Li)t reaction has been studied for the first time at an incident energy of 3A MeV at the new ISAC-2 facility at TRIUMF. An active target detector MAYA, … The p((11)Li, (9)Li)t reaction has been studied for the first time at an incident energy of 3A MeV at the new ISAC-2 facility at TRIUMF. An active target detector MAYA, built at GANIL, was used for the measurement. The differential cross sections have been determined for transitions to the (9)Li ground and first excited states in a wide range of scattering angles. Multistep transfer calculations using different (11)Li model wave functions show that wave functions with strong correlations between the halo neutrons are the most successful in reproducing the observation.
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Neutron spectroscopic factors of Ni isotopes from transfer reactions

2009-05-21
Jenny Lee , M. B. Tsang , W. G. Lynch +2 more
177 neutron spectroscopic factors for nickel isotopes have been extracted by performing a systematic analysis of the angular distributions measured from ($d,p$) transfer reactions. A subset of the extracted spectroscopic … 177 neutron spectroscopic factors for nickel isotopes have been extracted by performing a systematic analysis of the angular distributions measured from ($d,p$) transfer reactions. A subset of the extracted spectroscopic factors are compared to predictions of large-basis shell models in the full $\mathit{pf}$ model space using the GXPF1A effective interaction, and the $({f}_{5/2},{p}_{3/2},{p}_{1/2},{g}_{9/2})$ model space using the JJ4PNA interaction. For ground states, the predicted spectroscopic factors using the GXPF1A effective interaction in the full $\mathit{pf}$ model space agree very well with the experimental values, while predictions based on several other effective interactions and model spaces are about 30% higher than the experimental values. For low-energy excited states ($<3.5$ MeV), the agreement between the extracted spectroscopic factors and shell model calculations is not better than a factor of two.
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Modern theory of nuclear forces

2009-12-21
E. Epelbaum , H.‐W. Hammer , Ulf-G. Meißner
Effective field theory allows for a systematic and model-independent derivation of the forces between nucleons in harmony with the symmetries of Quantum Chromodynamics. We review the foundations of this approach … Effective field theory allows for a systematic and model-independent derivation of the forces between nucleons in harmony with the symmetries of Quantum Chromodynamics. We review the foundations of this approach and discuss its application for light nuclei at various resolution scales. The extension of this approach to many-body systems is briefly sketched.
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Influence of Induced Interactions on the Superfluid Transition in Dilute Fermi Gases

2000-09-18
H. Heiselberg , C. J. Pethick , H. Smith +1 more
We calculate the effects of induced interactions on the transition temperature to the BCS state in dilute Fermi gases. For a pure Fermi system with two species having equal densities, … We calculate the effects of induced interactions on the transition temperature to the BCS state in dilute Fermi gases. For a pure Fermi system with two species having equal densities, the transition temperature is suppressed by a factor (4e)(1/3) approximately 2.2, and for nu fermion species, the transition temperature is increased by a factor (4e)(nu/3-1) approximately 2.2(nu-3). For mixtures of fermions and bosons the exchange of boson density fluctuations gives rise to an attractive interaction, and we estimate the increase of the transition temperature due to this effect.
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Microscopically based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization

2010-11-11
M. V. Stoitsov , M. Kortelainen , S. K. Bogner +4 more
In a recent series of articles, Gebremariam, Bogner, and Duguet derived a microscopically based nuclear energy density functional by applying the density matrix expansion (DME) to the Hartree-Fock energy obtained … In a recent series of articles, Gebremariam, Bogner, and Duguet derived a microscopically based nuclear energy density functional by applying the density matrix expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory two- and three-nucleon interactions. Owing to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Because the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenology has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present article is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decomposition optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction of our test ${\ensuremath{\chi}}^{2}$ function compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.
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Superconductivity in fullerides

1997-04-01
O. Gunnarsson
Experimental studies of the superconductive properties of fullerides are briefly reviewed. Theoretical calculations of the electron-phonon coupling, in particular for the intramolecular phonons, are discussed extensively. The calculations are compared … Experimental studies of the superconductive properties of fullerides are briefly reviewed. Theoretical calculations of the electron-phonon coupling, in particular for the intramolecular phonons, are discussed extensively. The calculations are compared with coupling constants deduced from a number of different experimental techniques. It is discussed why ${\mathrm{A}}_{3}$${\mathrm{C}}_{60}$ are not Mott-Hubbard insulators, in spite of the large Coulomb interaction. Estimates of the Coulomb pseudopotential ${\mathrm{\ensuremath{\mu}}}^{\mathrm{*}}$, describing the effect of the Coulomb repulsion on the superconductivity, as well as possible electronic mechanisms for the superconductivity, are reviewed. The calculation of various properties within the Migdal-Eliashberg theory and attempts to go beyond this theory are described.
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New Skyrme interaction with improved spin-isospin properties

2012-09-20
X. Roca-Maza , G. Colò , H. Sagawa
A correct determination of the spin-isospin properties of the nuclear effective interaction should lead to, among other improvements, an accurate description of the Gamow-Teller resonance (GTR). These nuclear excitations impact … A correct determination of the spin-isospin properties of the nuclear effective interaction should lead to, among other improvements, an accurate description of the Gamow-Teller resonance (GTR). These nuclear excitations impact on a variety of physical processes: from the response in charge-exchange reactions of nuclei naturally present in the Earth, to the description of the stellar nucleosynthesis and of the pre-supernova explosion core-collapse evolution of massive stars in the Universe. A reliable description of the GTR provides also stringent tests for neutrinoless double-$\ensuremath{\beta}$ decay calculations. We present a new Skyrme interaction as accurate as previous forces in the description of finite nuclei and of uniform matter properties around saturation density, and that accounts well for the GTR in ${}^{48}$Ca, ${}^{90}$Zr, and ${}^{208}$Pb, and the isobaric analog resonance and spin dipole resonance in ${}^{90}$Zr and ${}^{208}$Pb.
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From Brueckner approach to Skyrme-type energy density functional

2006-01-26
Liyun Cao , U. Lombardo , Chen Shen +1 more
A Skyrme-like effective interaction is built up from the equation of state of nuclear matter. The latter is calculated in the framework of the Brueckner-Hartree-Fock approximation with two- and three-body … A Skyrme-like effective interaction is built up from the equation of state of nuclear matter. The latter is calculated in the framework of the Brueckner-Hartree-Fock approximation with two- and three-body forces. A complete Skyrme parametrization requires a fit of the neutron and proton effective masses and the Landau parameters. The new parametrization is probed on the properties of a set of closed-shell and closed-subshell nuclei, including binding energies and charge radii.
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<i>Ab initio</i>self-consistent Gorkov-Green's function calculations of semi-magic nuclei: Numerical implementation at second order with a two-nucleon interaction

2014-02-28
V. Somà , C. Barbieri , T. Duguet
Background: The newly developed self-consistent Gorkov-Green's function approach represents a promising path to the ab initio description of mid-mass open-shell nuclei. The formalism based on a two-nucleon interaction and the … Background: The newly developed self-consistent Gorkov-Green's function approach represents a promising path to the ab initio description of mid-mass open-shell nuclei. The formalism based on a two-nucleon interaction and the second-order truncation of Gorkov's self-energy has been described in detail in Ref. [Som\`a, Duguet, and Barbieri, Phys. Rev. C 84, 064317 (2011)].Purpose: The objective is to discuss the methodology used to solve Gorkov's equation numerically and to gauge its performance in view of carrying out systematic calculations of medium-mass nuclei in the future. In doing so, different sources of theoretical error and degrees of self-consistency are investigated.Methods: We employ Krylov projection techniques with a multi-pivot Lanczos algorithm to efficiently handle the growth of poles in the one-body Green's function that arises as a result of solving Gorkov's equation self-consistently. We first characterize the numerical scaling of Gorkov's calculations based on full self-consistency and on a partially self-consistent scheme coined as ``sc0''. Using small model spaces, the Krylov projection technique is then benchmarked against exact diagonalization of the original Gorkov matrix. Next, the convergence of the results as a function of the number ${N}_{\ensuremath{\ell}}$ of Lanczos iterations per pivot is investigated in large model spaces. Eventually, the convergence of the calculations with the size of the harmonic oscillator model space is examined.Results: Gorkov self-consistent Green's function (SCGF) calculations performed on the basis of Krylov projection techniques display a favorable numerical scaling that authorizes systematic calculations of mid-mass nuclei. The Krylov projection selects efficiently the appropriate degrees of freedom while spanning a very small fraction of the original space. For typical large-scale calculations of mid-mass nuclei, a Krylov projection making use of ${N}_{\ensuremath{\ell}}\ensuremath{\approx}50$ yields a sufficient degree of accuracy on the observables of interest. The partially self-consistent sc0 scheme is shown to reproduce fully self-consistent solutions in small model spaces at the 1$%$ level. Eventually, Gorkov-Green's function calculations performed on the basis of SRG-evolved interactions show a fast convergence as a function of the model-space size.Conclusions: The end result is a tractable, accurate and gently scaling ab initio scheme applicable to complete isotopic and isotonic chains in the medium-mass region. The partially self-consistent sc0 scheme provides an excellent compromise between accuracy and computational feasibility and will be the workhorse of systematic Gorkov-Green's function calculations in the future. The numerical scaling and performances of the algorithm employed offers the possibility (i) to apply the method to even heavier systems than those (e.g., ${}^{74}$Ni) already studied so far and (ii) to perform converged Gorkov SCGF calculations based on harder, e.g. original chiral interactions.
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Coupled-cluster calculations of nucleonic matter

2014-01-27
G. Hagen , T. Papenbrock , A. Ekström +5 more
Background: The equation of state (EoS) of nucleonic matter is central for the understanding of bulk nuclear properties, the physics of neutron star crusts, and the energy release in supernova … Background: The equation of state (EoS) of nucleonic matter is central for the understanding of bulk nuclear properties, the physics of neutron star crusts, and the energy release in supernova explosions. Purpose: This work presents coupled-cluster calculations of infinite nucleonic matter using modern interactions from chiral effective field theory (EFT). It assesses the role of correlations beyond particle-particle and hole-hole ladders, and the role of three-nucleon-forces (3NFs) in nuclear matter calculations with chiral interactions. Methods: This work employs the optimized nucleon-nucleon NN potential NNLOopt at next-to-next-to leading-order, and presents coupled-cluster computations of the EoS for symmetric nuclear matter and neutron matter. The coupled-cluster method employs up to selected triples clusters and the single-particle space consists of a momentum-space lattice. We compare our results with benchmark calculations and control finite-size effects and shell oscillations via twist-averaged boundary conditions. Results: We provide several benchmarks to validate the formalism and show that our results exhibit a good convergence toward the thermodynamic limit. While neutron matter with interactions from chiral EFT is perturbative, symmetric nuclear matter requires nonperturbative approaches. Correlations beyond the standard particle-particle ladder approximation yield non-negligible contributions. The saturation point of symmetric nuclear matter is sensitive to the employed 3NFs and the employed regularization scheme. 3NFs with nonlocal cutoffs exhibit a considerably improved convergence than their local cousins. We are unable to find values for the parameters of the short-range part of the local 3NF that simultaneously yield acceptable values for the saturation point in symmetric nuclear matter and the binding energies of light nuclei.
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Shell effects on rotational damping in superdeformed nuclei

1998-06-01
Kōji Yoshida , Masayuki Matsuo
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Microscopic calculation and local approximation of the spatial dependence of the pairing field with bare and induced interactions

2008-08-28
A. Pastore , F. Barranco , Ricardo A. Broglia +1 more
The bare nucleon-nucleon interaction is essential for the production of pair correlations in nuclei, but an important contribution also arises from the induced interaction resulting from the exchange of collective … The bare nucleon-nucleon interaction is essential for the production of pair correlations in nuclei, but an important contribution also arises from the induced interaction resulting from the exchange of collective vibrations between nucleons moving in time reversal states close to the Fermi energy. The pairing field resulting from the summed interaction is strongly peaked at the nuclear surface. It is possible to reproduce the detailed spatial dependence of this field by using either a local approximation, which fully takes into account finite size effects, or a contact interaction, with parameters that are quite different from those commonly used in more phenomenological approaches.
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Single-neutron transfer from 11Be via the (p, d) reaction with a radioactive beam

2001-02-01
J. S. Winfield , S. Fortier , W. N. Catford +7 more
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Quasiparticle-vibration coupling in a relativistic framework: Shell structure of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>120</mml:mn></mml:mrow></mml:math>isotopes

2012-02-17
Елена Литвинова
For the first time, the shell structure of open-shell nuclei is described in a fully self-consistent extension of the covariant energy density functional theory. The approach implies quasiparticle-vibration coupling for … For the first time, the shell structure of open-shell nuclei is described in a fully self-consistent extension of the covariant energy density functional theory. The approach implies quasiparticle-vibration coupling for superfluid systems. A one-body Dyson equation formulated in the doubled quasiparticle space of Dirac spinors is solved for nucleonic propagators in tin isotopes which represent the reference case: The obtained energies of the single-quasiparticle levels and their spectroscopic amplitudes are in agreement with data. The model is applied to describe the shell evolution in a chain of superheavy isotopes ${}^{292,296,300,304}$120 and finds a rather stable proton spherical shell closure at $Z=120$. An interplay of the pairing correlations and the quasiparticle-phonon coupling gives rise to a smooth evolution of the neutron shell gap between $N=172$ and $N=184$ neutron numbers. Vibrational corrections to the alpha-decay energies reach several hundred keV and can be either positive or negative, thus also smearing out the shell effects.
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Quantitative study of coherent pairing modes with two-neutron transfer: Sn isotopes

2013-05-20
G. Potel , A. Idini , F. Barranco +2 more
Pairing rotations and pairing vibrations are collective modes associated with a field, the pair field, which changes the number of particles by two. Consequently, they can be studied at profit … Pairing rotations and pairing vibrations are collective modes associated with a field, the pair field, which changes the number of particles by two. Consequently, they can be studied at profit with the help of two-particle transfer reactions in superfluid and in normal nuclei, respectively. The advent of exotic beams has opened, for the first time, the possibility to carry out such studies in medium heavy nuclei, within the same isotopic chain. The case studied in the present paper is that of the Sn isotopes [essentially from closed ($Z=N=50$) to closed ($Z=50$, $N=82$) shells]. The static and dynamic off-diagonal, long-range order phase coherence in gauge space displayed by pairing rotations and vibrations, respectively, leads to coherent states which behave almost classically. Consequently, these modes are amenable to an accurate nuclear structure description in terms of simple models containing the right physics, in particular, BCS plus quasiparticle random-phase approximation and Hartree-Fock mean field plus random-phase approximation, respectively. The associated two-nucleon transfer spectroscopic amplitudes predicted by such model calculations can thus be viewed as essentially ``exact.'' This fact, together with the availability of optical potentials for the different real and virtual channels involved in the reactions considered, namely ${}^{A+2}\text{Sn}+p$, ${}^{A+1}\text{Sn}+d$, and ${}^{A}\text{Sn}+t$, allows for the calculation of the associated absolute cross sections without, arguably, free parameters. The numerical predictions of the absolute differential cross sections, obtained making use of the above-mentioned nuclear structure and optical potential inputs, within the framework of second-order distorted-wave Born approximation, taking into account simultaneous, successive, and nonorthogonality contributions, provide, within experimental errors in general, and below $10%$ uncertainty in particular, an overall account of the experimental findings for all of the measured ${}^{A+2}\text{Sn}(p,t){}^{A}\text{Sn}(\text{gs})$ reactions, for which absolute cross sections have been reported to date.
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Casimir effect and the quantum vacuum

2005-07-12
R. L. Jaffe
In discussions of the cosmological constant, the Casimir effect is often invoked as decisive evidence that the zero point energies of quantum fields are "real''. On the contrary, Casimir effects … In discussions of the cosmological constant, the Casimir effect is often invoked as decisive evidence that the zero point energies of quantum fields are "real''. On the contrary, Casimir effects can be formulated and Casimir forces can be computed without reference to zero point energies. They are relativistic, quantum forces between charges and currents. The Casimir force (per unit area) between parallel plates vanishes as \alpha, the fine structure constant, goes to zero, and the standard result, which appears to be independent of \alpha, corresponds to the \alpha\to\infty limit.
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Global study of quadrupole correlation effects

2006-03-29
M. Bender , G. F. Bertsch , P.-H. Heenen
We discuss the systematics of ground-state quadrupole correlations of binding energies and mean-square charge radii for all even-even nuclei, from ${}^{16}$O up to the superheavies, for which data are available. … We discuss the systematics of ground-state quadrupole correlations of binding energies and mean-square charge radii for all even-even nuclei, from ${}^{16}$O up to the superheavies, for which data are available. To that aim we calculate their correlated $J=0$ ground state by means of the angular-momentum and particle-number projected generator coordinate method, using the axial mass quadrupole moment as the generator coordinate and self-consistent mean-field states restricted only by axial, parity, and time-reversal symmetries. The calculation is performed within the framework of a nonrelativistic self-consistent mean-field model by use of the same Skyrme interaction SLy4 and to a density-dependent pairing force to generate the mean-field configurations and to mix them. These are the main conclusions of our study: (i) The quadrupole correlation energy varies between a few 100 keV and about 5.5 MeV. It is affected by shell closures, but varies only slightly with mass and asymmetry. (ii) Projection on angular momentum $J=0$ provides the major part of the energy gain of up to about 4 MeV; all nuclei in the study, including doubly magic ones, gain energy by deformation. (iii) The mixing of projected states with different intrinsic axial deformations adds a few 100 keV up to 1.5 MeV to the correlation energy. (iv) Typically nuclei below mass $A\ensuremath{\le}60$ have a larger correlation energy than static deformation energy whereas the heavier deformed nuclei have larger static deformation energy than correlation energy. (v) Inclusion of the quadrupole correlation energy improves the description of mass systematics, particularly around shell closures, and of differential quantities, namely two-nucleon separation energies and two-nucleon gaps. The correlation energy provides an explanation of ``mutually enhanced magicity.'' (vi) The correlation energy tends to decrease the shell effect on binding energies around magic numbers, but the magnitude of the suppression is not large enough to explain the relative overbinding at $N=82$ and $N=126$ neutron-shell closures in mean-field models. (vii) Charge radii are also found to be sensitive to the quadrupole correlations. Static quadrupole deformations lead to a significant improvement of the overall systematics of charge radii. The dynamical correlations improve the local systematics of radii, in particular around shell closures. Although the dynamical correlations might reduce the charge radii for specific nuclei, they lead to an overall increase of radii when included, in particular in light nuclei.
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Beyond Mean-Field Theories with Zero-Range Effective Interactions: A Way to Handle the Ultraviolet Divergence

2010-12-23
K. Moghrabi , M. Grasso , G. Colò +1 more
Zero-range effective interactions are commonly used in nuclear physics and in other domains to describe many-body systems within the mean-field model. If they are used within a beyond-mean-field framework, contributions … Zero-range effective interactions are commonly used in nuclear physics and in other domains to describe many-body systems within the mean-field model. If they are used within a beyond-mean-field framework, contributions to the total energy that display an ultraviolet divergence are found. We propose a general strategy to regularize this divergence and we illustrate it in the case of the second-order corrections to the equation of state (EOS) of uniform symmetric matter. By setting a momentum cutoff $\ensuremath{\Lambda}$, we show that for every (physically meaningful) value of $\ensuremath{\Lambda}$ it is possible to determine a new interaction such that the EOS with the second-order corrections reproduces the empirical EOS, with a fit of the same quality as that obtained at the mean-field level.
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QRPA plus phonon coupling model and the photoabsorption cross section for 18,20,22O

2001-12-01
G. Colò , P. F. Bortignon
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The Skyrme interaction in finite nuclei and nuclear matter

2006-08-15
J. R. Stone , P.‐G. Reinhard
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Neutron Skin of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi>Pb</mml:mi><mml:mprescripts /><mml:none /><mml:mn>208</mml:mn></mml:mmultiscripts></mml:math>, Nuclear Symmetry Energy, and the Parity Radius Experiment

2011-06-21
X. Roca-Maza , M. Centelles , X. Viñas +1 more
A precise determination of the neutron skin $\ensuremath{\Delta}{r}_{np}$ of a heavy nucleus sets a basic constraint on the nuclear symmetry energy ($\ensuremath{\Delta}{r}_{np}$ is the difference of the neutron and proton … A precise determination of the neutron skin $\ensuremath{\Delta}{r}_{np}$ of a heavy nucleus sets a basic constraint on the nuclear symmetry energy ($\ensuremath{\Delta}{r}_{np}$ is the difference of the neutron and proton rms radii of the nucleus). The parity radius experiment (PREX) may achieve it by electroweak parity-violating electron scattering (PVES) on $^{208}\mathrm{Pb}$. We investigate PVES in nuclear mean field approach to allow the accurate extraction of $\ensuremath{\Delta}{r}_{np}$ of $^{208}\mathrm{Pb}$ from the parity-violating asymmetry ${A}_{\mathrm{PV}}$ probed in the experiment. We demonstrate a high linear correlation between ${A}_{\mathrm{PV}}$ and $\ensuremath{\Delta}{r}_{np}$ in successful mean field forces as the best means to constrain the neutron skin of $^{208}\mathrm{Pb}$ from PREX, without assumptions on the neutron density shape. Continuation of the experiment with higher precision in ${A}_{\mathrm{PV}}$ is motivated since the present method can support it to constrain the density slope of the nuclear symmetry energy to new accuracy.
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Cold Neutrons Trapped in External Fields

2011-01-05
Stefano Gandolfi , J. Carlson , Steven C. Pieper
The properties of inhomogeneous neutron matter are crucial to the physics of neutron-rich nuclei and the crust of neutron stars. Advances in computational techniques now allow us to accurately determine … The properties of inhomogeneous neutron matter are crucial to the physics of neutron-rich nuclei and the crust of neutron stars. Advances in computational techniques now allow us to accurately determine the binding energies and densities of many neutrons interacting via realistic microscopic interactions and confined in external fields. We perform calculations for different external fields and across several shells to place important constraints on inhomogeneous neutron matter, and hence the large isospin limit of the nuclear energy density functionals that are used to predict properties of heavy nuclei and neutron star crusts. We find important differences between microscopic calculations and current density functionals; in particular the isovector gradient terms are significantly more repulsive than in traditional models, and the spin-orbit and pairing forces are comparatively weaker.
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Dipole states in stable and unstable nuclei

2004-09-22
Davide Sarchi , P. F. Bortignon , G. Colò
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Deformed quasiparticle-random-phase approximation for neutron-rich nuclei using the Skyrme energy density functional

2008-12-29
Kenichi Yoshida , Nguyen Van Giai
We develop a new framework of the deformed quasiparticle-random-phase approximation (QRPA) where the Skyrme density functional and the density-dependent pairing functional are consistently treated. Numerical applications are carried out for … We develop a new framework of the deformed quasiparticle-random-phase approximation (QRPA) where the Skyrme density functional and the density-dependent pairing functional are consistently treated. Numerical applications are carried out for the isovector dipole and the isoscalar quadrupole modes in the spherical $^{20}\mathrm{O}$ and in the deformed $^{26}\mathrm{Ne}$ nuclei, and the effect of the momentum-dependent terms of the Skyrme effective interaction for the energy-weighted sum rule is discussed. As a further application, we present for the first time the moments of inertia of $^{34}\mathrm{Mg}$ and $^{36}\mathrm{Mg}$ using the Thouless-Valatin procedure based on the self-consistent deformed QRPA, and we show the applicability of our new calculation scheme not only for the vibrational modes but also for the rotational modes in deformed neutron-rich nuclei.
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Continuum linear response in coordinate space Hartree–Fock–Bogoliubov formalism for collective excitations in drip-line nuclei

2001-12-01
Masayuki Matsuo
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Kohn–Sham density functional inspired approach to nuclear binding

2008-04-12
M. Baldo , Peter Schuck , X. Viñas
A non-relativisitic nuclear density functional theory is constructed, not as usual, from an effective density dependent nucleon-nucleon force but directly introducing in the functional results from microscopic nuclear and neutron … A non-relativisitic nuclear density functional theory is constructed, not as usual, from an effective density dependent nucleon-nucleon force but directly introducing in the functional results from microscopic nuclear and neutron matter Bruckner G-matrix calculations at various densities. A purely phenomenological finite range part to account for surface properties is added. The striking result is that only four to five adjustable parameters, spin-orbit included, suffice to reproduce nuclear binding energies and radii with the same quality as obtained with the most performant effective forces, containing on the order of ten parameters. In this pilot work, for the pairing correlations, simply a density dependent zero range force is adopted from the literature. Possible future extensions of this approach are pointed out.
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Reactions of a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow /><mml:mn>10</mml:mn></mml:msup></mml:math>Be beam on proton and deuteron targets

2013-12-23
K. Schmitt , K. L. Jones , S. Ahn +7 more
The extraction of detailed nuclear structure information from transfer reactions requires reliable, well-normalized data as well as optical potentials and a theoretical framework demonstrated to work well in the relevant … The extraction of detailed nuclear structure information from transfer reactions requires reliable, well-normalized data as well as optical potentials and a theoretical framework demonstrated to work well in the relevant mass and beam energy ranges. It is rare that the theoretical ingredients can be tested well for exotic nuclei owing to the paucity of data. The halo nucleus Be-11 has been examined through the 10Be(d,p) reaction in inverse kinematics at equivalent deuteron energies of 12,15,18, and 21.4 MeV. Elastic scattering of Be-10 on protons was used to select optical potentials for the analysis of the transfer data. Additionally, data from the elastic and inelastic scattering of Be-10 on deuterons was used to fit optical potentials at the four measured energies. Transfers to the two bound states and the first resonance in Be-11 were analyzed using the Finite Range ADiabatic Wave Approximation (FR-ADWA). Consistent values of the spectroscopic factor of both the ground and first excited states were extracted from the four measurements, with average values of 0.71(5) and 0.62(4) respectively. The calculations for transfer to the first resonance were found to be sensitive to the size of the energy bin used and therefore could not be used to extract a spectroscopic factor.
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Quasiparticle random phase approximation based on the relativistic Hartree-Bogoliubov model. II. Nuclear spin and isospin excitations

2004-05-10
Ν. Paar , T. Nikšić , D. Vretenar +1 more
The proton-neutron relativistic quasiparticle random-phase approximation (PN-RQRPA) is formulated in the canonical single-nucleon basis of the relativistic Hartree-Bogoliubov model, for an effective Lagrangian characterized by density-dependent meson-nucleon couplings. The model … The proton-neutron relativistic quasiparticle random-phase approximation (PN-RQRPA) is formulated in the canonical single-nucleon basis of the relativistic Hartree-Bogoliubov model, for an effective Lagrangian characterized by density-dependent meson-nucleon couplings. The model includes both the $T=1$ and $T=0$ pairing channels. Pair configurations formed from the fully or partially occupied states of positive energy in the Fermi sea, and the empty negative-energy states from the Dirac sea, are included in PN-RQRPA configuration space. The model is applied to the analysis of charge-exchange modes: isobaric analog resonances and Gamow-Teller resonances.
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Dynamics of nuclear single-particle structure in covariant theory of particle-vibration coupling: From light to superheavy nuclei

2011-07-07
Елена Литвинова , A. V. Afanasjev
The impact of particle-vibration coupling and polarization effects due to deformation and time-odd mean fields on single-particle spectra is studied systematically in doubly magic nuclei from low-mass $^{56}\mathrm{Ni}$ up to … The impact of particle-vibration coupling and polarization effects due to deformation and time-odd mean fields on single-particle spectra is studied systematically in doubly magic nuclei from low-mass $^{56}\mathrm{Ni}$ up to superheavy ones. Particle-vibration coupling is treated fully self-consistently within the framework of the relativistic particle-vibration coupling model. Polarization effects due to deformation and time-odd mean field induced by odd particle are computed within covariant density functional theory. It has been found that among these contributions the coupling to vibrations makes a major impact on the single-particle structure. The impact of particle-vibration coupling and polarization effects on calculated single-particle spectra, the size of the shell gaps, the spin-orbit splittings and the energy splittings in pseudospin doublets is discussed in detail; these physical observables are compared with experiment. Particle-vibration coupling has to be taken into account when model calculations are compared with experiment since this coupling is responsible for observed fragmentation of experimental levels; experimental spectroscopic factors are reasonably well described in model calculations.
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Intrinsic-density functionals

2007-01-08
J. Engel
The Hohenberg-Kohn theorem and Kohn-Sham procedure are extended to functionals of the localized intrinsic density of a self-bound system such as a nucleus. After defining the intrinsic-density functional, we modify … The Hohenberg-Kohn theorem and Kohn-Sham procedure are extended to functionals of the localized intrinsic density of a self-bound system such as a nucleus. After defining the intrinsic-density functional, we modify the usual Kohn-Sham procedure slightly to evaluate the mean-field approximation to the functional, and carefully describe the construction of the leading corrections for a system of fermions in one dimension with a spin-degeneracy equal to the number of particles $N$. Despite the fact that the corrections are complicated and nonlocal, we are able to construct a local Skyrme-like intrinsic-density functional that, while different from the exact functional, shares with it a minimum value equal to the exact ground-state energy at the exact ground-state intrinsic density, to next-to-leading order in $1/N$. We briefly discuss implications for real Skyrme functionals.

Escape and spreading properties of charge-exchange resonances in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Bi</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:mn>208</mml:mn></mml:mrow><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow></mml:math>

1994-09-01
G. Colò , Nguyen Van Giai , P. F. Bortignon +1 more
The properties of charge-exchange excitations of ${}^ {208}$Pb with $\Delta L = 0$, i.e., the isobaric analog and Gamow-Teller resonances, are studied within a self-consistent model making use of an … The properties of charge-exchange excitations of ${}^ {208}$Pb with $\Delta L = 0$, i.e., the isobaric analog and Gamow-Teller resonances, are studied within a self-consistent model making use of an effective force of the Skyrme type. The well-known isobaric analog case is used to assess the reliability of the model. The calculated properties of the Gamow-Teller resonance are compared with recent experimental measurements with the aim of better understanding the microscopic structure of this mode.
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