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Shell Model Description of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">C</mml:mi><mml:mprescripts /><mml:none /><mml:mn>14</mml:mn></mml:mmultiscripts></mml:math>Dating<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>Decay with Brown-Rho-Scaled<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mi>N</mml:mi></mml:math…
We present shell model calculations for the beta decay of $^{14}\mathrm{C}$ to the $^{14}\mathrm{N}$ ground state, treating the states of the $A=14$ multiplet as two $0p$ holes in an $^{16}\mathrm{O}$ core. We employ low-momentum nucleon-nucleon ($NN$) interactions derived from the realistic Bonn-B potential and find that the Gamow-Teller (GT) matrix …