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Alpha Cluster Condensation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:mn>12</mml:mn></mml:mrow><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:…
A new $\ensuremath{\alpha}$-cluster wave function is proposed which is of the $\ensuremath{\alpha}$-particle condensate type. Applications to ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ show that states of low density close to the 3 and 4 $\ensuremath{\alpha}$-particle thresholds in both nuclei are possibly of this kind. It is conjectured that all self-conjugate $4n$ nuclei may …