On the ground–state energy of finite Fermi systems

Jérôme Roccia 1, Patricio Leboeuf 1

Physical Review C 76 (2007) 014301

We study the ground–state shell correction energy of a fermionic gas in a mean–field approximation. Considering the particular case of 3D harmonic trapping potentials, we show the rich variety of different behaviors (erratic, regular, supershells) that appear when the number–theoretic properties of the frequency ratios are varied. For self–bound systems, where the shape of the trapping potential is determined by energy minimization, we obtain accurate analytic formulas for the deformation and the shell correction energy as a function of the particle number $N$. Special attention is devoted to the average of the shell correction energy. We explain why in self–bound systems it is a decreasing (and negative) function of $N$.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI – Paris Sud
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