On the ground--state energy of finite Fermi systems

Details On the ground--state energy of finite Fermi systems On the ground--state energy of finite Fermi systems

2007-03-02

arxiv.org/abs/nucl-th/0703009v2

Phys.Rev.C76:014301,2007

Physics

Nuclear Physics

Nuclear Theory

10 pages, 5 figures, 2 tables

Scientific paper

10.1103/PhysRevC.76.014301

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 $N$.

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