On the ground--state energy of finite Fermi systems

Abstract

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 $N$.

arXiv comment10 pages, 5 figures, 2 tables

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• Quantum Monte Carlo Calculations of $A\le 6$ Nuclei
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Cited by in corpus (4)

• Random Matrices and Chaos in Nuclear Physics
• Shell structure and orbit bifurcations in finite fermion systems
• Closed orbits and spatial density oscillations in the circular billiard
• Curvature Correction in the Strutinsky's Method