Average ground-state energy of finite Fermi systems

TL;DR

This paper develops a theory to correct semiclassical methods for calculating the average ground-state energy of finite Fermi systems with fixed particle number, improving accuracy in various physical contexts.

Contribution

It introduces a new theoretical approach that accounts for particle number constraints, enhancing the predictive power of semiclassical energy calculations.

Findings

Improved agreement with quantum energies in harmonic traps

Accurate modeling of nuclear energies with deformation effects

Enhanced semiclassical methods for fixed N systems

Abstract

Semiclassical theories like the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in systems with a fixed number of particles N, these methods overbind the actual average of the quantum energy as N is varied. We describe a theory that accounts for this effect. Numerical illustrations are discussed for fermions trapped in a harmonic oscillator potential and in a hard wall cavity, and for self-consistent calculations of atomic nuclei. In the latter case, the influence of deformations on the average behavior of the energy is also considered.