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Average ground-state energy of finite Fermi systems
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Semiclassical theories such as 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.
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CENTELLES AIXALÀ, Mario, et al. Average ground-state energy of finite Fermi systems. Physical Review C. 2006. Vol. 74, num. 3, pags. 034332-1-034332-9. ISSN 0556-2813. [consulted: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/11021