Average ground-state energy of finite Fermi systems

M. Centelles ¹, P. Leboeuf ², A. G. Monastra ³, J. Roccia ², P. Schuck ⁴, X. Vinas ¹

Physical Review C 74 (2006) 034332

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.

• 1. Departament d’Estructura i Constituents de la Matèria, Facultat de Fisica,
  Universitat de Barcelona
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
  CNRS : UMR8626 – Université Paris XI – Paris Sud
• 3. TU Dresden Institut für Theoretische Physik,
  Institut für Theoretische Physik
• 4. Institut de Physique Nucléaire d’Orsay (IPNO),
  CNRS : UMR8608 – IN2P3 – Université Paris XI – Paris Sud