Reliability of the finite temperature Hartree-Fock approximation.

Abstract

The ensemble average of the internal energy in $^{20}\mathrm{Ne}$ is calculated in the finite temperature Hartree-Fock approximation and compared with the same quantity calculated exactly in the canonical ensemble. The thermal response of the different ensemble averages differs considerably for T\ensuremath{\le}2 MeV. The discrepancies can, however, easily be accounted for by the small fluctuations (1%) in the ensemble average of the number operator. A simple scheme using an approximation to the low-lying eigenspectrum of $^{20}\mathrm{Ne}$ yields far better agreement with exact canonical ensemble results.