Surface corrections to the Fermi-Thomas statistical theory

John Kozlowski, Natali Fisher, Aurora Pribram−Jones +1 more

M. Casas, Angel Ricardo Plastino, Antonio Puente

Heide Narnhofer, Walter E Thirring

S. A. Moszkowski, L. Wilets

The effect of a periodic potential on the particle and energy density of a degenerate Fermi gas is considered. It is found that for a weak and long wavelength potential the inhomogeneity correction (deviation from the Thomas Fermi statistical model) to the kinetic energy density is only 1/9 as large as the Weizsacker estimate. The potential energy density due to Majorana exchange two-body interactions of short range is also given to a high accuracy by the statistical model; the corrections are only 1/9 as large as for a short range Wigner (ordinary) interaction. For the analogous two dimensional Fermi gas, the inhomogeneity corrections vanish at least to high order unless the periodic potential contains short wavelength components. Relevance to the problem of the nuclear surface is discussed.

Gyula Bene, P. Szépfalusy

Corrections to the Thomas-Fermi-type solution of the Gross-Pitaevskii equation are inevitable in order to get correctly the frequencies of the low lying modes out of the Bogolyubov equations. These corrections are important in the bulk, too, thus the failure of the Thomas-Fermi approximation is not confined to the surface. We discuss this effect quantitatively and consider similar phenomena of spin fluctuations in Bose-Einstein condensed gases in an optical trap.