Semiclassical calculations with nuclear model potentials in the ħ-resummation approach

Abstract

The single-particle densityρ(r) of a system of fermions can be calculated in a tractable way as the Laplace inverse of the Bloch density describing the system. The complex integrals involved can be solved very easily by the saddle-point method. The semiclassical nature of this approach is illustrated in the simple example of the single-particle level density of a harmonic oscillator potential. It is then applied to calculate the total energy of particles in different mean field potentials. The exact Bloch density being generally unknown, different approximate forms are used in our calculations which correspond to a partial resummation of the Wigner-Kirkwoodħ-expansion. The resulting local densities reproduce the exact density distributions on the average, without quantal oscillations. They are well defined everywhere, even beyond the classical turning point, in contrast to the original Wigner-Kirkwood approach.