Semiclassical approximations for nuclear hamiltonians. I. Spin-independent potentials

Abstract

A systematic procedure for calculating semiclassical expansions of physically interesting quantities is presented. The method is based on the Wigner transform of operators. It is applied specifically to the case of fermions governed by a one-body Hamiltonian. Expansions up to fourth order in ħ of the density matrix for various spin-independent potentials are derived. Expressions of the kinetic energy density in terms of the matter density are given, which are of particular interest for nuclear structure calculations.