We consider the calculation of the nuclear level density parameter a = 1 62gs({lunate}F), where gs({lunate}) is the smoothed single-particle level density and {lunate}F is the Fermi energy. We present an exact (quantum mechanical) calculation of gs({lunate}) for bound and continuum states using a Green function approach with Strutinski smoothing. The accuracy and applicability of semiclassical approximations, such as the Thomas-Fermi (TF), TF+h{stroke}2 correction and the local density approximation (LDA) are investigated using finite and infinite single-particle potential wells with sharp or smooth surfaces. 1992.
