  A new high-performance algorithm for calculating the spin- and
parity-dependent shell model nuclear level densities using methods of
statistical spectroscopy in the proton-neutron formalism was recently proposed.
When used in valence spaces that cover more than one major harmonic oscillator
shell, this algorithm mixes the genuine intrinsic states with spurious
center-of-mass excitations. In this paper we present an advanced algorithm,
based on the recently proposed statistical moments method, that eliminates the
spurious states. Results for unnatural parity states of several sd-shell nuclei
are presented and compared with those of exact shell model calculations and
experimental data.
