Exact removal of the center-of-mass spurious states from level densities

We give recursive formulae for the exact removal of the contribution of the center-of-mass spurious states from the fixed-spin and parity nuclear level density found in shell-model calculations, provided the total level density for restricted configurations is known. The method is valid for a large class of problems using a harmonic oscillator basis. Using our earlier methods based on statistical spectroscopy that utilize the centroids and widths for a restricted class of fixed-spin configurations, such as N ω excitations, one can calculate very accurately level densities free of spurious states. The approach is applicable to other fermion and boson systems trapped by an oscillator potential.