Fixed spin and parity nuclear level density for restricted shell model configurations

In a recent paper [M. Horoi, J. Kaiser, and V. Zelevinsky, Phys. Rev. C 67, 054309 (2003)] proposed a method of calculating J-, T-, and parity-dependent shell model nuclear level densities using centroids and widths for configurations with fixed spin, isospin and parity quantum numbers, and the energies of the yrast states calculated with the exponential convergence method [M. Horoi, A. Volya, and V. Zelevinsky, Phys. Rev. Lett. 82, 2064 (1999); M. Horoi, B. A. Brown, and V. Zelevinsky, Phys. Rev. C 65, 027303 (2002); 67, 034303 (2003)]. When used in many major shell model spaces the results are affected by contributions of the spurious center-of-mass states. Attempts to eliminate these contributions would require knowledge of fixed-J centroids and widths for restricted shell model configurations, such as the Nℏω excitations. We derive explicit expressions for matrix elements that can be used to calculate the fixed-J configuration widths and use them to reduce the contribution of the spurious center-of-mass states to the nuclear level density for excitation energies <20 MeV. This approach could be also applied to other many-fermion systems, such as atomic clusters.