Width Configuration Research Articles

Behavior of shell-model configuration moments

An important input into reaction theory is the density of states or the level density. Spectral distribution theory (also known as nuclear statistical spectroscopy) characterizes the secular behavior of the density of states through moments of the Hamiltonian. One particular approach is to partition the model space into subspaces and find the moments in those subspaces; a convenient choice of subspaces are spherical shell-model configurations. We revisit these configuration moments and find, for complete $0\hbar\omega$ many-body spaces, the following behaviors: (a) the configuration width is nearly constant for all configurations; (b) the configuration asymmetry or third moment is strongly correlated with the configuration centroid; (c) the configuration fourth moment, or excess is linearly related to the square to the configuration asymmetry. Such universal behavior may allow for more efficient modeling of the density of states in a shell-model framework.

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); M. Horoi, B. A. Brown, and V. Zelevinsky, Phys. Rev. C 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 $N\ensuremath{\hbar}\ensuremath{\omega}$ 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 $<20\phantom{\rule{0.3em}{0ex}}\text{MeV}$. This approach could be also applied to other many-fermion systems, such as atomic clusters.