  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.
