Spectral Distributions in Nuclei

Given a finite many-particle vector space, which may be of large dimensionality, and a Hamiltonian which operates inside it, we may investigate the general properties of the system by a method of expanding preselected basis states in terms of the Hamiltonian eigenfunctions. The corresponding intensity, considered as a function of the Hamiltonian eigenvalues, is a spectral distribution which may be studied via its energy moments; we consider such distributions averaged over subsets of basis states. The properties of these averaged distributions are discussed, as well as methods for applying them in general studies of complicated systems; methods are given for evaluating the moments in some significant cases. Detailed formal results are given for configuration distributions in the spherical shell model.