Bivariate distributions in statistical spectroscopy studies: III. Non interacting particle strength densities for one-body transition operators

Abstract

In statistical spectroscopy, it was shown by French et al. (Ann. Phys., N.Y. 181, 235 (1988)) that the bivariate strength densities take a convolution form with the non interacting particle (NIP) strength density being convoluted with a spreading bivariate Gaussian due to interactions. Leaving aside the question of determining the parameters of the spreading bivariate Gaussian, one needs good methods for constructing the NIP bivariate strength densitiesI ^h_O (E,E′) (h is a one-body hamiltonian andO is a transition operator) in large shell model spaces. A formalism for constructingI ^h_O is developed for one-body transition operators by using spherical orbits and spherical configurations. For rapid construction and also for applying the statistical theory in large shell model spacesI ^h_O is decomposed into partial densities defined by unitary orbit configurations (unitary orbit is a set of spherical orbits). Trace propagation formulas for the bivariate momentsM _rs with r+s ≤2 of the partial NIP strength densities, which will determine the Gaussian representation, are derived. In a large space numerical example with Gamow-Tellerβ ⁻ transition operator, the superposition of unitary orbit partial bivariate Gaussian densities is shown to give a good representation of the exact NIP strength densities. Trace propagation formulas forM _rs with r+<—4 are also derived inm-particle scalar spaces which are useful for many purposes.