Application of the Phase Space Quasi-Probability Distribution to the Nuclear Shell Model

Abstract

The quantum mechanical joint position-momentum quasi-distribution function is applied to the nuclear shell model. By introducing approximate quasi-position and quasi-momentum variables, the quasi-distribution function is converted into a non-negative (and hence nonquasi) distribution. Numerical results are presented for one-dimensional and three-dimensional potentials leading in three dimensions to a nonisotropic nonindependent distribution with a predominance of low momenta at the nuclear surface. These results are in contrast with the usual Thomas-Fermi model and in addition provide a simple base for the discussion of direct nuclear reactions involving an average over many states of a residual nucleus for which linear momentum as opposed to angular momentum is a relevant quantity.