Partial Conservation Law in a Schematic Single j Shell Model

Abstract

We report the discovery of a partial conservation law obeyed by a schematic Hamiltonian of two protons and two neutrons in a j shell. In our Hamiltonian the interaction matrix element of two nucleons with combined angular momentum J is linear in J for even J and constant for odd J. It turns out that in some stationary states the sum J_p + J_n of the angular momenta J_p and J_n of the proton and neutron pairs is conserved. The energies of these states are given by a linear function of J_p + J_n. The systematics of their occurrence is described and explained.

Prepared for the volume "Quarks, Nuclei and Stars" dedicated to the memory of Gerald Edward Brown, eds. Holt et al., to be published with copyright by the World Scientific Publishing Company. In this version a figure was replaced and some errors corrected