Partial Conservation Law in a Schematic Single j Shell Model

TL;DR

This paper discovers a partial conservation law in a schematic nuclear shell model where certain stationary states conserve the sum of proton and neutron pair angular momenta, with energies linearly related to this sum.

Contribution

It introduces a novel partial conservation law in a simplified shell model with a specific interaction pattern, expanding understanding of nuclear angular momentum conservation.

Findings

Certain stationary states conserve J_p + J_n.

Energies are linear functions of J_p + J_n.

Systematic occurrence of these states is explained.

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.