Energy expressions for n=3 and 4 systems in a single-j shell

TL;DR

This paper derives simple analytical energy expressions for three- and four-fermion systems in a single-j shell, aiding understanding of isomeric states and seniority conservation.

Contribution

It provides new simplified energy formulas and algebraic conditions for seniority conservation in small fermion systems within a single-j shell.

Findings

Derived simple energy expressions for n=3 and 4 systems

Identified algebraic conditions for seniority conservation

Enhanced understanding of isomeric state structures

Abstract

For systems with three and four fermions within a single-j shell, analytical expressions for the state energies are presented from a decomposition of the angular momentum. In some important cases the expressions acquire a very simple form. The expression may help us in understanding the structure of isomeric states. The decomposition also makes it possible to construct the algebraic condition for conservation of seniority.