Single j-shell studies of cross-conjugate nuclei and isomerism

TL;DR

This paper investigates the energy levels and isomerism in cross-conjugate nuclei within a single j shell model, revealing specific low-energy states and proposing explanations using shell and rotational models.

Contribution

It introduces a novel observation of low-lying states at median angular momentum and explains the (J_{max}+1)/2 rule through a hybrid shell and rotational model approach.

Findings

States with J = (J_{max}+1)/2 are often low in energy or isomeric.

States with J = J_{max} are isomeric in certain orbits.

Comparison with experimental data supports the theoretical explanations.

Abstract

It is noted that in a calculation with 4 nucleons with isospin 1 in a single j shell (f_{7/2}, g_{9/2}, h_{11/2}) the state with median angular momentum J = (J_{max}+1)/2 lies very low in energy becoming either an isomeric state or a ground state. Also states with J = J_{max} are isomeric for the orbits g_{9/2} and h_{11/2}. Comparisons with experiment are made. A hybrid mixture of shell model and rotational model arguments are used to explain the (J_{max} +1)/2 rule.