Single j-shell studies of cross-conjugate nuclei and isomerism: (2j−1) rule

Abstract Isomeric states for 4 nucleons with isospin T = 1 are here considered. A comparison is made of the lighter and heavier members of cross-conjugate pairs where one member is obtained from the other by replacing protons by neutron holes and neutrons by proton holes. Although in the single j -shell the spectra in the two cases should be identical, this is not the case experimentally. For the former, the ground states all have angular momentum J = 2 . This result is found in a single j -shell calculation when the interaction is obtained from the spectrum of two particles. In a single j -shell ( f 7 / 2 , g 9 / 2 ) the state with angular momentum ( 2 j − 1 ) is the ground state for the heavier member of the pair provided one uses as an interaction the spectrum of two holes. The ground state behaviour can also be explained by rotational models. A new observation is that both in single j and in experiment the J = 2 state in the heavier member and the ( 2 j − 1 ) state in the lighter member are isomeric.