jjCoupling Model in Odd-Odd Nuclei

Abstract

An analysis has been made, using the $\mathrm{jj}$ coupling model, of the spins of 76 low-lying levels of odd-odd nuclei with $20<A<\mathrm{}120\mathrm{}$. Levels have been excluded from the analysis if any ambiguity exists in the assignment of a configuration. Excluding particle-hole configurations we find Nordheim's "strong" rule obeyed in the 22 cases in which it is applicable. Nordheim's "weak" rule is replaced by a rule predicting a ground state of the highest or lowest allowable spin. This revised rule is obeyed in 38 out of 41 cases. This competition between two levels of greatly differing spin results in the frequent occurrence of isomerism. For particle-hole configurations the state of the highest spin minus one is the ground state in 6 out of 13 cases. This agreement with experiment is obtained using proton and neutron configurations which, in 66 of the 76 cases, are found as ground states in the neighboring odd-even nuclei. The three revised coupling rules are predicted by the calculations of Schwartz, in which the residual proton-neutron interaction has a delta-function radial dependence, if the singlet-to-triplet strength is taken as 0.6, independent of mass number. This value is the same as that required to fit the free two-nucleon data. Exceptions to the empirical coupling rules and this theory will be discussed.