Different particle alignments in N approx Z Ru isotopes studied by the shell model

Experimentally observed heaviest $N \approx Z$ nuclei, Ru isotopes, are investigated by the shell model on a spherical basis with the extended $P+QQ$ Hamiltonian. The energy levels of all the Ru isotopes can be explained by the shell model with a single set of force parameters. The calculations indicate enhancement of quadrupole correlations in the $N=Z$ nucleus $^{88}$Ru as compared with the other Ru isotopes, but the observed moments of inertia seem to require much more enhancement of quadrupole correlations in $^{88}$Ru. It is discussed that the particle alignment takes place at $8^+$ in $^{90}$Ru but is delayed in $^{88}$Ru till $16^+$ where the simultaneous alignments of proton and neutron pairs take place. The calculations present interesting predictions for $^{89}$Ru that the ground state is the $1/2^-$ state and there are three $\Delta J=2$ bands with different particle alignments including the T=0 $p-n$ pair alignment.