Large basis untruncated shell model (SM) calculations have been done for the $A=138$ neutron-rich nuclei in the $\pi (\mathit{gdsh})\oplus \nu (\mathit{hfpi})$ valence space above the ${}^{132}\mathrm{Sn}$ core using two (1+2) -body nuclear Hamiltonians, viz., realistic CWG and empirical SMPN. Calculated binding energies, excitation spectra, and wave function structures are compared for even-even $A=138$ isobars for which experimental data are available. The nearly vibrational states in ${}^{138}\mathrm{Te}$, Xe, and the $B(E2;2^{+}\to 0^{+})$ value in ${}^{138}\mathrm{Xe}$ are excellently reproduced by both the interactions. For ${}^{138}\mathrm{Ba}$, the calculated spectra and the $B(E2;2^{+}\to 0^{+})$ value also agree very well with the experimental results. But the two theoretical results differ dramatically for ${}^{138}\mathrm{Sn}$, a nucleus on the $r$-process path. CWG predicts nearly constant energies of $2_1^{+}$ states for the even-even Sn isotopes above the ${}^{132}\mathrm{Sn}$ core, normally expected for semi-magic nuclei. But SMPN predicts a remarkable new feature: decreasing $E(2_1^{+})$ energies with increasing neutron number. The predicted energies for the Sn isotopes fit in the systematics for the $E(2_1^{+})$ energies of their isotones with $Z>50$. Despite their differences, both interactions predict the $6_1^{+}$ state to be a $\approx 0.3\hspace{0.5em}\mu \mathrm{s}$ isomer in ${}^{138}\mathrm{Sn}$. Calculated magnetic dipole moments and electric quadrupole moments of the states in these isobars are compared with the experimental data wherever available. The appearance of deformation and evolution of collectivity in nuclei in this valence space are discussed.

• Received 5 December 2007

DOI:https://doi.org/10.1103/PhysRevC.78.024308