Structure of even-even A=138 isobars and the yrast spectra of semi-magic Sn isotopes above the ¹³²Sn core

Large basis untruncated shell model (SM) calculations have been done for the A=138 neutron-rich nuclei in the π(gdsh)⊕ν(hfpi) valence space above the ¹³²Sn 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 ¹³⁸Te, Xe, and the B(E2;2⁺→0⁺) value in ¹³⁸Xe are excellently reproduced by both the interactions. For ¹³⁸Ba, the calculated spectra and the B(E2;2⁺→0⁺) value also agree very well with the experimental results. But the two theoretical results differ dramatically for ¹³⁸Sn, a nucleus on the r-process path. CWG predicts nearly constant energies of 2₁⁺ states for the even-even Sn isotopes above the ¹³²Sn core, normally expected for semi-magic nuclei. But SMPN predicts a remarkable new feature: decreasing E(2₁⁺) energies with increasing neutron number. The predicted energies for the Sn isotopes fit in the systematics for the E(2₁⁺) energies of their isotones with Z>50. Despite their differences, both interactions predict the 6₁⁺ state to be a ≈0.3 μs isomer in ¹³⁸Sn. 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.