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The quadrupole moments in the first 11/2- states in Cd isotopes are systematically measured from N=63 to N=81 (D. T. Yordanov et al., Phys. Rev. Lett. 110, 192501 (2013)), presenting a very clear linear increase from negative to positive values. Since this linearity well follows what the single-j shell model with the pairing force provides analytically, it is interpreted as a manifestation of the success of the single-j shell model.
In this study, we have carried out large-scale shell-model calculations to verify this conventional interpretation. With the valence shell consisting of the proton p1/2-g9/2 and the neutron d5/2-g7/2-h11/2-s1/2-d3/2 orbitals, and the effective interaction composed of the G matrix and an empirical interaction, we have successfully reproduced the trend of 2+ and 4+ energies in even-A Cd isotopes and the quadrupole and magnetic moments in odd-A Cd isotopes. By analyzing the wave functions, the first 11/2- levels in Cd isotopes are not dominated by the lowest seniority (v=1), thus contradicting to the conventional interpretation.
A natural question then arises: why are the observed quadrupole moments reproduced with the wave functions different from those of the seniority scheme? To answer this question, we examined deformation in Cd isotopes with the parity-projected Hartree-Fock calculations in the shell-model space, finding the dominance of prolate deformation throughout the isotopes chain. Based on those results, we propose that the change of the quadrupole moments in Cd isotopes is caused by the increasing K number with neutron number. This interpretation seems to be in good accordance with the calculated B(E2) systematics and the measured quadrupole moments in the 2+ states.