Quadrupole dominance in the light Sn and in the Cd isotopes

Abstract

[Background] The BE2 rates of the Sn isotopes for $N\le 64$ exhibit enhancements hitherto unexplained. The same is true for the Cd isotopes. [Purpose] Describe the electromagnetic properties of the Sn and Cd isotopes [Method] Shell model calculations with a minimally renormalized realistic interaction, supplemented by Quasi and Pseudo-SU3 symmetries and Nilsson-SU3 selfconsistent calculations. [Results for $N\le 64$] Shell model calculations with the neutron effective charge as single free parameter describe well the BE2(2>0) and BE2(4>2) rates for $N\le 64$ in the Cd and Sn isotopes. The former exhibit weak permanent deformation corroborating the prediction of a Pseudo-SU3 symmetry, which remains of heuristic value in the latter, where the pairing force erodes the quadrupole dominance. Calculations in $10^7$ and $10^{10}$-dimensional spaces exhibit almost identical patterns: A vindication of the shell model. [Results for $N\ge 64$] Nilsson-SU3 calculations describe BE2 patterns in [112-120]Cd and [116-118]Sn isotopes having sizable quadrupole moment of non-rotational origin denoted as q-vibrations. No calculations are proposed for the heavier species, for which the conventional seniority dscription is assumed for Sn, while in Cd the quadrupole moments change sign. [Conclusion] A radical reexamination of traditional interpretations in the region has been shown to be necessary, in which quadrupole dominance plays a major role. What emerges is a bumpy but coherent view.

10 pages 8 figures This is a radical revision of arXiv:1905.11479 which was accepted as a PRC rapid communication. I proposed a fully revised paper (the present one). The editors accepted. To avoid confusion, this article should be treated as a new submission. It is twice as long as the original and contains fundamental addition and improvements

References in corpus (2)

• Z=50 shell gap near ${}^{100}$Sn from intermediate-energy Coulomb excitations in even-mass ${}^{106--112}$Sn isotopes
• Shell model based deformation analysis of light Cadmium isotopes

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• Lifetime Measurements in the Even-Even ${}^{102-108}$Cd Isotopes
• The nucleon-pair approximation for nuclei from spherical to deformed regions
• E2 Rotational Invariants of $0_1^{+}$ and $2_1^{+}$ states for ${}^{106}$Cd: the Emergence of Collective Rotation
• Systematic shell-model study of ${}^{99-129}$Cd isotopes and isomers in neutron-rich ${}^{127-131}$In isotopes
• Systematic shell-model study of ${}^{98-130}$Cd isotopes and $8^{+}$ isomeric states
• Modification of single-hole-like states by configuration mixing in the ${}^{99-131}$In