Variational approach with the superposition of the symmetry-restored quasi-particle vacua for nuclear shell-model calculations

Abstract

We propose a variational calculation scheme utilizing the superposition of the angular-momentum, parity, number projected quasiparticle vacua, that is especially suitable for applying to medium-heavy nuclei in shell-model calculations. We derive a formula for the energy variance with quasi-particle vacua and apply the energy-variance extrapolation to the present scheme for further precise estimation of the exact shell-model energy. The validity of the method is presented for the shell-model calculation of ${}^{132}$Ba in the $50\le Z,N\le 82$ model space. We also discuss the feasibility of this scheme in the case of the ${}^{150}$Nd in the $50\le Z\le 82$ and $82\le Z\le 126$ model space and demonstrate that its neutrinoless-double-beta-decay matrix element is obtained showing good convergence.

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• Shape transition of Nd and Sm isotopes and neutrinoless double-beta decay nuclear matrix element of ${}^{150}$Nd
• Accurate and precise quantum computation of valence two-neutron systems
• Large-scale shell-model study of two-neutrino double-beta decay of ${}^{82}$Se, ${}^{94}$Zr, ${}^{108}$Cd, ${}^{124}$Sn, ${}^{128}$Te, ${}^{130}$Te, ${}^{136}$Xe, and ${}^{150}$Nd
• Constraints on the nuclear Schiff moment from its correlation with electromagnetic properties
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• Nuclear structure properties of ${}^{193-200}$Hg isotopes within large-scale shell model calculations
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• Probing Quadruple Deformation in Transitional Nuclei via Angular Momentum Projection