Variational approach with the superposition of the symmetry-restored quasiparticle vacua for nuclear shell-model calculations
Noritaka Shimizu, Y. Tsunoda, Y. Utsuno, Takaharu Otsuka
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 quasiparticle 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 $^{132}\mathrm{Ba}$ in the $50\ensuremath{\le}Z,N\ensuremath{\le}82$ model space. We also discuss the feasibility of this scheme in the case of the $^{150}\mathrm{Nd}$ in the $50\ensuremath{\le}Z\ensuremath{\le}82$ and $82\ensuremath{\le}Z\ensuremath{\le}126$ model space and demonstrate that its neutrinoless double-$\ensuremath{\beta}$-decay matrix element is obtained showing good convergence.