核壳模型计算中的准粒子真空叠加变分法
Variational approach with the superposition of the symmetry-restored quasi-particle vacua for nuclear shell-model calculations
摘要：
本文提出了一种利用角动量、宇称、数投影准粒子真空叠加的变分计算方案，特别适合于应用于中重核壳模型计算。我们推导出一个准粒子真空的能量方差公式，并将能量方差外推到本方案中，以进一步精确估计壳模型的精确能量。在$50 \leq Z,N \leq 82$模型空间中对$^{132}$ Ba进行了壳模型计算，验证了该方法的有效性。我们还讨论了在$50 \leq Z \leq 82$和$82 \leq Z \leq 126$模型空间中$^{150}$ Nd的情况下该方案的可行性，并证明了它的无中微子双β衰变矩阵元具有良好的收敛性。
英文摘要：
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 $50 \leq Z,N \leq 82$ model space. We also discuss the feasibility of this scheme in the case of the $^{150}$Nd in the $50 \leq Z \leq 82$ and $82 \leq Z \leq 126$ model space and demonstrate that its neutrinoless-double-beta-decay matrix element is obtained showing good convergence.
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