Neutrinoless double- β decay in the nucleon-pair shell model

Abstract

Nuclear matrix elements (NMEs) of neutrinoless double-$\ensuremath{\beta}$ decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) from ${0}_{1}^{+}$ to ${0}_{1}^{+}$ of $^{130}\mathrm{Te}\ensuremath{\rightarrow}^{130}\mathrm{Xe}$, $^{134}\mathrm{Xe}\ensuremath{\rightarrow}^{134}\mathrm{Ba}$, and $^{136}\mathrm{Xe}\ensuremath{\rightarrow}^{136}\mathrm{Ba}$ are calculated in the nucleon pair shell-model framework. It is found that the NMEs of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ calculated in the surface-$\ensuremath{\delta}$ approximation (SDI) and the BCS approximation with the model space truncated into the SD-pair subspace are close to each other and smaller than those predicted by the other models. The inclusion of the $G$ pair does not alter the results significantly. When the single-particle energies are assumed to be degenerate, the calculated results in the SD-pair shell model become close to those of the other models. It is also shown that the NMEs are sensitive to the model parameters.