Shape transition of Nd and Sm isotopes and the neutrinoless double- β -decay nuclear matrix element of Nd150

Neutron-rich Nd and Sm isotopes are known to exhibit shape phase transition as a function of neutron number. Among them, $^{150}\mathrm{Nd}$ and $^{150}\mathrm{Sm}$ are important not only because they are transitional nuclei but also because they are the parent and daughter nuclei of double-$\ensuremath{\beta}$ decay. We performed large-scale shell-model calculations of even-even Nd and Sm isotopes, including the spherical-deformed shape transition. The quasiparticle vacua shell model enables us to perform shell-model calculations with sufficiently large model space with the $^{110}\mathrm{Zr}$ inert core. The shell-model result well reproduces the experimental excitation energies and quadrupole properties of the yrast and nonyrast states. The nuclear matrix element of neutrinoless double-$\ensuremath{\beta}$ decay of $^{150}\mathrm{Nd}$ is evaluated showing its modest enhancement by shape mixing.