Shape transition of Nd and Sm isotopes and the neutrinoless double--decay nuclear matrix element of ¹⁵⁰Nd

Neutron-rich Nd and Sm isotopes are known to exhibit shape phase transition as a function of neutron number. Among them, Nd-150 and Sm-150 are important not only because they are transitional nuclei but also because they are the parent and daughter nuclei of double-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 Zr-110 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-beta decay of Nd-150 is evaluated showing its modest enhancement by shape mixing.