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Neutron-rich Nd and Sm isotopes are known to exhibit shape phase transitionas a function of neutron number. Among them, $^{150}$Nd and $^{150}$Sm areimportant not only because they are transitional nuclei, but also the parentand daughter nuclei of double-beta decay. We performed large-scale shell-modelcalculations of even-even Nd and Sm isotopes including the spherical-deformedshape transition. The quasi-particle vacua shell model enables us to performshell-model calculations with sufficiently large model space with the$^{110}$Zr inert core. The shell-model result well reproduces the experimentalexcitation energies and quadrupole properties of the yrast and non-yraststates. The nuclear matrix element of neutrinoless double-beta decay of$^{150}$Nd is evaluated showing its modest enhancement by shape mixing.

Shape transition of Nd and Sm isotopes and neutrinoless double-beta decay nuclear matrix element of $^{150}$Nd