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