Microscopic explanation of the shape-phase transition atN=88–90and theZ=64subshell effect for Ba–Dy

Background: The shape-phase transition at $N$ $=$ 88\char21{}90, and the role of $Z$ $=$ 64 subshell effect therein has been a subject of study on empirical basis and in the context of the ${N}_{p}$N${}_{n}$ scheme, but a microscopic view of the same has been lacking.