Large scale shell model calculation for collectivity in nuclei beyond Ni78

A shell model effective interaction for nuclei beyond the double magic nucleus ${}^{78}\mathrm{Ni}$ is constructed. First, the single-particle evolutions for valence neutrons above the double magic ${}^{78}\mathrm{Ni}$ are systematically explored in the $N=51$ isotones using the large scale shell model (LSSM) calculations based on the constructed effective interaction. Subsequently, we calculate the excitation energies of $2_1^{+}$ states and reduced electric quadrupole transition probabilities $B(E2;2^{+}\to 0^{+})$ for $N=52$ isotones. Notably, our calculation gives the result most consistent with the trend of the $B\left(E2\right)$ values observed in the $N=52$ isotones, especially for ${}^{84}\mathrm{Ge}$, a result that poses a serious challenge to the theoretical model. Furthermore, the collectivity in $N=52$ isotones, as well as the roles of pseudo-SU(3) symmetry, are investigated via the calculated primary configurations of their ground states and the first excited states. Additionally, the low-lying structures and band characteristics of neutron-rich Ge and Se isotopes are investigated. The ground state and the $\gamma$-soft band are constructed in our LSSM calculations, aligning well with available experimental evidence. Finally, we present the calculated evolutions of low-lying states in neutron-rich Ge and Se isotopes. The predictions for the as-yet unobserved low-lying states in these nuclei provide a comprehensive dataset to guide and inform future experimental efforts to decipher the evolution of shell structures and collectivity.