Large-scale shell model calculations including two major shells are carried out, and the ingredients of nuclear matrix element for two-neutrino double beta decay are investigated. Based on the comparison between the shell model calculations accountin
g only for one major shell ($pf$-shell) and those for two major shells ($sdpf$-shell), the effect due to the excitation across the two major shells is quantitatively evaluated.
The shapes of neutron-rich exotic Ni isotopes are studied. Large-scale shell model calculations are performed by advanced Monte Carlo Shell Model (MCSM) for the $pf$-$g_{9/2}$-$d_{5/2}$ model space. Experimental energy levels are reproduced well by a
single fixed Hamiltonian. Intrinsic shapes are analyzed for MCSM eigenstates. Intriguing interplays among spherical, oblate, prolate and gamma-unstable shapes are seen including shape fluctuations, $E$(5)-like situation, the magicity of doubly-magic $^{56,68,78}$Ni, and the coexistence of spherical and strongly deformed shapes. Regarding the last point, strong deformation and change of shell structure can take place simultaneously, being driven by the combination of the tensor force and changes of major configurations within the same nucleus.
