Shell-model description of $N=Z$, $A\sim 70$ nuclei

We present the results of shell-model calculations in the model space consisting of four single-particle orbits $1p_{3/2}$, $0f_{5/2}$, $1p_{1/2}$ and $0g_{9/2}$ using a new semi-microscopic effective interaction. The structure of $N=Z$ nuclei around $^{68}$Se is discussed focusing especially on the role of the $g_{9/2}$ orbit. The development of the band structure is interpreted in terms of successive excitations of nucleons into the $g_{9/2}$ orbit. The triaxial/$\gamma$-soft structure in $^{64}$Ge and the prolate/oblate shape-coexistence in $^{68}$Se are predicted, showing a good correspondence with the experimental data. The isomeric states in $^{66}$As and $^{70}$Br are obtained with the structure of an aligned proton-neutron pair in the $g_ {9/2}$ orbit. In spite of the modest model space, the new interaction turns out to describe rather well properties related to the $g_{9/2}$ orbit in various cases including moderately deformed nuclei.