The structure of the collective bands in⁷⁷Kr is investigated within our deformed shell model (DSM) based on Hartree-Fock states. The different levels are classified into collective bands on the basis of their B(E2) values. The calculatedK = 5/2⁺ ground band agrees reasonably well with the experiment. An attempt has been made to study the structure of the 3-quasiparticle band based on large J state in this nucleus. The calculated collective bands, the B(E2), and B(M1) values are compared with available experimental data. The nature of alignments in the low-lying bands is also analyzed.

The spectroscopic properties of ⁶⁴Zn and ⁶⁴Ni are calculated within the framework of the deformed shell model (DSM) based on Hartree–Fock states. GXPF1A interaction in 1 $f_{7/2}$, 2$p_{3/2}$, 1$f_{5/2}$ and 2$p_{1/2}$ space with ⁴⁰Ca as the core is employed. After ensuring that DSM gives good description of the spectroscopic properties of low-lying levels in these two nuclei considered, nuclear transition matrix elements (NTME) for the neutrinoless positron double beta decay (0$\nu \beta^+$ and $0\nu \beta^+$EC) of ⁶⁴Zn are calculated. The two-neutrino positron double beta decay halflife is also calculated for this nucleus.