Deformed shell model results for neutrinoless double beta decay of nuclei in A=60-90 region

Abstract

Nuclear transition matrix elements (NTME) for the neutrinoless double beta decay of $^{70}$Zn, $^{80}$Se and $^{82}$Se nuclei are calculated within the framework of the deformed shell model based on Hartree-Fock states. For $^{70}$Zn, jj44b interaction in $^{2}p_{3/2}$, $^{1}f_{5/2}$, $^{2}p_{1/2}$ and $^{1}g_{9/2}$ space with $^{56}$Ni as the core is employed. However, for $^{80}$Se and $^{82}$Se nuclei, a modified Kuo interaction with the above core and model space are employed. Most of our calculations in this region were performed with this effective interaction. However, jj44b interaction has been found to be better for $^{70}$Zn. The above model space was used in many recent shell model and interacting boson model calculations for nuclei in this region. After ensuring that DSM gives good description of the spectroscopic properties of low-lying levels in these three nuclei considered, the NTME are calculated. The deduced half-lives with these NTME, assuming neutrino mass is 1 eV, are $1.1 \times 10^{26}$ yr, $2.3 \times 10^{27}$ yr and $2.2 \times 10^{24}$ yr for $^{70}$Zn, $^{80}$Se and $^{82}$Se, respectively.