The study of $0\nu\beta\beta$ decay of $^{136}$Xe using nonclosure approach in nuclear shell model

In this investigation, we compute the nuclear matrix elements (NMEs) relevant to the light neutrino-exchange mechanism governing neutrinoless double beta ($0\nu\beta\beta$) decay in $^{136}$Xe. Our method is based on the nonclosure approach within the interacting nuclear shell model framework. This approach considers the genuine effects arising from the excitation energies of two hundred states for each spin-parity of the intermediary nucleus $^{136}$Cs. All computations are performed using the effective shell model Hamiltonian GCN5082. To understand the impact of nuclear structure on $0\nu\beta\beta$ decay, we explore the dependence of the NME on various factors, including the number of intermediate states and their spin-parity characteristics. We identify an optimal closure energy of approximately 3.7 MeV for the $0\nu\beta\beta$ decay of $^{136}$Xe that reproduces the nonclosure NME using the closure approach. The calculated total NME for the light neutrino-exchange $0\nu\beta\beta$ decay of $^{136}$Xe is 2.06 with the CD-Bonn short-range correlation (SRC). These results can be valuable for future experimental investigations into the $0\nu\beta\beta$ decay of $^{136}$Xe.