The $\lambda$ and $m_{\beta \beta }$ mechanisms of neutrinoless double beta decay ($0\nu \beta \beta$) occur with light neutrino exchange via $W_L-W_R$ and $W_L-W_L$ mediation, respectively. In the present study, we calculate the nuclear matrix elements (NMEs) for the $m_{\beta \beta }$ and $\lambda$ mechanisms of $0\nu \beta \beta$, which has origin in the left-right symmetric model with right-handed gauge boson at TeV scale. The NMEs are calculated for one of the $0\nu \beta \beta$ decaying isotope ${}^{48}\mathrm{Ca}$ in the interacting nuclear shell-model using the GXPF1A effective interaction of $pf$ shell. The NMEs are calculated in both closure and nonclosure approaches using four different methods: closure, running closure, running nonclosure, and mixed methods. All the NMEs are calculated incorporating the effects of the finite size of nucleons and the revisited higher-order terms such as pseudoscalar and weak magnetism terms of the nucleon currents. Inclusion of the short-range nature of nucleon-nucleon interaction in Miller-Spencer, CD-Bonn, and AV18 parametrizations is also taken care of. We have used closure energy $\langle E\rangle =0.5$ MeV, which is near to the optimal value of closure energy that is extracted by examining the dependence of NMEs with closure energy in closure and mixed methods. The comparative dependence of the running closure and running nonclosure NMEs with the spin-parity of the allowed states of intermediate nucleus ${}^{48}\mathrm{Sc}$, the coupled spin-parity of the two initial decaying neutrons and the final two protons, the cutoff excitation energy of ${}^{48}\mathrm{Sc}$, and the cutoff number of states of ${}^{48}\mathrm{Sc}$ are examined. The neutrino momentum and radial distribution of different types of NMEs are explored. It is found that there is a significant enhancement in $M_{qGT}$-type NMEs, which originates from the large momentum distribution for the inclusion of the higher-order pseudoscalar term of the nucleon currents.

• Received 10 March 2020
• Revised 5 August 2020
• Accepted 25 August 2020

DOI:https://doi.org/10.1103/PhysRevC.102.034317