In this study, we calculate the nuclear matrix elements (NMEs) for the light neutrino-exchange mechanism of neutrinoless double beta decay ($0\nu \beta \beta$) of ${}^{124}\mathrm{Sn}$ within the framework of the interacting nuclear shell model, using the effective shell model Hamiltonian GCN5082. The NMEs are calculated employing both closure and nonclosure approaches. For the intermediate nucleus ${}^{124}\mathrm{Sb}$, effects of energy of 100 states for each $J_k^{\pi }=0^{+}$ to ${11}^{+}$ and $2^{-}$ to $9^{-}$ ($\mathrm{\Delta }{J}_k=1)$ are explicitly included in the nonclosure approach. The optimal closure energy, which reproduces nonclosure NMEs using the closure approach, is found to be $\approx$ 3 MeV for $0\nu \beta \beta$ decay of ${}^{124}\mathrm{Sn}$. The NMEs for $0\nu \beta \beta$ decay of ${}^{124}\mathrm{Sn}$ did not fully converge with 100 intermediate states for each spin-parity of ${}^{124}\mathrm{Sb}$. A comparison of NMEs and lower limits of $T_{1/2}^{0\nu }$ with some of the recent calculations is presented. Further, to gain a comprehensive understanding of the role of nuclear structure on the $0\nu \beta \beta$ decay, the dependence of NMEs on the spin-parity of the intermediate states, coupled spin-parity of neutrons and protons, and the number of intermediate states, is explored. The estimated lower limit on the half-life $T_{1/2}^{0\nu }\approx 7.49\times {10}^{26}$ yr provides valuable input for the experimental investigations of $0\nu \beta \beta$ decay of ${}^{124}\mathrm{Sn}$ in India and elsewhere.

• Received 17 August 2023
• Accepted 22 December 2023

DOI:https://doi.org/10.1103/PhysRevC.109.024301