We carry out the nuclear shell model calculations for nuclei with $A=76$ and $A=82$, and the energy levels are compared with the experimental data for nuclei with $A=82$.
We then estimate the nuclear matrix element (NME) for the $0\nu\beta\beta$ decay by using the ground state wavefunctions.
In order to investigate the model dependence of the NMEs, the pair-truncated shell model calculations are performed and the NMEs in terms of the wavefunctions are also calculated.
It is found that the NMEs are considerably different in the models,
although the number occupancies in the ground states of the parent and the daughter nuclei are almost unchanged.