Nucleon pair shell model in M scheme

The nucleon pair shell model (NPSM) is cast into the so-called M scheme for the cases with isospin symmetry and without isospin symmetry. The odd system and even system are treated on the same footing. The uncoupled commutators for nucleon pairs, which are suitable for the M scheme, are given. Explicit formula of matrix elements in M scheme for overlap, one-body operators, and two-body operators are obtained. It is found that the CPU time used in calculating the matrix elements in M scheme is much shorter than that in the J scheme of NPSM.