In a similar way it is easy to show that the potential energy contribution to the ground state energy in \( m \)-scheme $$ \frac{1}{2}\sum_{ij\le F}\langle (j_im_ij_jm_j)M | \hat{V} | (j_im_ij_jm_j)M\rangle_{AS}, $$ can be rewritten as $$ \frac{1}{2}\sum_{j_i,j_j\le F}\sum_J(2J+1) \langle (j_ij_j)J | \hat{V} | (j_ij_j)J\rangle_{AS}, $$ This reduces the number of floating point operations with an order of magnitude on average.