The \( \hat{V} \)-matrix in terms of harmonic oscillator wave functions reads $$ \langle (ab)JT|\hat{V}|(cd)JT\rangle= {\displaystyle \sum_{\lambda \lambda ' SS' {\cal J}}\sum_{nln'l'NN'L} \frac{\left(1-(-1)^{l+S+T}\right)}{\sqrt{(1+\delta_{ab}) (1+\delta_{cd})}}} $$ $$ \times\langle ab|\lambda SJ\rangle \langle cd|\lambda 'S'J\rangle \left\langle nlNL| n_{a}l_{a}n_{b}l_{b}\lambda\right\rangle \left\langle n'l'NL| n_{c}l_{c}n_{d}l_{d}\lambda ' \right\rangle $$ $$ \times \hat{{\cal J}}(-1)^{\lambda + \lambda ' +l +l'} \left\{\begin{array}{ccc}L&l&\lambda\\S&J&{\cal J} \end{array}\right\} \left\{\begin{array}{ccc}L&l'&\lambda '\\S&J&{\cal J} \end{array}\right\} $$ $$ \times\langle nNlL{\cal J}ST\vert\hat{V}\vert n'N'l'L'{\cal J}S'T\rangle. $$ The label \( a \) represents here all the single particle quantum numbers \( n_{a}l_{a}j_{a} \).