Normally, we start we a nucleon-nucleon interaction fitted to reproduce scattering data. It is common then to represent this interaction in terms relative momenta \( k \), the center-of-mass momentum \( K \) and various partial wave quantum numbers like the spin \( S \), the total relative angular momentum \( {\cal J} \), isospin \( T \) and relative orbital momentum \( l \) and finally the corresponding center-of-mass \( L \). We can then write the free interaction matrix \( V \) as $$ \langle kKlL{\cal J}ST\vert\hat{V}\vert k'Kl'L{\cal J}S'T\rangle. $$ Transformations from the relative and center-of-mass motion system to the lab system will be discussed below.