To parameterize the nucleon-nucleon interaction we solve the Lippman-Scwhinger equation $$ T_{ll'}^{\alpha}(kk'K)=V_{ll'}^{\alpha}(kk') +\frac{2}{\pi}\sum_{l''}\int_{0}^{\infty} dqq^2 V_{ll''}^{\alpha}(kq) \frac{1}{k^2-q^2 +i\epsilon} T_{l''l'}^{\alpha}(qk'K). $$ The shorthand notation $$ T(\hat{V})_{ll'}^{\alpha}(kk'K\omega)=\langle kKlL{\cal J}S\vert T(\omega)\vert k'Kl'L{\cal J}S\rangle, $$ denotes the \( T(V) \)-matrix with momenta \( k \) and \( k' \) and orbital momenta \( l \) and \( l' \) of the relative motion, and \( K \) is the corresponding momentum of the center-of-mass motion. Further, \( L \), \( {\cal J} \), and \( S \) are the orbital momentum of the center-of-mass motion, the total angular momentum and spin, respectively. We skip for the moment isospin.