The Lippman-Schwinger equation for two-nucleon scattering

The shorthand notation $$ T_{ll'}^{\alpha}(kk'K\omega)= \langle kKlL{\cal J}S\vert T(\omega)\vert k'Kl'L{\cal J}S\rangle, $$ denotes the \( T \)-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, \( L \), \( {\cal J} \), \( S \) and \( T \) are the orbital momentum of the center-of-mass motion, the total angular momentum, spin and isospin, respectively. Due to the nuclear tensor force, the interaction is not diagonal in \( ll' \).