Models for nuclear forces and derivation of non-relativistic expressions

To describe the interaction between the various baryons and mesons of the previous table we choose the following phenomenological lagrangians for spin \( 1/2 \) baryons $$ {\cal L}_{ps} =g^{ps}\overline{\Psi}\gamma^{5} \Psi\phi^{(ps)}, $$ $$ {\cal L}_{s} =g^{s}\overline{\Psi}\Psi\phi^{(s)}, $$ and $$ {\cal L}_{v} =g^{v}\overline{\Psi}\gamma_{\mu}\Psi\phi_{\mu}^{(v)} +g^{t}\overline{\Psi}\sigma^{\mu\nu}\Psi\left (\partial_{\mu}\phi_{\nu}^{(v)} -\partial_{\nu}\phi_{\mu}^{(v)}\right), $$ for pseudoscalar (ps), scalar (s) and vector (v) coupling, respectively. The factors \( g^{v} \) and \( g^{t} \) are the vector and tensor coupling constants, respectively.