Models for nuclear forces and derivation of non-relativistic expressions

Expanding the free Dirac spinors in terms of \( 1/m \) (\( m \) is here the mass of the relevant baryon) results, to lowest order, in the familiar non-relativistic expressions for baryon-baryon potentials. The configuration space version of the interaction can be approximated as $$ V(\mathbf{r})= \left\{ C^0_C + C^1_C + C_\sigma \mathbf{\sigma}_1\cdot\mathbf{\sigma}_2 + C_T \left( 1 + {3\over m_\alpha r} + {3\over \left(m_\alpha r\right)^2} \right) S_{12} (\hat r)\right. $$ $$ + C_{SL}\left. \left( {1\over m_\alpha r} + {1\over \left( m_\alpha r\right)^2} \right) \mathbf{L}\cdot \mathbf{S} \right\} \frac{\exp{-(m_\alpha r)}}{m_\alpha r}, $$ where \( m_{\alpha} \) is the mass of the relevant meson and \( S_{12} \) is the familiar tensor term.