Nuclear tensor force ($S_{12}=3({\mathbf{\sigma }}_1\cdot \hat{\mathbf{r}})({\mathbf{\sigma }}_2\cdot \hat{\mathbf{r}})-{\mathbf{\sigma }}_1\cdot {\mathbf{\sigma }}_2$)

The linear operator $V_T(r)S_{12}$ couples nucleon spin orientations to their separation direction $\hat{\mathbf{r}}$. Here ${\mathbf{\sigma }}_i$ are Pauli matrices. A scalar radial potential energy alone omits this directional dependence.