Components of the force and quantum numbers

Similarly, the expectation value of the spin-orbit term is $$ \langle \mathbf{l}\mathbf{S} \rangle = \frac{1}{2}\left( J(J+1)-l(l+1)-S(S+1)\right), $$ which means that for \( s \)-waves with either \( S=0 \) and thereby \( J=0 \) or \( S=1 \) and \( J=1 \), the expectation value for the spin-orbit force is zero. With the above phenomenological model, the only contributions to the expectation value of the potential energy for \( s \)-waves stem from the central and the spin-spin components since the expectation value of the tensor force is also zero.