Components of the force and quantum numbers

For \( s=1/2 \) spin values only for two nucleons, the expectation value of the tensor force operator is

\( l' \)
\( l \) \( J+1 \) \( J \) \( J-1 \)
\( J+1 \) \( -\frac{2J(J+2)}{2J+1} \) 0 \( \frac{6\sqrt{J(J+1)}}{2J+1} \)
\( J \) 0 2 0
\( J-1 \) \( \frac{6\sqrt{J(J+1)}}{2J+1} \) 0 \( -\frac{2(2J+1)}{2J+1} \)

We will derive these expressions after we have discussed the Wigner-Eckart theorem.