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.