The tensor operator in the nucleon-nucleon potential can be written as $$ V=\frac{3}{r^{2}}\left[ \left[ {\bf \sigma}_1 \otimes {\bf \sigma}_2\right]^ {(2)} \otimes\left[{\bf r} \otimes {\bf r} \right]^{(2)}\right]^{(0)}_0 $$ Since the irreducible tensor \( \left[{\bf r} \otimes {\bf r} \right]^{(2)} \) operates only on the angular quantum numbers and \( \left[{\bf \sigma}_1 \otimes {\bf \sigma}_2\right]^{(2)} \) operates only on the spin states we can write the matrix element $$ \begin{eqnarray*} \langle lSJ\vert V\vert lSJ\rangle & = & \langle lSJ \vert\left[ \left[{\bf \sigma}_1 \otimes {\bf \sigma}_2\right]^{(2)} \otimes \left[{\bf r} \otimes {\bf r} \right]^{(2)}\right]^{(0)}_0\vert l'S'J\rangle \\ & = & (-1)^{J+l+S} \left\{\begin{array}{ccc} l&S&J \\ l'&S'&2\end{array}\right\} \langle l \vert\vert\left[{\bf r} \otimes {\bf r} \right]^{(2)} \vert \vert l'\rangle\\ & & \times \langle S\vert\vert\left[{\bf \sigma}_1 \otimes {\bf \sigma}_2\right]^{(2)} \vert\vert S'\rangle \end{eqnarray*} $$