The matrix elements of \( \mathbf{s} \) has the selection rules \( \delta_{ \ell_{a} , \ell_{b} } \) and \( \delta_{n _{a} ,n _{b} } \). Thus the orbits which are connected by the GT operator are very selective; they are those in the same major oscillator shell with the same \( \ell \) value. The matrix elements such as \( 1s_{1/2}-0d_{3/2} \) which have the allowed \( \Delta j \) coupling but are zero due to the \( \Delta\ell \) coupling are called \( \ell \)-forbidden matrix elements.