The selection rules are given by the triangle condition for the angular momenta, \( \Delta(J_{i},J_{f},\lambda) \).

The electromagnetic interaction conserves parity, and the elements of the operators for \( E\lambda \) and \( M\lambda \) can be classified according to their transformation under parity change $$ \hat{P}\hat{O}\hat{P}^{-1}=\pi_{O}\hat{O}, $$ where we have \( \pi _{O}=(-1)^{\lambda } \) for \( Y^{\lambda } \), \( \pi _{O}=-1 \) for the vectors \( \mathbf{r} \), \( \mathbf{\nabla} \) and \( \mathbf{p} \), and \( \pi _{O}=+1 \) for the pseudo vectors \( \mathbf{l}=\mathbf{r}\times\mathbf{p} \) and \( \mathbf{\sigma} \). For a given matrix element we have: $$ \langle\Psi _{f}\vert {\cal O}\vert \Psi _{i}\rangle =\langle\Psi _{f}\vert P^{-1}P{\cal O}P^{-1}P\vert \Psi _{i}\rangle=\pi _{i}\pi _{f}\pi _{O} \langle\Psi _{f}\vert {\cal O}\vert \Psi _{i}\rangle. $$ The matrix element will vanish unless \( \pi _{i}\pi _{f}\pi _{O}=+1 \).