Exclusion of Parity Unfavored Transitions in Forward Scattering Collisions

Functions ${\mathcal{Y}}_{l{l}^{\prime }\mathrm{LM}}(\hat{k}, {\hat{k}}^{\prime })$ of the directions of incidence and scattering are considered which transform like spherical harmonics $Y_{\mathrm{LM}}$ and are linear combinations of products $Y_{\mathrm{lm}}\left(\hat{k}\right)Y_{l^{\prime }{m}^{\prime }}\left({\hat{k}}^{\prime }\right)$. When they are parity unfavored ($l+l^{\prime }-L$ odd), these functions vanish for $\hat{k}·\hat{k}=\pm 1$. This property accounts for selection rules pointed out previously for particular types of collision.