Interaction of Diatomic Molecules with Photon Angular Momentum

The interaction of a diatomic molecule with photons carrying well-defined angular momentum and parity is investigated to determine whether photon absorption can induce molecular rotational transitions between states having angular momentum $\Delta J >1$. A transformation from laboratory coordinates to coordinates with origin at the center-of-mass of the nuclei is used to obtain the interaction between the photons and the molecule's center-of-mass, electronic, and rotational degrees of freedom. For molecules making transitions between rotational levels, there is a small parameter, $k a \ll 1$, where $k$ is the photon wave vector and $a$ is the size of the molecule, which enters into the $Ej$ and $Mj$ photon absorption probabilities. For electric photons having arbitrary angular momentum $j \hbar$, the probability of absorbing an $E(j+1)$ photon divided by the probability of absorbing an $Ej$ photon, scales as $(k a)^2 /(2 j+1)^2$. The probability of absorbing an $Mj$ photon, divided by the probability of absorbing and $Ej$ photon scales according to the same factor.