  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.
