Interaction of Diatomic Molecules with Photon Angular Momentum

TL;DR

This paper investigates how diatomic molecules interact with photons carrying angular momentum, revealing that photon absorption can induce rotational transitions with probabilities depending on the molecule size and photon angular momentum.

Contribution

It provides a theoretical analysis of molecular-photon interactions, showing how angular momentum transfer affects rotational transitions and quantifying absorption probabilities for different photon types.

Findings

Absorption probabilities scale with (k a)^2 for small molecules.

Transitions with ΔJ > 1 are possible but have low probability.

Probability ratios depend on photon angular momentum j and molecule size a.

Abstract

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.