# Rotational state changes in collisions of diatomic molecular ions with atomic ions

## TL;DR

This paper studies how diatomic molecular ions change their rotational states during collisions with atomic ions, using a classical-quantum approach to derive approximations for rotational excitation.

## Contribution

It introduces a classical-quantum method to analyze rotational state changes and derives closed-form formulas for excitation per collision based on system parameters.

## Key findings

- Derived closed-form approximations for rotational excitation per collision.
- Numerical analysis of various diatomic molecular ion systems.
- Provides a basis for estimating rotational excitation in sympathetic cooling.

## Abstract

We investigate rotational state changes in a single collision of diatomic molecular ions, polar or apolar, with an atomic ion. Rotational state changes may occur since the angular degree of freedom of the molecular ions interacts with the electric field due to the atomic ion. Thanks to the very different time and energy scales of translational and rotational motion, we may treat the collision classically and describe only the rotations quantum mechanically. We first investigate a number of example systems numerically and then derive closed-form approximations for the rotational excitation per collision, depending on the scattering energy and the molecular parameters. These findings provide the basis for estimating the accumulated rotational excitation in sympathetic cooling of molecular ions by laser-cooled atomic ions [arXiv:2410.22458 ] which involves many single collisions.