# New method to study ion-molecule reactions at low temperatures and application to the H$_2^+$ + H$_2$ $\rightarrow$ H$_3^+$ + H reaction

## TL;DR

This paper introduces a novel merged-beam experimental technique using Rydberg states to study low-temperature ion-molecule reactions, exemplified by the H$_2^+$ + H$_2$ reaction, achieving collision energies below 10 K.

## Contribution

The authors develop a new method employing Rydberg-Stark states and a merged-beam approach to measure ion-molecule reactions at very low collision energies, overcoming stray field issues.

## Key findings

- Reaction cross sections follow a classical Langevin model.
- Collision energies as low as 10 K were achieved.
- Rydberg electron acts as a spectator, not affecting the reaction.

## Abstract

Studies of ion-molecule reactions at low temperatures are difficult because stray electric fields in the reaction volume affect the kinetic energy of charged reaction partners. We describe a new experimental approach to study ion-molecule reactions at low temperatures and present, as example, a measurement of the ${\rm H}_2^+ + {\rm H}_2\rightarrow {\rm H}_3^+ + {\rm H}$ reaction with the ${\rm H}_2^+$ ion prepared in a single rovibrational state at collision energies in the range $E_{\rm col}/k_{\rm B} = 5$-60 K. To reach such low collision energies, we use a merged-beam approach and observe the reaction within the orbit of a Rydberg electron, which shields the ions from stray fields. The first beam is a supersonic beam of pure ground-state H$_2$ molecules and the second is a supersonic beam of H$_2$ molecules excited to Rydberg-Stark states of principal quantum number $n$ selected in the range 20-40. Initially, the two beams propagate along axes separated by an angle of 10$^\circ$. To merge the two beams, the Rydberg molecules in the latter beam are deflected using a surface-electrode Rydberg-Stark deflector. The collision energies of the merged beams are determined by measuring the velocity distributions of the two beams and they are adjusted by changing the temperature of the pulsed valve used to generate the ground-state ${\rm H}_2$ beam and by adapting the electric-potential functions to the electrodes of the deflector. The collision energy is varied down to below $E_{\rm col}/k_{\rm B}= 10$ K, i.e., below $E_{\rm col}\approx 1$ meV, with an energy resolution of 100 $\mu$eV. We demonstrate that the Rydberg electron acts as a spectator and does not affect the cross sections, which are found to closely follow a classical-Langevin-capture model in the collision-energy range investigated. Because all neutral atoms and molecules can be excited to Rydberg states, this method of studying