# Pressure Shifts in High-Precision Hydrogen Spectroscopy: II. Impact Approximation and Monte-Carlo Simulations

## TL;DR

This paper analyzes collisional frequency shifts in high-precision hydrogen spectroscopy, using impact approximation and Monte-Carlo simulations to evaluate intra-beam and background gas effects, with implications for current and future experiments.

## Contribution

It provides a detailed assessment of pressure-induced spectral line shifts in hydrogen, including numerical data and simulation methods for experimental conditions.

## Key findings

- Intra-beam collisional shifts are negligible (~10 Hz) in the Garching experiment.
- Monte-Carlo simulations effectively model the impact of experimental geometry.
- Pressure shifts can vary significantly with experimental conditions.

## Abstract

We investigate collisional shifts of spectral lines involving excited hydrogenic states, where van der Waals coefficients have recently been shown to have large numerical values when expressed in atomic units. Particular emphasis is laid on the recent hydrogen 2S-4P experiment (and an ongoing 2S-6P experiment) in Garching, but numerical input data are provided for other transitions (e.g., involving S states), as well. We show that the frequency shifts can be described, to sufficient accuracy, in the impact approximation. The pressure related effects were separated into two parts, (i) related to collisions of atoms inside of the beam, and (ii) related to collisions of the atoms in the atomic beam with the residual background gas. The latter contains both atomic as well as molecular hydrogen. The dominant effect of intra-beam collisions is evaluated by a Monte-Carlo simulation, taking the geometry of the experimental apparatus into account. While, in the Garching experiment, the collisional shift is on the order of 10 Hz, and thus negligible, it can decisively depend on the experimental conditions. We present input data which can be used in order to describe the effect for other transitions of current and planned experimental interest.