# Cross-damping effects in 1S-3S spectroscopy of hydrogen and deuterium

## TL;DR

This paper calculates the cross-damping frequency shift in 1S-3S hydrogen and deuterium spectroscopy, finding it to be below 1 kHz, which is negligible compared to current measurement uncertainties.

## Contribution

It introduces a method to estimate cross-damping shifts in two-photon spectroscopy by adapting Raman scattering analogy, applied specifically to hydrogen and deuterium.

## Key findings

- Frequency shift estimated to be less than 1 kHz.
- Shift is smaller than current statistical uncertainties.
- Method can be used for precise spectroscopic measurements.

## Abstract

We calculate the cross-damping frequency shift of a laser-induced two-photon transition monitored through decay fluorescence, by adapting the analogy with Raman scattering developed by Amaro et al. [P. Amaro et al., PRA 92, 022514 (2015)]. We apply this method to estimate the frequency shift of the 1S-3S transition in hydrogen and deuterium. Taking into account our experimental conditions, we find a frequency shift of less than 1 kHz, that is smaller than our current statistical uncertainty.