# Importance of nonresonant corrections for the description of atomic spectra

## TL;DR

This paper highlights the significance of nonresonant corrections in atomic spectra measurements, showing that at high precision, transition frequencies become ambiguous due to asymmetric line profiles influenced by experimental conditions.

## Contribution

It provides closed-form expressions for atomic photon scattering cross sections including all quantum numbers, emphasizing the impact of nonresonant corrections on frequency determination.

## Key findings

- Transition frequencies can be non-uniquely defined at high measurement accuracy.
- Nonresonant corrections cause spectral line asymmetry affecting frequency extraction.
- Expressions for scattering cross sections depend on experimental setup and quantum states.

## Abstract

We demonstrate that the present superaccurate measurements of transition processes between atomic states in hydrogen atom reached the limit of accuracy when transition frequency cannot be defined anymore in a unique way. This was predicted earlier and is due to the necessity to include the nonresonant corrections in the description of resonant processes. The observed spectral line profile becomes asymmetric, and it becomes impossible to extract the value of transition frequency from this profile in a unique way. Nonresonant corrections depend on the type of experiment and on the experimental arrangement. However, the line profile itself for any resonant process can be defined with any desired level of accuracy. A popular trend in modern search for atomic frequency standards and atomic clocks is the search for transitions where the nonresonant corrections are negligible. In this paper we present closed expressions for the resonant photon scattering cross sections on an atomic level with dependence on all atomic quantum numbers including fine and hyperfine structure. These expressions are given for different types of experiments with fixing of the incident (outgoing) photon propagation directions and incident (outgoing) photon polarization. Using these expressions we demonstrate that the transition frequencies in particular cases cannot be derived uniquely if the accuracy of measurement reaches the level quoted in A. Beyer {\it et al}. Our interpretation of the results of this experiment is alternative to the interpretation given by A. Beyer {\it et al}.