# Calculation of resonance energies from Q-values

## TL;DR

This paper highlights the importance of accounting for electron binding energy differences when calculating resonance energies from Q-values, as neglecting this can significantly affect thermonuclear reaction rate estimates in stellar environments.

## Contribution

It introduces a correction method for resonance energy calculations that considers electron binding energy differences, improving accuracy in stellar plasma conditions.

## Key findings

- Neglecting electron binding energy differences can lead to ~40% overestimation of reaction rates.
- The correction is significant at temperatures below 1 GK, especially around 70 MK.
- Applying the correction alters the predicted reaction rates in stellar nucleosynthesis models.

## Abstract

Resonance energies are frequently derived from precisely measured excitation energies and reaction Q-values. The latter quantities are usually calculated from atomic instead of nuclear mass differences. This procedure disregards the energy shift caused by the difference in the total electron binding energies before and after the interaction. Assuming that the interacting nuclei in a stellar plasma are fully ionized, this energy shift can have a significant effect, considering that the resonance energy enters exponentially into the expression for the narrow-resonance thermonuclear reaction rates. As an example, the rate of the $^{36}$Ar(p,$\gamma$)$^{37}$K reaction is discussed, which, at temperatures below 1 GK, depends only on the contributions of a single resonance and direct capture. In this case, disregarding the energy shift caused by the total electron binding energy difference erroneously enhances the rate by $\approx$40\% near temperatures of 70 MK.