Calculation of resonance energies from Q-values

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.