Reexamination of Astrophysical Resonance Reaction Rate Equations for An Isolated, Narrow Resonance

TL;DR

This paper critically reexamines the classical equations used to calculate astrophysical reaction rates for narrow resonances, revealing limitations and integration issues that impact stellar evolution models and nucleosynthesis calculations.

Contribution

It identifies the conditions under which traditional narrow resonance reaction rate equations are valid and uncovers hidden integration issues, suggesting these equations should be used cautiously.

Findings

Classical reaction rate equations are only valid under specific circumstances.

A hidden integration-range issue affects the accuracy of these equations.

Implications for stellar evolution and nucleosynthesis calculations at low temperatures.

Abstract

The well-known astrophysical resonant reaction rate equations for an isolated narrow resonance have been reexamined. The validity of those `look reliable' assumptions used in deriving the analytic reaction rate equations has been checked, and the reality is they only hold for certain circumstances. Importantly an integration-range issue hidden in the classical integration equations has been revealed and it hints us not to use those analytic equations in the future. This work may influence all those work in which the classical narrow resonant equations were used for calculating the stellar reaction rates, especially at low stellar temperatures, and may affect the results of stellar evolution and nucleosynthesis network calculations considerably.