Astrophysical S-factors for fusion reactions involving C, O, Ne and Mg isotopes

TL;DR

This paper provides comprehensive calculations and parameterizations of astrophysical S-factors for 946 fusion reactions involving C, O, Ne, and Mg isotopes, aiding stellar nucleosynthesis modeling.

Contribution

It introduces a universal 9-parameter analytic expression for S(E) and provides fit parameters for a wide range of fusion reactions involving key isotopes.

Findings

Accurate S(E) parameterizations for 946 fusion reactions.

A simplified 3-parameter fit effective below the Coulomb barrier.

Procedures for converting S(E) into reaction rates for astrophysical applications.

Abstract

Using the Sao Paulo potential and the barrier penetration formalism we have calculated the astrophysical factor S(E) for 946 fusion reactions involving stable and neutron-rich isotopes of C, O, Ne, and Mg for center-of-mass energies E varying from 2 MeV to 18-30 MeV (covering the range below and above the Coulomb barrier). We have parameterized the energy dependence S(E) by an accurate universal 9-parameter analytic expression and present tables of fit parameters for all the reactions. We also discuss the reduced 3-parameter version of our fit which is highly accurate at energies below the Coulomb barrier, and outline the procedure for calculating the reaction rates. The results can be easily converted to thermonuclear or pycnonuclear reaction rates to simulate various nuclear burning phenomena, in particular, stellar burning at high temperatures and nucleosynthesis in high density environments.