A simple analytic model for astrophysical S-factors

TL;DR

This paper introduces a simple, physically transparent analytic model for astrophysical S-factors that accurately describes non-resonant fusion reactions across a range of energies, facilitating better extrapolation and understanding of nuclear fusion in astrophysics.

Contribution

The paper presents a new analytic S-factor model with four parameters that can be easily interpolated and used to reconstruct potential barriers, improving predictions for various nuclear reactions.

Findings

Model accurately reproduces S(E) suppression at low energies.

Parameterization of 946 reactions involving isotopes of C, O, Ne, Mg.

Comparison with experimental data for 12C+12C reaction.

Abstract

We propose a physically transparent analytic model of astrophysical S-factors as a function of a center-of-mass energy E of colliding nuclei (below and above the Coulomb barrier) for non-resonant fusion reactions. For any given reaction, the S(E)-model contains four parameters [two of which approximate the barrier potential, U(r)]. They are easily interpolated along many reactions involving isotopes of the same elements; they give accurate practical expressions for S(E) with only several input parameters for many reactions. The model reproduces the suppression of S(E) at low energies (of astrophysical importance) due to the shape of the low-r wing of U(r). The model can be used to reconstruct U(r) from computed or measured S(E). For illustration, we parameterize our recent calculations of S(E) (using the Sao Paulo potential and the barrier penetration formalism) for 946 reactions involving stable and unstable isotopes of C, O, Ne, and Mg (with 9 parameters for all reactions involving many isotopes of the same elements, e.g., C+O). In addition, we analyze astrophysically important 12C+12C reaction, compare theoretical models with experimental data, and discuss the problem of interpolating reliably known S(E) values to low energies (E <= 2-3 MeV).