# S-factor

The astrophysical S-factor S(E) is a rescaled variant of the total cross section σ(E) that accounts for the Coulomb repulsion between charged reactants.

## Definition

The quantity is defined as[1]

${\displaystyle S(E)\equiv {\frac {E}{\exp(-2\pi \eta )}}\sigma (E)}$

Here, η is the dimensionless Sommerfeld parameter,

${\displaystyle \eta \equiv {\frac {Z_{1}Z_{2}e^{2}}{4\pi \epsilon _{0}\hbar v}}}$

where

• Z1 Z2 e2 is the product of the charges of the reactants and
• v is the magnitude of the relative incident velocity.

## Motivation

The Coulomb barrier causes the cross section to have a strong exponential dependence on the center-of-mass energy E. The S-factor remedies this by factoring out the Coulomb component of the cross section.

## References

1. ^ Thompson, Ian J.; Nunes, Filomena M. (2009). Nuclear Reactions for Astrophysics: Principles, Calculations and Applications of Low-Energy Reactions. Cambridge University Press. p. 5. ISBN 978-0-521-85635-5.