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]

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

Here, η is the dimensionless Sommerfeld parameter,

$\eta \equiv \frac{Z_1 Z_2 e^2}{4 \pi \epsilon_0 \hbar v}$

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.