S-factor

In nuclear physics, the astrophysical S-factor $S(E)$ is a rescaling of a nuclear reaction's total cross section $σ(E)$ to account for the Coulomb repulsion between the charged reactants. It determines the rates of nuclear fusion reactions that occur in the cores of stars.

Definition
The quantity is defined as


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

where $E$ is the energy, $σ$ is the cross section, $η$ is the dimensionless Sommerfeld parameter:


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

$Z_{1} Z_{2} e^{2}$ is the product of the charges of the reactants, $$\epsilon_0$$ is the permittivity of free space, $$\hbar$$ is the reduced Planck constant and $v$ is 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.