S-factor

In nuclear physics, the astrophysical S-factor Template:Math is a rescaling of a nuclear reaction's total cross section Template:Math 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 Template:Mvar is the energy, Template:Mvar is the cross section, Template:Mvar is the dimensionless Sommerfeld parameter:

$\eta \equiv \frac{Z_1{Z}_2{e}^2}{4\pi {ϵ}_0\hslash v}$,

Template:Math is the product of the charges of the reactants, ${ϵ}_0$ is the permittivity of free space, $\hslash$ is the reduced Planck constant and Template:Mvar is the relative incident velocity.

Motivation

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