S-factor

In nuclear physics, the astrophysicalS-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^[1]

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.

References

^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.

[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.

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