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In [[nuclear physics]], the [[astrophysical]] '''S-factor''' {{math|''S''(''E'')}} is a rescaling of a [[nuclear reaction]]'s total [[cross section (physics)|cross section]] {{math|''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 [[star]]s.

== Definition ==

The quantity is defined as<ref>{{cite book |last1=Thompson |first1=Ian J. |last2=Nunes |first2=Filomena M.|author2-link=Filomena Nunes |date=2009 |title=Nuclear Reactions for Astrophysics: Principles, Calculations and Applications of Low-Energy Reactions. |publisher=[[Cambridge University Press]] |page=5 |isbn=978-0-521-85635-5 }}</ref>

: <math>S(E) \equiv \frac{E}{\exp(-2 \pi \eta)} \sigma(E)</math>,

where {{mvar|E}} is the energy, {{mvar|σ}} is the cross section, {{mvar|η}} is the dimensionless [[Sommerfeld parameter]]:

: <math>\eta \equiv \frac{Z_1 Z_2 e^2}{4 \pi \epsilon_0 \hbar v}</math>,

{{math|''Z''<sub>1</sub> ''Z''<sub>2</sub> ''e''<sup>2</sup>}} is the product of the [[electric charge|charge]]s of the reactants, <math>\epsilon_0</math> is the [[permittivity of free space]], <math>\hbar</math> is the [[reduced Planck constant]] and {{mvar|v}} is the relative incident [[velocity]].

== Motivation ==
{{see also|Gamow factor}}
The Coulomb barrier causes the cross section to have a strong exponential dependence on the center-of-mass energy {{math|''E''}}. The S-factor remedies this by factoring out the Coulomb component of the cross section.

== References ==

{{reflist}}

[[Category:Concepts in astrophysics]]
[[Category:Equations of astronomy]]
[[Category:Nuclear physics]]