S-factor

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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 {{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 stars.

Definition

The quantity is defined as{{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 }}

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

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

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

{{math|Z1 Z2 e2}} is the product of the charges of the reactants, \epsilon_0 is the permittivity of free space, \hbar 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