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Formulas of fusion cross sections

The Naval Research Lab's plasma physics formulary gives the total cross section in barns as a function of the energy (in keV) of the incident particle towards a target ion at rest fit by the formula:

Bosch-Hale also reports a R-matrix calculated cross sections fitting observation data with Padé rational approximating coefficients. With energy in units of keV and cross sections in units of millibarn, the factor has the form:

where σ Bosch-Hale (ϵ) = S Bosch-Hale (ϵ) ϵ exp (ϵ G / ϵ) {\displaystyle \sigma ^{\text{Bosch-Hale}}(\epsilon)={\frac {S^{\text{Bosch-Hale}}(\epsilon)}{\epsilon \exp(\epsilon _{G}/{\sqrt {\epsilon }})}}}