On resonant thermonuclear reaction rate integrals‐ closed‐form evaluation and approximation considerations

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Abstract
The central problem in the theory of stellar nucleosynthesis (and in reaction theory of controlled thermonuclear fusion as well) is the determination of thermonuclear reaction rates. Continuing our preceding paper on closed‐form evaluation of nonresonant reaction rate integral (HAUBOLD and JOHN 1978) now we consider a general thermonuclear reaction rate integral involving the full BREIT‐WIGNER resonance cross section. Discerning between two cases – energy‐independent partial widths and energy‐dependent partial width – we evaluate the arising parameter‐dependent integrals in closed form by means of MEIJER's G‐functions of one and two variables. At next, by using the BUNJAKOVSKIJ‐SCHWARZ inequality we derive global upper bounds for thermonuclear reaction rate integrals with arbitrary admissible values of input parameters. Finally, in case of great values of the characteristic parameter COULOMB barrier energy divided by thermal energy we give an asymptotic representation of the general resonant reaction rate integral.

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