Astrophysical Thermonuclear Functions

Stars are gravitationally stabilized fusion reactors changing their chemical composition while transforming light atomic nuclei into heavy ones. The atomic nuclei are supposed to be in thermal equilibrium with the ambient plasma. The majority of reactions among nuclei leading to a nuclear transformation are inhibited by the necessity for the charged participants to tunnel through their mutual Coulomb barrier. As theoretical knowledge and experimental verification of nuclear cross sections increases it becomes possible to refine analytic representations for nuclear reaction rates. Over the years various approaches have been made to derive closed-form representations of thermonuclear reaction rates (Critchfield 1972, Haubold and John 1978, Haubold, Mathai and Anderson 1987). They show that the reaction rate contains the astrophysical cross section factor and its derivatives which has to be determined experimentally, and an integral part of the thermonuclear reaction rate independent from experimental results which can be treated by closed-form representation techniques in terms of generalized hypergeometric functions. In this paper mathematical/statisti cal techniques for deriving closed-form representations of thermonuclear functions, particularly the four integrals I1(z, ν) def = ∫ ∞ 0 yee − 1 2 dy, I2(z, d, ν) def = ∫ d 0 yee − 1 2 dy, I3(z, t, ν) def = ∫ ∞ 0 yee − 1 2 dy, I4(z, δ, b, ν) def = ∫ ∞ 0 yee δ e − 1 2 dy, will be summarized and numerical results for them will be given. The separation of thermonuclear functions from thermonuclear reaction rates is our preferred result. The purpose of the paper is also to compare numerical results for approximate and closed-form representations of thermonuclear functions. This paper completes the work of Haubold, Mathai, and Anderson (1987).