ASTROPHYSICAL THERMONUCLEAR FUNCTIONS

Stars are gravitationally stabilized fusion reactors changing their ch emical composition while transforming light atomic nuclei into heavy o nes. 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 charge d participants to tunnel through their mutual Coulomb barrier. As theo retical knowledge and experimental verification of nuclear cross secti ons increases it becomes possible to refine analytic representations f or 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 astroph ysical cross section factor and its derivatives which has to be determ ined experimentally, and an integral part of the thermonuclear reactio n rate independent from experimental results which can be treated by c losed-form representation techniques in terms of generalized hypergeom etric functions. In this paper mathematical/statistical techniques for deriving closed-form representations of thermonuclear functions, part icularly the four integrals I1(z,nu)=def integral-infinity/0 y(nu) e(- y) e(-zy-1/2) dy, I2(z,d,nu)=def integral-infinity/0 y(nu) e(-y) e(-zy -1/2) dy, I3(z,t,nu)=def integral-infinity/0 y(nu) e(-y) e(-y+t)-1/2 d y, I4(z,delta,b,nu)=def integral-infinity/0 y(nu) e(-y) e(-by(delta)) e(-zy-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 a lso to compare numerical results for approximate and closed-form repre sentations of thermonuclear function. This paper completes the work of Haubold, Mathai, and Anderson (1987).