天体物理热核函数
Astrophysical thermonuclear functions
摘要：
恒星是引力稳定的聚变反应堆，在将轻原子核转变为重原子核的同时，改变它们的化学成分。原子核应该与周围的等离子体处于热平衡。大多数导致核转变的原子核之间的反应都受到带电参与者穿越相互库仑势垒的必要性的抑制。随着核截面理论知识和实验验证的增加，使核反应速率的解析表示法的改进成为可能。多年来，人们采用了各种方法来推导热核反应速率的封闭形式表示（Critchfield 1972，Haubold and John 1978，Haubold，Mathai and Anderson 1987）。它们表明，反应率包含的天体物理截面因子及其衍生物，这是必须确定的实验，热核反应率的一个组成部分，独立于实验结果，可以处理的封闭形式的表示技术的广义超几何函数。本文将总结推导热核函数封闭形式表示的数学/统计技术，并给出数值结果。从热核反应速率分离热核函数是我们的首选结果。本文的目的也是比较数值结果近似和封闭形式的热核函数表示。本文完成了Haubold、Mathai和Anderson（1987）的工作。
英文摘要：
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/statistical techniques for deriving closed-form representations of thermonuclear functions 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).
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