Screening Factors for Nuclear Reactions. 11. Intermediate Screen-Ing and Astrophysical Applications

Abstract

The theory of intermediate screening is developed from the cluster expansion for the screening function. This systematic perturbation technique is used to extend weak-screening theory analytically to higher order in the screening parameter, and is solved numerically to yield screeningfunction data for intermediate and strong screening regions. For both the one-component system, equal charge reactions, and the two-component system in the form of 10 mixtures of low-Z elements, the resultant intermediate-screening function is shown to obey a simple power-law dependence on the screening parameter, H13(0) x f(zt)A23b, where b = 0.860. This result is found to be equivalent to the general screening function presented in Paper I. The new screening theory is studied in relation to various astrophysical situations. Three areas are found where screening effects may produce quantitative changes in evolutionary star models: minimum mass limits for H, D, He, C, and 0 main sequences; the structure and extent of flash events in red-giant interiors; and the strength of detonations in degenerate carbon and oxygen cores. This latter case may require screening-factor increases of two orders of magnitude. Subject headings: interiors, stellar - late-type stars - nuclear reactions - plasmas