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

The theory of intermediate screening is developed from the cluster expansion for the screening function. This systematic perturabation technique is used to extend weak-screening theory analytically to higher order in the scrcening parameters, and is solved numerically to yield screening-function 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, H12(0) xf(z/sub i/) LAMBDA /sub 12/ sup b/, where b=0.860. This result is found to be equivalent to the general screening function presented in Paper I. The new screening thceory is studied in relation to various astrophysical situations. Three areas are found where screen~ng 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. (auth)