Nuclear Reaction Rates at High Densities

Abstract

In this paper we calculate general expressions which are suitable for use in numerical stellar-interior calculations for nuclear reaction rates. We consider the density-temperature combinations which are called the weak-screening, strong-screening, and pycnonuclear regimes. Except in the pycnonuclear case we express our results in the form of "correction factors" with which one multiplies the ordinary thermo- nuclear reaction rate evaluated at the same temperature and density. By considering the extreme cases of Z1 = Z2 and Z1 >> Z2, where Z1 and Z2 are the atomic numbers of the two reacting nuclei, we are able to devise interpolation formulae which are valid for any ratio of charges Z1/Z2 throughout the entire weak- and strong-screening regimes. We also discuss strong-screening corrections to resonant nuclear reaction rates, and we give an explicit formula for the important special case of the triple-alpha reaction. Finally, by applying our results to the case of the proton chain, we show that the hydrogen abundance in the white dwarf Sirius B must be less than 3.5 X 1O~