Effects of ion and electron screening on thermonuclear reaction rates

The effects of screening by ions and electrons on thermonuclear reaction rates in stellar plasmas are considered. The enhancement of the reaction rate ranges from negligible to extremely large (on the order of 1026 or greater). In order to calculate these effects, the potential about a given reacting nucleus is determined. First, Boltzmann-Vlasov and Poisson-Boltzmann equations are solved to yield a Yukawa potential. A suitable approximation to this potential is integrated in the action integral to give the barrier penetration. The screened reaction rate is then found by the saddle-point method. In developing a general formalism to calculate the screened reaction rate and the screening factor, effects due to the finite size of the nucleus are considered and found to be negligible. An expression for the screening factor for resonant reaction rates is also derived. A different and relatively simple approach, based on work of Stewart and Pyatt (1966), is used to find the barrier penetration from the action integral in two approximations: a modified Coulomb potential and a constant-shift potential. Screening factors are calculated for carbon burning at T6 = 100 and T6 = 400 for a wide range of densities and also for several examples in late stellar evolution. These screening factors are, for the most part, greater than those given by most others by a few percent at low density to 4 or more orders of magnitude at T6 = 100 and rho = 1010 g/cm3. Near the edge of the crystalline lattice region, however, they are significantly lower than those of some others. The increase in reaction rates for carbon burning indicates that carbon ignition may occur at lower densities than previously thought and may affect the density at which a supernova shock may occur