THE RATE OF THE PROTON-PROTON REACTION

We reevaluate the nuclear matrix element for the proton-proton reactio n p + p -> H-2 + e(+) + v(e), which is important for stellar-evolution calculations referring to stars with masses less than or similar to 1 M. and for the solar-neutrino problem. We self-consistently determine the effect of vacuum polarization on the matrix element by first corr ecting the low-energy scattering data to account for vacuum polarizati on. We then calculate the proton-proton wave function by integrating t he Schrodinger equation with vacuum polarization included. We use impr oved data for proton-proton scattering and for the deuteron wave funct ion. We evaluate the uncertainties that are due to experimental error and estimate those that are due to theoretical inadequacies. Without v acuum polarization, we find that the square of the overlap integral is Lambda(2) = 6.96 with an uncertainty of 0.2% due to errors in the exp erimental parameters and an uncertainty of 1% due to lack of knowledge of the shape of the nuclear potentials. We estimate the theoretical u ncertainty by using six different deuteron potentials and five differe nt proton-proton potentials. Vacuum polarization decreases the calcula ted value by 0.6(-0.4)(+0.1)%. The complete result is Lambda(2) = 6.92 x (1 +/- 0.002(-0.009)(+0.014)) where the first uncertainty is due to experimental errors and the second uncertainty is due to theoretical uncertainties. Our value of Lambda(2) is 2% smaller than the value obt ained in 1969 by Bahcall & May, The improved calculations of the rate of the pp reaction described here increase slightly the predicted even t rates for the chlorine and the Kamiokande solar-neutrino experiments .