The Electron-Screening Correction for the Proton-Proton Reaction

We test the Salpeter formalism for calculating electron screening of nuclear fusion reactions by solving numerically the relevant Schrodinger equation for the fundamental proton-proton reaction. We evaluate exactly the square of the overlap integral of the two-proton wave function and the deuteron wave function and compare with the usual analytic approximation. The usual WKB solution agrees with the numerical solution to $O(10^{-4})$.