The enhancement factor to the thermonuclear reaction rate in the center of the Sun is calculated using the Feynman-Kac path integral of the grand-canonical partition function. Using the generalized virial expansion for a multicomponent quantum plasma, we have calculated the truncated pair distribution function for solar conditions up to the order ρ5/2 in density. The enhancement factor is calculated for the p - p channel. This result extends the well-known Salpeter calculation of the enhancement factor in the classical limit and exhibits the various classical and quantum corrections beyond the Debye-Hückel screening correction. In this issue, it comes out that quantum corrective terms related to the statistics are the leading corrections beyond the Salpeter's result. Indeed, this result can induce significant changes in the prediction of solar neutrino deficit.