Near Threshold Proton-Proton Fusion in Effective Field Theory

TL;DR

This paper calculates the proton-proton fusion S-factor near threshold using pionless effective field theory, providing precise derivatives and confirming consistency with current values, with implications for solar fusion rates.

Contribution

It introduces an analytical calculation of the S-factor and its derivatives up to second order in pionless EFT, including the first calculation of the second energy derivative.

Findings

Calculated S_11(0) and S'_11(0) consistent with current values

First-time calculation of the second energy derivative S''_11(0)

Second derivative contributes less than 1% to solar fusion rate

Abstract

The astrophysical S-factor for proton-proton fusion, S_11(E), is obtained with the nuclear matrix element analytically calculated in pionless effective field theory. To the third order, the zero-energy result S_11(0) and the first energy derivative S'_11(0) are found to be (3.99 \pm 0.14)* 10^-25 MeV b and S_11(0)*(11.3 \pm 0.1) MeV^-1, respectively; both consistent with the current adopted values. The second energy derivative is also calculated for the first time, and the result S"_11(0) = S_11(0)*(170 \pm 2) MeV^-2 contributes at the level of 0.5% to the fusion rate at the solar center, which is smaller than 1% as previously estimated.