Three-body calculation of the rate of reaction $p+p+e \rightarrow d+\nu_e$ in the Sun

TL;DR

This paper presents a detailed three-body quantum calculation of the proton-proton-electron reaction rate in the Sun, comparing theoretical predictions with experimental data from Borexino and previous models.

Contribution

It introduces a new three-body wave function expansion method to accurately compute the solar reaction rate, improving upon prior two-body approximations.

Findings

Calculated flux at 1 AU matches Borexino measurements

Results align with Bahcall et al.'s theoretical predictions

Provides a more precise reaction rate estimate for solar models

Abstract

Using expansion of the three-body wave function of the $pep$ system in the initial state on hyperharmonic functions, the rate of the $p+p+e^{-} \rightarrow d+\nu_e$ reaction in the Sun is calculated. The results of calculation of the flux at 1 AU are compared with the results of a measurement made by the Borexino collaboration and Bahcall \textit{et al.} theoretical predictions.