A new analysis of the "hep" S-factor and the "hen" cross section

TL;DR

This paper presents a precise theoretical analysis of the hep reaction's S-factor at astrophysical energies using advanced nuclear models and chiral effective field theory, including uncertainty quantification.

Contribution

It introduces a state-of-the-art computational approach for the hep S-factor and assesses theoretical uncertainties, improving the accuracy of astrophysical reaction rates.

Findings

Recommended hep S(0) value: (8.7 ± 0.9) × 10^{-20} keV b

The energy spectrum of outgoing hep positrons provided for future measurements

Validation of the model through successful reproduction of the hen reaction cross section

Abstract

We present a new accurate analysis of the $^3$He$(p,e^+\nu_e)$${}^4$He (''hep'') reaction at astrophysical energies. The S-factor is computed using a state-of-the-art method to calculate the four-nucleon scattering and bound-state wave functions (the hyperspherical harmonic expansion), and by using nuclear interactions and accompanying electroweak nuclear currents obtained within the chiral effective field theory framework. Our analysis includes a detailed examination of the theoretical uncertainties coming from two different sources: the truncation of the interaction and current chiral expansions, and the model dependence. Our recommended final theoretical value for the hep S-factor at zero energyis $S(0)=(8.7\pm 0.9)\times 10^{-20}$ keV b. We provide also the energy spectrum of the outgoing hep positrons which may be measured in future experiments. We include also an analysis of the ''sister'' reaction $^3$He$(n,\gamma)$${}^4$He (''hen'') at low energies, showing that the calculation well reproduce the total cross section from thermal energies to few MeV, validating our results on the hep reaction.