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

Abstract

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