We present a new accurate analysis of the ${}^3\mathrm{He}(p,e^{+}{\nu }_e){}^4\mathrm{He}$ (“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 energy is $S\left(0\right)=(8.7\pm 0.9)\times {10}^{-20}$ 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 ${}^3\mathrm{He}(n,\gamma ){}^4\mathrm{He}$ (“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.

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• Effective field theory
• Few-body systems
• H & He burning
• Nuclear astrophysics
• Nuclear reaction rates
• Nuclear reactions
• S-factor
• Solar neutrinos
• A ≤ 5
• Hyperspherical method