The astrophysical factor for the proton weak capture on ${}^3\mathrm{He}$ is calculated with correlated hyperspherical harmonic wave functions corresponding to a realistic Hamiltonian consisting of the Argonne $v_{18}$ two-nucleon and Urbana-IX three-nucleon interactions. The nuclear weak current has vector and axial-vector components with one- and many-body terms. All possible transitions connecting any of the $p{}^3\mathrm{He}$ $S$- and $P$-wave channels to ${}^4\mathrm{He}$ are considered. The $S$ factor at a $p{}^3\mathrm{He}$ center-of-mass energy of $10\mathrm{keV}$ is predicted to be $10.1\times {10}^{-20\mathrm{}}\mathrm{keV}\mathrm{b}$, a factor of $\simeq 4.5$ larger than the value adopted in the standard solar model. The $P$-wave transitions are found to contribute about $40\%$ of the calculated $S$ factor.

• Received 29 March 2000

DOI:https://doi.org/10.1103/PhysRevLett.84.5959