The astrophysical factor for the proton weak capture on ^ { 3 } He is calculated with correlated-hyperspherical-harmonics bound and continuum wave functions corresponding to a realistic Hamiltonian consisting of the Argonne v _ { 18 } two-nucleon and Urbana-IX three-nucleon interactions .
The nuclear weak charge and current operators have vector and axial-vector components , that include one- and many-body terms .
All possible multipole transitions connecting any of the p ^ { 3 } He S- and P-wave channels to the ^ { 4 } He bound state are considered .
The S -factor at a p ^ { 3 } He center-of-mass energy of 10 keV , close to the Gamow-peak energy , is predicted to be 10.1 \times 10 ^ { -20 } keV b , a factor of five larger than the standard-solar-model value .
The P-wave transitions are found to be important , contributing about 40 % of the calculated S -factor .