Three-body calculation of the rate of reaction $p+p+e\to d+{\nu }_e$ in the Sun

Using expansion of the three-body wave function of the $pep$ system in the initial state on hyperharmonic functions, the rate of the $p+p+e^{-} \rightarrow d+\nu_e$ reaction in the Sun is calculated. The results of calculation of the flux at 1 AU are compared with the results of a measurement made by the Borexino collaboration and Bahcall $\mathit{\text{et}}\mathit{\text{al.}}$ theoretical predictions.