  The experimental result of the solar neutrino flux at one AU produced by the
$p+p+e \rightarrow d+\nu_e$ reaction (\textit{pep}) was announced for the first
time in 2012 by the Borexino collaboration. This neutrino flux was
significantly greater than the flux predicted by Bahcall and May, who used two
body approaches for calculation of this reaction. We have used the three-body
model for the proton-proton-electron system in the continuous spectrum of
energy to determine the rate of the \textit{pep} reaction and have estimated
the neutrino flux. Our result of the neutrino flux is 25-40\% more than the
Bachall \textit{et al.} value and depends on the shape of nucleon-nucleon
($NN$) potential. Moreover, the calculated flux lies within the confidence
interval of the experimental data in the case of pure attractive potentials as
well as potential having repulsion at small distances between nucleons.
