Three-particle Coulomb on-shell vertex functions. Behavior of the amplitude for simultaneous transfer of two charged particles in the vicinity of the nearest singularity in $\cos \theta$

The connection between the on-shell vertex function (OSVF) and the asymptotic normalized coefficient of the three-particle wave function of the bound system in the configuration space is found. The explicit form of the leading singular term of the OSVF and its Faddeev component for decay of the three-particle bound state into three charged particles is established. An expression is found for the leading singular term of the exact (in the model of four charged particles) amplitude of sub-Coulomb binary reactions in the vicinity of the nearest singularity.