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A new dispersion (asymptotic) theory is proposed for the peripheral sub- andabove-barrier charged particle transfer $A(x,y)B$ reaction in the three-body($A$, $a$ and $y$) model where $ x= y +a$ and $B=A+a$, and $ a$ is atransferred particle. It is based on the combination of the dispersion theoryand the conventional DWBA method. The explicit forms have been derived for theexact three-body pole amplitude and differential cross section in which thecontribution of the three-body ($A$, $a$ and $y$) Coulomb dynamics of thetransfer mechanism in the peripheral partial amplitudes, corresponding topartial waves with $l_i>>1$, is taken into account correctly. For the specificperipheral proton and triton transfer reactions, the comparative analysis ofthe peripheral partial amplitudes at $l_i>>1$ , which correspond to theone-step pole and exact three-body pole amplitudes as well as those of the"post"-approximation and the post form of the conventional DWBA, is performedwith each other. It shows the absolute inapplicability of the"post"-approximation usually applied for getting an information about specificasymptotic normalization coefficients being astrophysical interest.

Dispersion (asymptotic) theory of charged particle transfer reactions at low energies and nuclear astrophysics: I. the "non-dramatic" case