Analytic Representation of the Overlap Integral of Three Wave Functions of Nucleus Scattering in a Coulomb Field

Based on the formalism of integral representations of hypergeometric-type functions, we find two ways to describe the Coulomb decay of light weakly bound atomic nuclei on heavy multiple-charge nuclei. In the first way, the overlap integral containing the product of three wave functions of scattering of nuclei in the Coulomb field is expanded into a double hypergeometric-type series in products of two Gauss hypergeometric functions. The series is convergent, at least if the three-particle kinematic relations are satisfied. In the second way, the same overlap integral reduces to a single contour integral containing the Gauss hypergeometric function and two additional binomial functions.