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TMF, 2006, Volume 146, Number 2, Pages 311–328 (Mi tmf2037)  

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

A. P. Il'in

Institute for Nuclear Research National Academy of Sciences of Ukraine

Abstract: 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.

Keywords: Coulomb decay, integral representations, contour integrals, hypergeometric functions

DOI: https://doi.org/10.4213/tmf2037

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English version:
Theoretical and Mathematical Physics, 2006, 146:2, 259–274

Bibliographic databases:

Received: 11.01.2005
Revised: 05.09.2005

Citation: A. P. Il'in, “Analytic Representation of the Overlap Integral of Three Wave Functions of Nucleus Scattering in a Coulomb Field”, TMF, 146:2 (2006), 311–328; Theoret. and Math. Phys., 146:2 (2006), 259–274

Citation in format AMSBIB
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