Analytic Representation of the Overlap Integral of Three Wave Functions of Nucleus Scattering in a Coulomb Field |
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Authors: | A P Il'in |
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Institution: | (1) Institute for Nuclear Research, Kiev, Ukraine |
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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.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 2, pp. 311–328, November, 2005. |
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Keywords: | Coulomb decay integral representations contour integrals hypergeometric functions |
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