Geodesic
Analytic Representation of the Overlap Integral of Three Wave Functions of Nucleus Scattering in a~Coulomb Field
Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 2, pp. 311-328

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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.
Mots-clés : Coulomb decay
Keywords: integral representations, contour integrals, hypergeometric functions. 
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     author = {A. P. Il'in},
     title = {Analytic {Representation} of the {Overlap} {Integral} of {Three} {Wave} {Functions} of {Nucleus} {Scattering} in {a~Coulomb} {Field}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {311--328},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2006_146_2_a6/}
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A. P. Il'in. Analytic Representation of the Overlap Integral of Three Wave Functions of Nucleus Scattering in a~Coulomb Field. Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 2, pp. 311-328. http://geodesic.mathdoc.fr/item/TMF_2006_146_2_a6/