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Regge poles and Mandelstam representation in potential scattering; Poles de regge et representation de Mandelstam en theorie du potentiel

Abstract

We deal with the scattering of two spinless particles interacting by a superposition of Yukawa potentials. We first obtain an upper bound for the scattering amplitude for simultaneous complex values of energy and angular momentum. We then show that the Regge poles remain confined in small domains of the complex angular momentum plane, we study the variation of these domains when the energy (complex) varies. These first results allow us to deduce an upper bound for the double spectral function, this upper bound is used to rigorously show that the Schroedinger equation implies the Mandelstam representation for the type of potentials we deal with. Finally, the problem of subtractions is entirely solved, showing that the Mellin transform of the double spectral function can be analytically continued into the different simple spectral functions. (author) [French] On traite de la diffusion de deux particules sans spin interagissant par l'intermediaire d'une superposition de potentiels de Yukawa. Nous obtenons tout d'abord une majorante pour l'amplitude de diffusion pour des valeurs simultanement complexes de l'energie et du moment cinetique. On montre alors que les Poles de Regge restent confines dans des domaines restreints du plan complexe du moment cinetique, domaines dont nous etudions la variation  More>>
Authors:
Bessis, D [1] 
  1. Commissariat a l'Energie Atomique, Saclay (France). Centre d'Etudes Nucleaires
Publication Date:
Mar 01, 1965
Product Type:
Thesis/Dissertation
Report Number:
CEA-R-2753
Resource Relation:
Other Information: TH: These ES sciences physiques; 26 refs
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MANDELSTAM REPRESENTATION; MELLIN TRANSFORM; POTENTIAL SCATTERING; REGGE POLES; SCHROEDINGER EQUATION; YUKAWA POTENTIAL
OSTI ID:
20680235
Research Organizations:
CEA Saclay, 91 - Gif-sur-Yvette (France); Faculte des Sciences de l'Universite de Paris, 75 (France)
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR05R2753115125
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
130 pages
Announcement Date:
Jan 07, 2006

Citation Formats

Bessis, D. Regge poles and Mandelstam representation in potential scattering; Poles de regge et representation de Mandelstam en theorie du potentiel. France: N. p., 1965. Web.
Bessis, D. Regge poles and Mandelstam representation in potential scattering; Poles de regge et representation de Mandelstam en theorie du potentiel. France.
Bessis, D. 1965. "Regge poles and Mandelstam representation in potential scattering; Poles de regge et representation de Mandelstam en theorie du potentiel." France.
@misc{etde_20680235,
title = {Regge poles and Mandelstam representation in potential scattering; Poles de regge et representation de Mandelstam en theorie du potentiel}
author = {Bessis, D}
abstractNote = {We deal with the scattering of two spinless particles interacting by a superposition of Yukawa potentials. We first obtain an upper bound for the scattering amplitude for simultaneous complex values of energy and angular momentum. We then show that the Regge poles remain confined in small domains of the complex angular momentum plane, we study the variation of these domains when the energy (complex) varies. These first results allow us to deduce an upper bound for the double spectral function, this upper bound is used to rigorously show that the Schroedinger equation implies the Mandelstam representation for the type of potentials we deal with. Finally, the problem of subtractions is entirely solved, showing that the Mellin transform of the double spectral function can be analytically continued into the different simple spectral functions. (author) [French] On traite de la diffusion de deux particules sans spin interagissant par l'intermediaire d'une superposition de potentiels de Yukawa. Nous obtenons tout d'abord une majorante pour l'amplitude de diffusion pour des valeurs simultanement complexes de l'energie et du moment cinetique. On montre alors que les Poles de Regge restent confines dans des domaines restreints du plan complexe du moment cinetique, domaines dont nous etudions la variation pour des valeurs complexes de l'energie. Ces premiers resultats nous permettent alors de deduire une majorante pour la fonction spectrale double, majorante qui est utilisee pour demontrer rigoureusement que l'equation de Schroedinger implique la representation de Mandelstam pour la classe des potentiels envisages. Enfin le probleme des soustractions est entierement resolu, en montrant que la transformee de Mellin de la fonction spectrale double se prolonge analytiquement dans les diverses fonctions spectrales simples. (auteur)}
place = {France}
year = {1965}
month = {Mar}
}