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On-shell T-matrices in multiple scattering
Institution:1. Helsinki Institute of Physics, University of Helsinki, 00014 University of Helsinki, Finland;2. Department of Physics, University of Jyväskylä, 40014 University of Jyväskylä, Finland;3. GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt 64291, Germany;1. Programa de Pós Graduação em Engenharia Mecânica, UFMG, Brazil;2. Centro Universitário UNA, Brazil;3. Laboratório de Termometria – LabTerm, Departamento de Engenharia Mecânica da UFMG, Brazil;1. Hunan Province Cooperative Innovation Center for Molecular Target New Drug Study, Institute of Pharmacy and Pharmacology, University of South China, Hengyang 421001, China;2. CAS Key Laboratory of Receptor Research, CAS Center for Excellence in Molecular Cell Science, Center for Biotherapeutics Discovery Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, Shanghai 201203, China;3. University of Chinese Academy of Sciences, Beijing 100049, China;1. Research Institute of the University of Bucharest (ICUB), 050663 Bucharest, Romania;2. Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering, 077126 Magurele-Ilfov, Romania;3. University of Bucharest, Faculty of Physics, Materials and Devices for Electronics and Optoelectronics Research Center, 077125 Magurele-Ilfov, Romania;4. University of Bucharest, Faculty of Physics, Doctoral School of Physics, 077125 Magurele-Ilfov, Romania;1. Department of Physics and Geology, University of Perugia, I.N.F.N. Sezione di Perugia, Via Pascoli, I-06123 Perugia, Italy;2. Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, V6T 1Z1, Canada;1. Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, 730000, People’s Republic of China;2. KEK Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), 1-1, Oho, Tsukuba, Ibaraki 305-0801, Japan
Abstract:The transition operator T for the scattering of a particle from N potentials Vj(x) can be expanded into a series featuring the transition operators tj associated with the individual potentials. For Vj(x) both absolutely and square integrable in x, we show, using an analytic continuation argument, that if T is on-shell, i.e. in 〈k|T(k02±i0)|k′〉, |k| = |k′| = k0, then each tj is also on-shell.
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