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Birkhäuser Basel eBooks

New Channels of Scattering for Long-Range Potential

Dimitri R. Yafaev

Published Jan 1, 1995• 0 citations
Publisher

Abstract

We consider a system of three one-dimensional particles with one of pair potentials V α ( x α ) decaying at infinity as \( |{{x}^{\alpha }}{{|}^{{ - \rho }}},0 < \rho < 1/2 \) . It is shown that such a system can possess channels of scattering not included in the usual list of channels called the asymptotic completeness. Similar channels arise in a two-body system with a long-range potential if a traditional condition on its derivatives is relaxed. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/978-3-0348-9092-2_44

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We consider a system of three one-dimensional particles with one of pair potentials V α ( x α ) decaying at infinity as ( |{{x}^{\alpha }}{{|}^{{ - \rho }}},0 < \rho < 1/2 ) . It is shown that such a system can possess channels of scattering not included in the usual list of channels called the asymptotic completeness. Similar channels arise in a two-body system with a long-range potential if a traditional condition on its derivatives is relaxed. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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