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Communications in Theoretical Physics

High Energy Scattering Theory and Collective Coordinate

Zhang Yu-shun, Yang-Guo Li, Wang Wei-wei, Ruan Tu-Nan

Published Mar 1, 1982• 0 citations
Publisher

Abstract

In this paper, by the collective coordinate of A. Bohr, the scattering amplitudes of two composite many-particle systems can be obtained. And the collective excitation for two complex many-particle systems in the scattering process is discussed.
DOI
10.1088/0253-6102/1/2/147

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Based on the composite particle representation presented in the last paper (I), a method of solving the many-body problem known as the composite particle approximation is proposed. It is shown that a many-body system can be simplified to a composite particle system (plus one or more uncorrelated basic particles if any existed) if the following conditions are satisfied: 1) the binding energies of the composite particles are much larger than the excitation energies of the system; 2) there is domination of the collective mode for the composite particles. The interactions between the composite particles, as well as the interactions between composite particles and the basic particles can be evaluated from the original particle-particle interactions. Applications of this theory are indicated.
In the textbooks of elementary quantum mechanics, two-particle scattering is treated by introducing the concept of off-the-energy shell scattering amplitude. On the other hand, in relativistic quantum field theory, the need to treat momentum and energy on the same footing forces one to use an off-the-mass shell scattering amplitude. We believe the introducing the off-the-mass shell extrapolation of the scattering amplitude in nonrelativistic quantum mechanics should be illuminating. We try to show this in this paper.
Motivated by realistic scattering processes of composite systems, we study the dynamics of a two-particle bound system which is scattered at a mirror. We consider two different scenarios: In the first case we assume that only one particle interacts directly with the mirror whereas in the second case both particles are scattered. The coherence between the transmitted and the reflected wave packet is reduced when the internal degree of freedom (the relative coordinate) of the bound system becomes excited. Depending on the particular system-mirror interaction, long-lived resonances can occur.