Abstract
The present paper which represents the fourth part of the series devoted to analysis of a simple Lee-type model of two-particle decay deals with three problems. The first one concerns relation of the model to the scattering theory. We prove asymptotic completeness for the elastic scattering of the two light particles and show that for a sufficiently weak coupling this system has just one resonance whose position is the same as that of the pole which yield the main contribution to the decay law. The second problem concerns spectral concentration; we prove its occurrence for families of intervals aroundE that shrink slower than quadratically ing. Finally, necessary and sufficient conditions for the existence of bound states are discussed.
Similar content being viewed by others
References
Dittrich J., Exner P.: Czech. J. Phys. B37 (1987) 503.
Dittrich J., Exner P.: Czech. J. Phys. B37 (1987) 1028.
Dittrich J., Exner P.: Czech. J. Phys. B38 (1988) 591.
Reed M., Simon B.: Methods of Modern Mathematical Physics, III. Scattering Theory. Academic Press, New York, 1979.
Amrein W. O., Jauch J. M., Sinha K. B.: Scattering Theory in Quantum Mechanics. Benjamin, Reading, 1977.
Akhiezer N. I., Glazman I. M.: The Theory of Linear Operator sin Hilbert Space. Nauka, Moscow, 1966; § 106 (in Russian).
Wollenberg M.: Math. Nachr.78 (1977) 223.
Tabakin F.: Phys. Rev.174 (1968) 1208.
We do not reproduce the full list of references from the preceding parts of the paper. Here we have referred to
Reed M., Simon B.: Methods of Modern Mathematical Physics, I. Functional Analysis, IV. Analysis of Operators. Academic Press, New York, 1972, 1978.
Author information
Authors and Affiliations
Additional information
The authors are indebted to Dr. M. Sotona for Remark 5.7.
Rights and permissions
About this article
Cite this article
Dittrich, J., Exner, P. A non-relativistic model of two-particle decay IV. Relation to the scattering theory, spectral concentration, and bound states. Czech J Phys 39, 121–138 (1989). https://doi.org/10.1007/BF01597321
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01597321