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The Three-Body Problem

  • Conference paper
Elementary Particle Physics

Part of the book series: Acta Physica Austriaca ((FEWBODY,volume 9/1972))

Abstract

The quantum mechanical three-body problem has been studied with increasing interest in the last decade. The main progress was achieved by deriving integral equations which are not only theoretically correct, but also practically applicable. Such equations allow us in particular to investigate, besides three-body bound states, the scattering of an elementary particle from a bound two-particle system.

Lecture given at XI. Internationale Universitätswochen für Kernphysik, Schladming, February 21 – March 4, 1972.

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References and Footnotes

  1. Formal scattering theory is explained in several well known text books. Original papers, where the single-channel case is extended to multichannel problems, are: H. Ekstein, Phys. Rev. 101, 880 (1956); Nuovo Cim. 4, 1017 (1956);

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  71. This is discussed in detail by W. Sandhas, loc. cit. (Ref. 9). Here also the relation to the “weak convergence method” of axiomatic field theory (see Ref. 43) is established.

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  72. In this way also a treatment of the four-(and even of the n-) body problem becomes possible, without starting from four-body integral equations with connected kernels. Incorporating step by step the dominant two-and three-body subsystem properties, by means of separable terms, we directly arrive at effective two-particle equations also in the four-body case: P. Grassberger and W. Sandhas, Nucl. Phys. B2, 181 (1967); Zeitschr. f. Physik 217, 9 (1968). Practical applications of this approach are given in E. O. Alt, P. Grassberger and W. Sandhas, Phys. Rev. Cl, 85 (1970). For a short description see Ref. 26.

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  1. Institut für Physik, Universität Mainz, Germany

    W. Sandhas

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  1. W. Sandhas
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  1. Vorstand des Institutes für Theoretische Physik, Universität Graz, Graz, Austria

    Paul Urban

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Sandhas, W. (1972). The Three-Body Problem. In: Urban, P. (eds) Elementary Particle Physics. Acta Physica Austriaca, vol 9/1972. Springer, Vienna. https://doi.org/10.1007/978-3-7091-4034-5_3

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  • DOI: https://doi.org/10.1007/978-3-7091-4034-5_3

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