Abstract
In the past decade it has become possible to solve certain three-body problems with strong interactions between pairs. In most cases, the essential trick has been to reduce the number of coordinates needed to specify intermediate states by the use of separable interactions; calculations of n-d scattering and breakup, and of d-α scattering using separable two-body potentials have been remarkably successful [5.1]. In this chapter we extend such methods to the relativistic domain, deriving and applying equations of the type first proposed by BLANKENBECLER and SUGAR [5.2], and by FREEDMAN et al. [5.3]. Because of difficulties in formulation and practical application we shall not discuss more general approaches to relativistic three-body equations such as that of ALESSANDRINI and OMNES [5.4]. In our relativistic theory we assume that the two-body interactions are dominated by a few bound states or resonances (isobars.) and write down linear integral equations for the scattering amplitudes which include Lorentz invariance, two- and three-body unitarity and the cluster property. In essence, the result is an isobar model which incorporates unitarity and a significant amount of analyticity. Such a formalism may be applied, for example, to the πN and KN systems below ~1 GeV where single pion production is the dominant inelastic process and we are thus dealing mostly with three-body final states. Also, the two-body systems (πN, ππ, and Kπ) are dominated by low-lying elastic resonances [a(1236), p, e, K*] and hence the two-body subsystems entering the three-body calculation can be described by separable interactions.
Supported in part by National Science Foundation grant MPS71–03134A04.
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Aaron, R. (1977). A Relativistic Three-Body Theory. In: Thomas, A.W. (eds) Modern Three-Hadron Physics. Topics in Current Physics, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81070-1_5
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DOI: https://doi.org/10.1007/978-3-642-81070-1_5
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