The Quantum Mechanical Three-Body Problem

Book Reviews particles are non-relativistic, then with the help of Faddeev’s theory such systems csn be solved in some way exactly, if the forces are not of infinite range. This book is an excellent introduction to this theory and its applications. The authors describe in detail much numerical work, and discuss the difficulties therein and how they can be handled. This book is a10 easy to read for students and experimental physicists. In the Introduction, the authors show that the three-body problem in nuclear physics is of special interest, because it yields information about the neutronneutron interaction and the off-shell behaviour of nuclear forces. Besides these, the problem of the off-shell electromagnetic form factors of nucleons can be investigated and also the simplest bound state of hypernuclei is a three-body system. There exists already also a wealth of experimental information from scattering processes. If the target is a deuteron, protons, neutrons, pions and kaons can be scattered and measurements of the crosssections and polarization parameters can be made in the elastic and break-up channel. On the other side, deuteron scattering and pick-up reactions with nuclei can be investigated with the help of the Faddeev theory. In the first chapter, the basic concepts are introduced and the Faddeev equations for the T-matrix, the resolvent, the scattering states and the transition operators are derived. Then the partial wave decomposition of the Faddeev equation is studied. After a

Vol. 301, No. 3, March 1976

short review of the theory of integral equations, the application of this theory to the solution of Faddeev equations is investigated. The next chapter deals with separable potentials and the numerical solution of the Faddeev equations for these potentials. Another approach in the theory of integral equations can be applied if the potentials are not separable and is known as the “quasi particle method”. Application of this method to the Faddeev equations leads to the Alt-Grassberger-Sandhas equations, and again practical calculations are given in detail. Then the technique of Pade approximation is explained and applied to the solution of integral equations and especially of Faddeev equations. The final topic is a comparison with variational methods and the possible combination of this method with the Faddeev approach. More than 100 references are listed, mainly the most important work in the field. In reference 3 the authors make a remark about the difficulties which arise, if in the three-body system in addition the long range Coulomb force is present. Indeed, this gives rise to many problems for practical calculations. Therefore the community of physicists would appreciate, if the authors add to this excellent book a second volume, dealing especially with those problems.

Institut Physik

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H. ZINGL Theoretiache

der Universittit Graz, Austria

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