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Calculable methods for many-body scattering

R. F. Barrett, B. A. Robson*, and W. Tobocman

R. F. Barrett

  • Department of Physics, The University of Western Australia, Nedlands, W.A., 6009, Australia

B. A. Robson*

  • Research School of Physical Sciences, The Australian National University, Canberra, A.C.T. 2600, Australia and Sektion Physik, Universität München, 8046 Garching, West Germany

W. Tobocman

  • Physics Department, Case Western Reserve University, University Circle, Cleveland, Ohio 44106

  • *Permanent address: Research School of Physical Sciences, The Australian National University, Canberra, A.C.T., 2600, Australia.
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Rev. Mod. Phys. 55, 155 – Published 1 January, 1983Erratum Rev. Mod. Phys. 56, 567 (1984)

DOI: https://doi.org/10.1103/RevModPhys.55.155

Abstract

The review consists of two major parts. In the first part, several calculable R-matrix and related theories are described and discussed. These include the Kapur-Peierls, Wigner-Eisenbud, calculable standard R-matrix, extended R-matrix, finite-element, natural boundary condition, and variational methods. The various approaches are critically compared using four selected applications: (i) exactly soluble model using two coupled square-well potentials, (ii) elastic scattering of neutrons from C12, (iii) elastic scattering of electrons from He atoms, and (iv) α−α elastic scattering. In the second part, the Baer, Kouri, Levin, and Tobocman many-body scattering theory is reviewed. The principal results of the theory are derived, and a survey of calculations applying the theory is presented. The derivation is carried out in the context of the R-matrix method wherein the many-body scattering is treated ab initio as a steady-state process. This has the advantage that the channel states form a complete orthogonal set. These same channel states are used to provide explicit representations of the partition Green's-function operators.

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Erratum

Erratum: Calculable methods for many-body scattering

R. F. Barrett, B. A. Robson, and W. Tobocman
Rev. Mod. Phys. 56, 567 (1984)

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Rev. Mod. Phys. 55, 155– Published 1 January, 1983

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