# Introduction to ill-posed aspects of nuclear scattering

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## Abstract

This pedagogical survey is presented following a suggestion of the Workshop Committee. It is tried to present in a simple way the main ill-posed aspects of inverse problems arising in nuclear scattering. One also explains on some examples how they are dealt with or how they are circumvented.

## Keywords

Inverse Problem Inverse Scattering Born Approximation Compressive Mapping Fixed Energy
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## References

- (1).For more details, and references, see K. Chadan & P.C. Sabatier “Inverse Problems in Quantum Scattering Theory” Springer-Verlag, New York Heidelberg Berlin 1977.Google Scholar
- (2).Ref (1) page 146 and ff.Google Scholar
- (3).Ref (1) page 64Google Scholar
- (4)a.For recent references on the three-dimensional inverse problem see R.G. Newton “The Marchenko and Gel'fand Levitan Methods in the Inverse Scattering Problem in one and three dimensions” in “Conference on Inverse Scattering: Theory and Application” J. Bee Bednar et al. ed. SIAM Philadelphia (1983) and (same author)Google Scholar
- (4)b.A Faddeev — Marchenko method for Inverse Scattering in three dimensions. Inverse Problems 2 (1985). A study of the ill-posed aspects of the inverse problem at fixed energy in the class of truncated potentials by Y. Loubatières will be published soon.Google Scholar
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- (7).See for example P.E. Hodgson: Nuclear Reactions and Nuclear Structure — Clarenton Press, Oxford, 1971. For a recent monograph on applications of inversion theory, particulary in nuclear scattering, see Zachariev B.N. and Suzko A.A. “Potentials and quantum scattering direct and inverse problems”, to be published by Energoatomisdat (Moscow) in 1985).Google Scholar
- (8).A recent example is given by A.A. Ioannides and R.S. Mackintosh: A method for S-matrix to Potential Inversion at Fixed Energy. Nucl. Phys. A 438, 354 (1985).Google Scholar
- (9).For a review and references see: P.C. Sabatier: “Rational Reflection Coefficients in One-Dimensional Inverse Scattering and Applications. In “Conference on Inverse Scattering: Theory and Application” J. Bee Bednar et al. eds. SIAM, Philadelphia 1983.Google Scholar
- (10)a.R. Lipperheide and H. Fiedeldey: Inverse Problem for Potential Scattering at fixed Energy I: Z. Phys. A 286, 45–46 (1978) and id. II: Z. Phys. A 301, 81–89 (1981). R. Lipperheide, S. Sofianos and H. Fiedeldey Potential Inversion for scattering at fixed energy: Phys. Rev. C 26, 770–772 (1982).Google Scholar
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^{2}, E, plane). Phys. Scripts 29, 515–517, (1984).Google Scholar - (11).A. Erdelyi, W. Magnus, F. Oberhettinger, F.G. Tricomi: Higher transcendental functions. Mac Graw Hill Ed. 1953.Google Scholar

## Copyright information

© Springer-Verlag 1985