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On the direct inversion of total scattering cross sections in the glory region

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  • Mason, E.A.
  • van den Meijdenberg, C.J.N.

Abstract

The total scattering cross section as a function of velocity in the glory region can be accurately described semiclassically as the sum of an average part and an undulating part. In practice the velocity dependence of the average cross section is complicated because of contributions from different dispersion terms in the attractive part of the potential and eventually from repulsive terms as well. It is shown that the average cross section can be accurately retrieved from the data, without the assumption of a mathematical model for the potential, and that the retrieved values can be directly inverted to numerical values of the potential tail. The separated results for the undulating part yield numerical values for five of the usual glory parameters. The procedure is tested on simulated total cross section data showing several full glory oscillations, and the glory parameters and potential tail are reproduced to accuracies consistent with the graphical-numerical methods employed.

Suggested Citation

  • Mason, E.A. & van den Meijdenberg, C.J.N., 1983. "On the direct inversion of total scattering cross sections in the glory region," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 117(1), pages 139-159.
    • Handle: RePEc:eee:phsmap:v:117:y:1983:i:1:p:139-159
    DOI: 10.1016/0378-4371(83)90026-2
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    1. Borchardt Knut & Münnich Frank E. & Andel Norbert & Bohnet Michael & Hemmer Hans-Rimbert & Wagner Adolf & Bordiardt Knut & Born Karl Erich, 1970. "Einzelbesprechungen Hans-Rimbert Hemmer," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 184(6), pages 557-568, May.
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    1. Mason, E.A. & Hermans, R.M. & Van Den Meijdenberg, C.J.N., 1983. "On the direct inversion of total scattering cross sections beyond the glory region," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 117(1), pages 160-170.
    2. van den Biesen, J.J.H. & van den Meijdenberg, C.J.N., 1982. "Relation between total cross section data and the interaction potential; A comparison with closely connected data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 115(3), pages 375-395.
    3. Mason, E.A. & Nyeland, C. & Van Den Biesen, J.J.H. & Van Den Meijdenberg, C.J.N., 1982. "Improved calculation of total scattering cross sections in the glory region," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(1), pages 133-154.

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