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

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  • Mason, E.A.
  • Hermans, R.M.
  • Van Den Meijdenberg, C.J.N.

Abstract

A method is described for directly inverting measurements of the total scattering cross section at velocities beyond the glory undulations to determine the intermolecular potential, without the use of specific mathematical models for the potential. The only parameter needed is a quantity describing the potential well area, which is accurately obtained from the spacing of the glory undulations. A second quantity obtained from the glory spacings allows the use of relative rather than absolute cross sections. The method is illustrated with simulated cross section data. The results of this paper and the preceding one show that virtually the entire potential curve can in principle be obtained from only relative measurements of the total cross section, without the use of specific models.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:117:y:1983:i:1:p:160-170
    DOI: 10.1016/0378-4371(83)90027-4
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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. & 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.
    2. 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.
    3. 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.

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