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Higher-Order Levinson Theorems and the Planck-Larkin Partition Function for Reacting Plasmas

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Strongly Coupled Plasma Physics

Part of the book series: NATO ASI Series ((ASIB,volume 154))

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Abstract

We review higher-order spectral sum rules in scattering theory for d ≤ 3 dimensions. These rules generalize the well-known Levinson theorem [1] for partial-wave scattering, relating the number of bound states with the value of the scattering phase shift at the threshold energy zero, and they are valid for non-spherically symmetric short-range interactions. They involve the scattering matrix, the bound-state wave functions and some correction terms arising from the high-energy behavior of the scattering problem. These correction terms are shown to be d-dimensional generalizations of the polynomial conserved densities of the Korteweg-de Vries equation [2], [3]. The modifications of these rules necessary to allow Coulomb-type interactions are presented.

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Author information

Authors and Affiliations

  1. Instituut voor Theoretische Fysica, Universiteit Leuven, B-3030, Leuven, Belgium

    D. Bollé (Onderzoeksleider)

  2. N.F.W.O., Belgium

    D. Bollé (Onderzoeksleider)

Authors
  1. D. Bollé
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Editors and Affiliations

  1. Lawrence Livermore National Laboratory, Livermore, California, USA

    Forrest J. Rogers  & Hugh E. Dewitt  & 

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© 1987 Plenum Press, New York

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Bollé, D. (1987). Higher-Order Levinson Theorems and the Planck-Larkin Partition Function for Reacting Plasmas. In: Rogers, F.J., Dewitt, H.E. (eds) Strongly Coupled Plasma Physics. NATO ASI Series, vol 154. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1891-0_21

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  • DOI: https://doi.org/10.1007/978-1-4613-1891-0_21

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-9053-7

  • Online ISBN: 978-1-4613-1891-0

  • eBook Packages: Springer Book Archive

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