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Resonances — Models and Phenomena pp 64–77Cite as

On the shape resonance

  • II Mathematical Framework
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Part of the book series: Lecture Notes in Physics ((LNP,volume 211))

Abstract

We computed poles of the S-matrix as the poles of some expectation values of the resolvent through a perturbation by a Dirichlet boundary condition. They are exponentially close to the real axis. Our results are valid if k is small (large masses, quasiclassical regime).

The perturbation theory is based upon the equation rч = r Dч + πч.

The resonant energies are given in terms of a convergent power series expansion in the tunneling parameter t. This parameter is exponentially small in k−2.

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Author information

Authors and Affiliations

  1. Université de Toulon et du Var and Centre de Physique Théorique, CNRS, Marseille Cedex 9, France

    J. M. Combes & P. Duclos

  2. Fachbereich Mathematik, Technische Universität Berlin, D-1000, Berlin 12

    R. Seiler

Authors
  1. J. M. Combes
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  2. P. Duclos
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  3. R. Seiler
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Editor information

S. Albeverio L. S. Ferreira L. Streit

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© 1984 Springer-Verlag

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Combes, J.M., Duclos, P., Seiler, R. (1984). On the shape resonance. In: Albeverio, S., Ferreira, L.S., Streit, L. (eds) Resonances — Models and Phenomena. Lecture Notes in Physics, vol 211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13880-3_66

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  • DOI: https://doi.org/10.1007/3-540-13880-3_66

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13880-8

  • Online ISBN: 978-3-540-39077-0

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