Abstract
The modified Newton-Sabatier method is extended to the inverse scattering problem for coupled channels at fixed energy. The coupled Schrödinger equations are assumed to depend on a potential matrix which couples the channels. This potential matrix is taken as independent on the angular coordinates of the relative motion. In order to test the inversion method it is applied to analytic S-matrices corresponding to potential matrices consisting of square well potentials. The scattered particles can be neutral or charged. In the latter case the S-matrix with the asymptotic Coulomb potential is transformed to the S-matrix with an asymptotic constant potential and then the inverse scattering problem for neutral particles is solved.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Chadan K. and Sabatier P.C. (1989): Inverse Problems in Quantum Scattering Theory ( 2nd Edition, Springer-Verlag, New York )
Cox J.R. (1967): On the determination of the many-channel potential matrix and S-matrix from a single function. Journ.Math.Phys. 8, 12, 2327
Eberspächer M. (1996): Das Modifizierte Newton-Sabatier-Verfahren für das Inverse Streuproblem bei gekoppelten Kanälen. Diploma thesis, Gießen
Lovas R.G. (1972): Solution of coupled square well models. Atomki Közlemenyek 14, 3, 161
May K.E., Münchow M. and Scheid W. (1984): The modified Newton method for the solution of the inverse scattering problem with charged particles at fixed energy. Phys.Lett. 141, 1
Münchow M. and Scheid W. (1980): Modification of the Newton Method for the Inverse-Scattering Problem at Fixed Energy. Phys.Rev.Lett 44, 1299
Newton R.G. (1962): Construction of potentials from the phase shifts at fixed energy. Journ. Math. Phys. 3, 75
Newton R.G. (1982): Scattering Theory of Waves and Particles ( 2nd Edition, Springer Verlag, New York )
Sabatier P.C. (1966): Asymptotic Properties of the Potentials in The Inverse-Scattering Problem at Fixed Energy. Journ.Math.Phys. 7, 1515
Satchler G.R. (1983): Direct Nuclear Reactions (Oxford University Press, New York)
Zakhariev B.N. and Suzko A.A. (1990): Direct and Inverse Problems ( Springer Verlag, Berlin )
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Eberspächer, M., Apagyi, B., Scheid, W. (1997). The Inverse Scattering Problem for Coupled Channels with the Modified Newton-Sabatier Method. In: Apagyi, B., Endrédi, G., Lévay, P. (eds) Inverse and Algebraic Quantum Scattering Theory. Lecture Notes in Physics, vol 488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-14145-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-662-14145-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-14147-2
Online ISBN: 978-3-662-14145-8
eBook Packages: Springer Book Archive