The J-Matrix Method: Developments and Applications / Edition 1

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More About This Textbook


This volume aims to provide the fundamental knowledge to appreciate the advantages of the J-matrix method and to encourage its use and further development. The J-matrix method is an algebraic method of quantum scattering with substantial success in atomic and nuclear physics. The accuracy and convergence property of the method compares favourably with other successful scattering calculation methods. Despite its thirty-year long history new applications are being found for the J-matrix method.

This book gives a brief account of the recent developments and some selected applications of the method in atomic and nuclear physics. New findings are reported in which experimental results are compared to theoretical calculations. Modifications, improvements and extensions of the method are discussed using the language of the J-matrix.

The volume starts with a Foreword by the two co-founders of the method, E.J. Heller and H.A. Yamani and it contains contributions from 24 prominent international researchers.

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Product Details

  • ISBN-13: 9789048175277
  • Publisher: Springer Netherlands
  • Publication date: 11/25/2010
  • Edition description: Softcover reprint of hardcover 1st ed. 2008
  • Edition number: 1
  • Pages: 356
  • Product dimensions: 0.78 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

1: Two of the Original Papers. 1.1. New L2 approach to quantum scattering: Theory; E.J. Heller and H.A. Yamani. 1.2. J-matrix method: Extensions to arbitrary angular momentum and to Coulomb scattering; H.A. Yamani and L. Fishman.
2: Theoretical and Mathematical Considerations. 2.1: Oscillator basis in the J-matrix method: convergence of expansions, asymptotic of expansion coefficients and boundary conditions; S.Yu. Igashov. 2.2. Scattering phase shift for relativistic separable potential with Laguerre-type form factors; A.D. Alhaidari. 2.3. Accurate evaluation of the S-matrix for multi-channel analytic and non-analytic poetentials in complex L2 bases; H.A. Yamani and M.S. Abdelmonem. 2.4. J-matrix and isolated states; A.M. Shirokov and S.A. Zaytsev. 2.5. On the regularization in J-matrix methods; J. Broeckhove, V.S. Vasilevsky, F. Arickx and A.M. Sythcheva.
3: Applications in Atomic Physics. 3.1. The J-matrix method: a universial approach for the description of the process of ionization of atoms; V.A. Knyr, V.V. Nasyrov, Yu.V. Popov and S.A. Zaytsev. 3.2. Coulomb-Sturmian separable expansion approach to the Faddeev-type integral equations of the three-body Coulomb problem; Z. Papp. 3.3. The use of complex scaling method to calculate resonance partial widths; H.A. Yamani and M.S. Abdelmonem.
4: Applications in Nuclear Physics. 4.1. J-matrix approach to loosely-bound three-body nuclear systems; Yu.A. Lurie and A.M. Shirokov. 4.2. Nucleon-nucleon interaction in the J-matrix inverse scattering approach and few-nucleon systems; A.M. Shirokov, S.A. Zaytsev, A.I. Mazur, J.P. Vary and T.A. Weber. 4.3. The modified J-matrix approach for cluster descriptions of light nuclei; F. Arickx, J. Broeckhove, A. Nesterov, V. Vasilevsky and W. Vanroose.
5: Other Related Methods: Chemical Physics Application. 5.1. A generalized formulation of density functional theory with auxiliary basis sets; B.G. Johnson and D.A. Holder

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