The J-Matrix Method Developments and Applications - Alhaidari, Abdulaziz D.; Yamani, Hashim A.; Heller, Eric J.; Abdelmonem, Mohamed S.; SpringerLink (Online service) (Dordrecht : Springer Netherlands, 2008)
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.
Two of the Original Papers -- New L2 Approach to Quantum Scattering: Theory -- J-Matrix Method: Extensions to Arbitrary Angular Momentum and to Coulomb Scattering -- Theoretical and Mathematical Considerations -- Oscillator Basis in the J-Matrix Method: Convergence of Expansions, Asymptotics of Expansion Coefficients and Boundary Conditions -- Scattering Phase Shift for Relativistic Separable Potentials with Laguerre-Type Form Factors -- Accurate Evaluation of the S-Matrix for Multi-Channel Analytic and Non-Analytic Potentials in Complex L2 Bases -- J-Matrix and Isolated States -- On the Regularization in J-Matrix Methods -- Applications in Atomic Physics -- The J-Matrix Method: A Universal Approach to Description of Ionization of Atoms -- J-Matrix Green's Operators and Solving Faddeev Integral Equations for Coulombic Systems -- The Use of a Complex Scaling Method to Calculate Resonance Partial Widths -- Applications in Nuclear Physics -- J-Matrix Approach to Loosely-Bound Three-Body Nuclear Systems -- Nucleon-Nucleon Interaction in the J-Matrix Inverse Scattering Approach and Few-Nucleon Systems -- The Modified J-Matrix Approach for Cluster Descriptions of Light Nuclei -- Other Related Methods: Chemical Physics Application -- A Generalized Formulation of Density Functional Theory with Auxiliary Basis Sets.
Keywords: PHYSICS; MATRIX THEORY; QUANTUM THEORY; NUCLEAR PHYSICS; PHYSICS; NUCLEAR PHYSICS, HEAVY IONS, HADRONS; QUANTUM PHYSICS; LINEAR AND MULTILINEAR ALGEBRAS, MATRIX THEORY