The J-Matrix Method

1. Front Matter

   Pages I-XVII

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2. Two of the Original Papers

   1. Front Matter

      Pages 1-1

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   2. New L2 Approach to Quantum Scattering: Theory

      • Eric J. Heller, Hashim A. Yamani

      Pages 3-17

   3. J-Matrix Method: Extensions to Arbitrary Angular Momentum and to Coulomb Scattering

      • Hashim A. Yamani, Louis Fishman

      Pages 19-46

3. Theoretical and Mathematical Considerations

   1. Front Matter

      Pages 47-47

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   2. Oscillator Basis in the J-Matrix Method: Convergence of Expansions, Asymptotics of Expansion Coefficients and Boundary Conditions

      • S.Yu. Igashov

      Pages 49-66

   3. Scattering Phase Shift for Relativistic Separable Potentials with Laguerre-Type Form Factors

      • A.D. Alhaidari

      Pages 67-81

   4. Accurate Evaluation of the S-Matrix for Multi-Channel Analytic and Non-Analytic Potentials in Complex L2 Bases

      • H.A. Yamani, M.S. Abdelmonem

      Pages 83-102

   5. J-Matrix and Isolated States

      • A.M. Shirokov, S.A. Zaytsev

      Pages 103-115

   6. On the Regularization in J-Matrix Methods

      • J. Broeckhove, V.S. Vasilevsky, F. Arickx, A.M. Sytcheva

      Pages 117-134

4. Applications in Atomic Physics

   1. Front Matter

      Pages 135-135

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   2. The J-Matrix Method: A Universal Approach to Description of Ionization of Atoms

      • V.A. Knyr, S.A. Zaytsev, Yu.V. Popov, A. Lahmam-Bennani

      Pages 137-143

   3. J-Matrix Green’s Operators and Solving Faddeev Integral Equations for Coulombic Systems

      • Z. Papp

      Pages 145-171

   4. The Use of a Complex Scaling Method to Calculate Resonance Partial Widths

      • H.A. Yamani, M.S. Abdelmonem

      Pages 173-179

5. Applications in Nuclear Physics

   1. Front Matter

      Pages 181-181

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   2. J-Matrix Approach to Loosely-Bound Three-Body Nuclear Systems

      • Yu.A. Lurie, A.M. Shirokov

      Pages 183-217

   3. Nucleon–Nucleon Interaction in the J-Matrix Inverse Scattering Approach and Few-Nucleon Systems

      • A.M. Shirokov, A.I. Mazur, S.A. Zaytsev, J.P. Vary, T.A. Weber

      Pages 219-268

   4. The Modified J-Matrix Approach for Cluster Descriptions of Light Nuclei

      • F. Arickx, J. Broeckhove, A. Nesterov, V. Vasilevsky, W. Vanroose

      Pages 269-307

6. Other Related Methods: Chemical Physics Application

   1. Front Matter

      Pages 309-309

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   2. A Generalized Formulation of Density Functional Theory with Auxiliary Basis Sets

      • Benny G. Johnson, Dale A. Holder

      Pages 311-343

Although introduced30 years ago, the J-matrix method has witnessed a resurgence of interest in the last few years. In fact, the interest never ceased, as some authors have found in this method an effective way of handling the continuous spectrum of scattering operators, in addition to other operators. The motivation behind the introduction of the J-matrix method will be presented in brief. The introduction of fast computing machines enabled theorists to perform cal- lations, although approximate, in a conveniently short period of time. This made it possible to study varied scenarios and models, and the effects that different possible parameters have on the ?nal results of such calculations. The ?rst area of research that bene?ted from this opportunity was the structural calculation of atomic and nuclear systems. The Hamiltonian element of the system was set up as a matrix in a convenient, ?nite, bound-state-like basis. A matrix of larger size resulted in a better con?guration interaction matrix that was subsequently diagonalized. The discrete energy eigenvalues thus obtained approximated the spectrum of the system, while the eigenfunctions approximated the wave function of the resulting discrete state. Structural theorists were delighted because they were able to obtain very accurate values for the lowest energy states of interest.

• J-matrix method
• Matrix
• Potential
• atomic collision
• cluster
• nuclear physics
• numerical regularization
• quantum scattering
• resonance calculation
• scattering
• scattering calculations
• scattering theory
• matrix theory

• Shura Council, Riyadh 11212, Saudi Arabia

  Abdulaziz D. Alhaidari

• Ministry of Commerce&Industry, Riyadh 11127, Saudi Arabia

  Hashim A. Yamani

• Dept. of Chemistry&Physics, Harvard University, Cambridge, USA

  Eric J. Heller

• Dept. of Physics, King Fahd University of Petroleum&Minerals, Dhahran 31261, Saudi Arabia

  Mohamed S. Abdelmonem

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