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Title: Numerical calculation of supercritical Dirac resonance parameters by analytic continuation methods

Abstract

The spectrum of the Dirac equation for hydrogenlike systems with extended nuclei becomes complicated when the nuclear charge exceeds a critical value Z{approx_equal}170, since the lowest bound state becomes a resonance in the negative energy continuum. We address the problem of computing the resonance parameters by extending the mapped Fourier grid method to incorporate either complex scaling of the radial coordinate, or alternatively a complex absorbing potential. The method is tested on the case of quasimolecular collisions in the monopole approximation.

Authors:
;  [1]
  1. Department of Physics and Astronomy, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3 (Canada)
Publication Date:
OSTI Identifier:
20982107
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.022508; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; ATOMIC NUMBER; BOUND STATE; COLLISIONS; COMPUTER CALCULATIONS; DIRAC EQUATION; MONOPOLES; NUMERICAL ANALYSIS; POTENTIALS; RESONANCE; SCALING

Citation Formats

Ackad, Edward, and Horbatsch, Marko. Numerical calculation of supercritical Dirac resonance parameters by analytic continuation methods. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.022508.
Ackad, Edward, & Horbatsch, Marko. Numerical calculation of supercritical Dirac resonance parameters by analytic continuation methods. United States. doi:10.1103/PHYSREVA.75.022508.
Ackad, Edward, and Horbatsch, Marko. Thu . "Numerical calculation of supercritical Dirac resonance parameters by analytic continuation methods". United States. doi:10.1103/PHYSREVA.75.022508.
@article{osti_20982107,
title = {Numerical calculation of supercritical Dirac resonance parameters by analytic continuation methods},
author = {Ackad, Edward and Horbatsch, Marko},
abstractNote = {The spectrum of the Dirac equation for hydrogenlike systems with extended nuclei becomes complicated when the nuclear charge exceeds a critical value Z{approx_equal}170, since the lowest bound state becomes a resonance in the negative energy continuum. We address the problem of computing the resonance parameters by extending the mapped Fourier grid method to incorporate either complex scaling of the radial coordinate, or alternatively a complex absorbing potential. The method is tested on the case of quasimolecular collisions in the monopole approximation.},
doi = {10.1103/PHYSREVA.75.022508},
journal = {Physical Review. A},
number = 2,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
  • The analytic continuation methods of complex scaling (CS), smooth exterior scaling (SES), and complex absorbing potential (CAP) are investigated for the supercritical quasimolecular ground state in the U{sup 92+}-Cf{sup 98+} system at an internuclear separation of R=20 fm. Pade approximants to the complex-energy trajectories are used to perform an extrapolation of the resonance energies, which, thus, become independent of the respective stabilization parameter. Within the monopole approximation to the two-center potential is demonstrated that the extrapolated results from SES and CAP are consistent to a high degree of accuracy. Extrapolated CAP calculations are extended to include dipole and quadrupole termsmore » of the potential for a large range of internuclear separations R. These terms cause a broadening of the widths at the per mille level when the nuclei are almost in contact, and at the % level for R values where the 1S{sigma} state enters the negative continuum.« less
  • Previous work [E. Ackad and M. Horbatsch, Phys. Rev. A 78, 062711 (2008)] on supercritical Dirac resonance parameters from extrapolated analytic continuation, obtained with a Fourier grid method, is generalized by numerically solving the coupled Dirac radial equations to a high precision. The equations, which contain the multipole decomposition of the two-center potential, are augmented by a complex absorbing potential and truncated at various orders in the partial wave expansion to demonstrate convergence of the resonance parameters in the limit of vanishing absorber. The convergence of the partial-wave spinor and of the multipole potential expansions is demonstrated in the supercriticalmore » regime. The comparison of critical distances with literature values shows that the work provides benchmark results for future two-center calculations without multipole expansion.« less
  • The numerical solving of certain singular boundary value problems of quantum mechanics and quantum field theory by using a common computational approach, which is briefly exposed, is considered. One simple problem, which arose in the theory of composite hadrons, is investigated in detail. Using this problem as a typical example one formulates a method of analytic continuation of the numerical solution defined on the real axis into the whole complex plane.
  • We propose a new approach to the dynamics of systems of several particles, based on analytic continuation in the coupling constant by the use of Pade approximants of the second kind. In the present paper this approach is used to construct a theory of resonant states in nuclei by means of analytic continuation in the coupling constant of the attractive part of the interaction. A technique for finding the parameters of resonances is described; these include the energies, widths, and wave functions of Gamow states and the corresponding quantities for antibound (virtual) states of real and complex Hamiltonians. The samemore » technique of analytic extrapolation is used to calculate matrix elements involving resonance wave functions. It is shown that this theory leads to a procedure for regularizing resonance matrix elements which is exactly equivalent in its result to the well known Zel'dovich regularization but is much simpler than that method in practice. The possibility is discussed of applying this formalism to a shell model with two particles in the continuum and to the theory of many-particle resonances.« less
  • We suggest a method of finding an analytic function which has an imaginary part directly related to the e/sup +/e/sup -/ annihilation data and which leads to the determination of Wilson-operator-product-expansion coefficients of vector-current-current correlation functions.