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Title: Resonance positions and lifetimes for flexible complex absorbing potentials

Abstract

By adding any complex absorbing potential (CAP) -i{lambda}V(r-vector) to a system Hamiltonian, the corresponding complex eigenvalues are analytical functions of {lambda},E{sub j}({lambda}). It is shown here that for a quite general flexible class of CAP's the real part of lim{sub {lambda}}{sub /0}E{sub j}({lambda}) provides the resonance energy. The imaginary part of that limit is the resonance width (i.e., inverse lifetime) in spite of the fact that Im E{sub j}(0)=0. The need for the Pade approximation within this approach is explained. Application to an illustrative numerical test case model Hamiltonian is given. This method could open a gate for studying systems that could not be studied until now due to the complexity of the numerical computations. In particular, one may in this way obtain resonance energies by a modification, in a straightforward simple manner, of the widely used conventional methods that were developed for the calculations of bound states.

Authors:
; ;  [1]
  1. Department of Chemistry and Minerva Center of Nonlinear Physics in Complex Systems, Technion--Israel Institute of Technology, Haifa 32000 (Israel)
Publication Date:
OSTI Identifier:
20786507
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.052704; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUND STATE; EIGENFUNCTIONS; EIGENVALUES; HAMILTONIANS; LIFETIME; PADE APPROXIMATION; POTENTIALS; RESONANCE; SCHROEDINGER EQUATION; VECTORS

Citation Formats

Lefebvre, Roland, Sindelka, Milan, and Moiseyev, Nimrod. Resonance positions and lifetimes for flexible complex absorbing potentials. United States: N. p., 2005. Web. doi:10.1103/PHYSREVA.72.0.
Lefebvre, Roland, Sindelka, Milan, & Moiseyev, Nimrod. Resonance positions and lifetimes for flexible complex absorbing potentials. United States. doi:10.1103/PHYSREVA.72.0.
Lefebvre, Roland, Sindelka, Milan, and Moiseyev, Nimrod. Tue . "Resonance positions and lifetimes for flexible complex absorbing potentials". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786507,
title = {Resonance positions and lifetimes for flexible complex absorbing potentials},
author = {Lefebvre, Roland and Sindelka, Milan and Moiseyev, Nimrod},
abstractNote = {By adding any complex absorbing potential (CAP) -i{lambda}V(r-vector) to a system Hamiltonian, the corresponding complex eigenvalues are analytical functions of {lambda},E{sub j}({lambda}). It is shown here that for a quite general flexible class of CAP's the real part of lim{sub {lambda}}{sub /0}E{sub j}({lambda}) provides the resonance energy. The imaginary part of that limit is the resonance width (i.e., inverse lifetime) in spite of the fact that Im E{sub j}(0)=0. The need for the Pade approximation within this approach is explained. Application to an illustrative numerical test case model Hamiltonian is given. This method could open a gate for studying systems that could not be studied until now due to the complexity of the numerical computations. In particular, one may in this way obtain resonance energies by a modification, in a straightforward simple manner, of the widely used conventional methods that were developed for the calculations of bound states.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 5,
volume = 72,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}