Doublebound equivalent of the threebody Coulomb doublecontinuum wave function
Abstract
In crosssection calculations of electron or photon double ionization processes of twoelectron atoms, it is desirable to have a symmetric description of initial and final states. In this contribution, we search the doubly bound analog, for S states, of the wellknown and widely used threebody Coulomb (C3) doublecontinuum wave function. This is performed with two alternative approaches: through an analytic continuation of the C3 continuum and through a 'C3 approach' of the Hylleraas equation for S bound states. The doublebound analog consists of the product of two Coulomb bound states (one for each electronnucleus interaction) multiplied by a Coulomb distortion factor which describes the electronelectron correlation. Our result differs from Pluvinage's wave function which is commonly misbelieved to be the bound counterpart of the C3 double continuum. With a rigorous treatment of the analytic continuation of the distortion factor, the doublebound equivalent of the C3 model is also found. Though the purpose is not to obtain good twoelectron bound states, the found bound wave functions are tested, in the case of helium, through various local and mean quantities which probe different regions of the configuration space, in particular those close to the twoparticle coalescence points.
 Authors:
 Laboratoire de Physique Moleculaire et des Collisions, Universite Paul VerlaineMetz, 57078 Metz (France)
 Departamento de Fisica, Universidad Nacional del Sur and Consejo Nacional de Investigaciones Cientificas y Tecnicas, 8000 Bahia Blanca, Buenos Aires (Argentina)
 Publication Date:
 OSTI Identifier:
 20982326
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032706; (c) 2007 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; ATOMS; BOUND STATE; COALESCENCE; CONFIGURATION; CROSS SECTIONS; ELECTRON CORRELATION; ELECTRONATOM COLLISIONS; ELECTRONS; HELIUM; PHOTOIONIZATION; PHOTONATOM COLLISIONS; PHOTONS; S STATES; THREEBODY PROBLEM; WAVE FUNCTIONS
Citation Formats
Ancarani, L. U., and Gasaneo, G. Doublebound equivalent of the threebody Coulomb doublecontinuum wave function. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.032706.
Ancarani, L. U., & Gasaneo, G. Doublebound equivalent of the threebody Coulomb doublecontinuum wave function. United States. doi:10.1103/PHYSREVA.75.032706.
Ancarani, L. U., and Gasaneo, G. Thu .
"Doublebound equivalent of the threebody Coulomb doublecontinuum wave function". United States.
doi:10.1103/PHYSREVA.75.032706.
@article{osti_20982326,
title = {Doublebound equivalent of the threebody Coulomb doublecontinuum wave function},
author = {Ancarani, L. U. and Gasaneo, G.},
abstractNote = {In crosssection calculations of electron or photon double ionization processes of twoelectron atoms, it is desirable to have a symmetric description of initial and final states. In this contribution, we search the doubly bound analog, for S states, of the wellknown and widely used threebody Coulomb (C3) doublecontinuum wave function. This is performed with two alternative approaches: through an analytic continuation of the C3 continuum and through a 'C3 approach' of the Hylleraas equation for S bound states. The doublebound analog consists of the product of two Coulomb bound states (one for each electronnucleus interaction) multiplied by a Coulomb distortion factor which describes the electronelectron correlation. Our result differs from Pluvinage's wave function which is commonly misbelieved to be the bound counterpart of the C3 double continuum. With a rigorous treatment of the analytic continuation of the distortion factor, the doublebound equivalent of the C3 model is also found. Though the purpose is not to obtain good twoelectron bound states, the found bound wave functions are tested, in the case of helium, through various local and mean quantities which probe different regions of the configuration space, in particular those close to the twoparticle coalescence points.},
doi = {10.1103/PHYSREVA.75.032706},
journal = {Physical Review. A},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}

The asymptotic wave function derived by Alt and Mukhamedzhanov [Phys. Rev. A47, 2004 (1993)] and Mukhamedzhanov and Lieber [Phys. Rev. A54, 3078 (1996)] has been refined in the region where the pair ({beta},{gamma}) remains close to each other while the third particle {alpha} is far away from them ({rho}{sub {alpha}}{yields}{infinity},r{sub {alpha}}/{rho}{sub {alpha}}{yields}0). The improved wave function satisfies the Schroedinger equation up to the terms of order O(1/{rho}{sub {alpha}}{sup 3}), provides the leading asymptotic terms of the threebody scattering wave function with Coulomb interactions, and gives further insight into the continuum behavior of the threechargedparticle wave function, and helps to obtainmore »

Asymptotic Properties of the Wave Function for a Bound Nonrelativistic ThreeBody System
BS>The asymptotic properties of a Schrodinger wave function that represents the bound ground state of a system of three interacting particles are examined. It is assumed that the interaction can be described by a static potential that is the sum of three twobody potentials and one threebody potential, where the potentials have the property that if any one of the particles is separated from the other two by a distance that tends to infinity, then the part of the potential energy that depends on the position of that particle tends to zero. The problem is treated nonrelativistically. Decreasing exponential boundsmore » 
Threebody unitary transformations, threebody forces, and trinucleon bound state properties. [Charge form factor, Coulomb energy difference]
A threebody unitary transformation method for the study of threebody forces is presented. Starting with a threebody Hamiltonian with twobody forces, unitary transformations are introduced to generate Hamiltonians that have both two and threebody forces. For cases of physical interest, the twobody forces of the altered Hamiltonians are phase equivalent (for twobody scattering) to the original and the threebody force vanishes when any interparticle distance is large. Specific examples are presented. Applications for studying the possible role of threebody forces in accounting for trinucleon bound state properties are examined. Calculations of the /sup 3/He and /sup 3/H charge form factorsmore » 
Discretizing the threebody continuum: bound states and twobody amplitudes
In this paper, we use a soluble model to investigate the accuracy of a discretization approximation for calculating bound states and twobody collision parameters. The model is that of three identical particles interacting via shortrange, separable, Swave pair potentials. Both weakl;y (spinquartet fermion) and strongly (boson) interacting systems are examined. Discretization is achieved by diagonalizing the Hamiltonian for the twoparticle subsystems in a finite set of L/sup 2/ functions, here chosen to be Laguerre polynomials. By requiring that the energy and eigenfunction of the lowestlying member of the resulting set of pseudostates be in excellent agreement with the actual boundstatemore »