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Title: Calculation of loosely bound levels for three-body quantum systems using hyperspherical coordinates with a mapping procedure

Abstract

In view of modelization of experiments involving cold atoms and molecules, we develop a method that allows us to calculate weakly bound levels of triatomic molecules. The method combines (1) the hyperspherical coordinates to describe interparticle motion in the three-body system, (2) the solution of the Schroedinger equation in two steps: determination of adiabatic states for a fixed hyper-radius and then solution of a set of coupled hyper-radial equations using the slow variable representation of Tolstikhin et al. [J. Phys. B: At. Mol. Opt. Phys. 29, L389 (1996)], (3) and a mapping procedure that reduces considerably the number of basis functions needed to represent wave functions of weakly bound levels. We apply the method to the three different systems: the helium trimer {sup 4}He{sub 3}, isotopomers of the H{sub 3}{sup +} ion, and finally a model three-body problem involving three nucleons. For all these systems, we show that the suggested method provides accurate results.

Authors:
 [1];  [2];  [3]
  1. Department of Physics, University of Central Florida, Orlando, Florida 32816 (United States)
  2. (France)
  3. Laboratoire Aime Cotton, CNRS, Bat. 505, Campus d'Orsay, 91405 Orsay Cedex (France)
Publication Date:
OSTI Identifier:
20786706
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.73.012702; (c) 2006 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; COORDINATES; HELIUM; HYDROGEN IONS 3 PLUS; ISOTOPE EFFECTS; MAPPING; MATHEMATICAL SOLUTIONS; MOLECULES; NUCLEONS; SCHROEDINGER EQUATION; THREE-BODY PROBLEM; VIBRATIONAL STATES; WAVE FUNCTIONS

Citation Formats

Kokoouline, Viatcheslav, Laboratoire Aime Cotton, CNRS, Bat. 505, Campus d'Orsay, 91405 Orsay Cedex, and Masnou-Seeuws, Francoise. Calculation of loosely bound levels for three-body quantum systems using hyperspherical coordinates with a mapping procedure. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.0.
Kokoouline, Viatcheslav, Laboratoire Aime Cotton, CNRS, Bat. 505, Campus d'Orsay, 91405 Orsay Cedex, & Masnou-Seeuws, Francoise. Calculation of loosely bound levels for three-body quantum systems using hyperspherical coordinates with a mapping procedure. United States. doi:10.1103/PHYSREVA.73.0.
Kokoouline, Viatcheslav, Laboratoire Aime Cotton, CNRS, Bat. 505, Campus d'Orsay, 91405 Orsay Cedex, and Masnou-Seeuws, Francoise. Sun . "Calculation of loosely bound levels for three-body quantum systems using hyperspherical coordinates with a mapping procedure". United States. doi:10.1103/PHYSREVA.73.0.
@article{osti_20786706,
title = {Calculation of loosely bound levels for three-body quantum systems using hyperspherical coordinates with a mapping procedure},
author = {Kokoouline, Viatcheslav and Laboratoire Aime Cotton, CNRS, Bat. 505, Campus d'Orsay, 91405 Orsay Cedex and Masnou-Seeuws, Francoise},
abstractNote = {In view of modelization of experiments involving cold atoms and molecules, we develop a method that allows us to calculate weakly bound levels of triatomic molecules. The method combines (1) the hyperspherical coordinates to describe interparticle motion in the three-body system, (2) the solution of the Schroedinger equation in two steps: determination of adiabatic states for a fixed hyper-radius and then solution of a set of coupled hyper-radial equations using the slow variable representation of Tolstikhin et al. [J. Phys. B: At. Mol. Opt. Phys. 29, L389 (1996)], (3) and a mapping procedure that reduces considerably the number of basis functions needed to represent wave functions of weakly bound levels. We apply the method to the three different systems: the helium trimer {sup 4}He{sub 3}, isotopomers of the H{sub 3}{sup +} ion, and finally a model three-body problem involving three nucleons. For all these systems, we show that the suggested method provides accurate results.},
doi = {10.1103/PHYSREVA.73.0},
journal = {Physical Review. A},
number = 1,
volume = 73,
place = {United States},
year = {Sun Jan 15 00:00:00 EST 2006},
month = {Sun Jan 15 00:00:00 EST 2006}
}