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

Journal Article · Sun Jan 15 04:00:00 EST 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.73.0· OSTI ID:20786706

Kokoouline, Viatcheslav ^[1]; Masnou-Seeuws, Francoise ^[2]

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1. Department of Physics, University of Central Florida, Orlando, Florida 32816 (United States)
2. Laboratoire Aime Cotton, CNRS, Bat. 505, Campus d'Orsay, 91405 Orsay Cedex (France)

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.

• OSTI ID: 20786706
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 73; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

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