Adiabatic representation in the three-body problem with Coulomb interaction
An effective method for solving the three-body problem with Coulomb interaction is presented systematically. The essential feature of the method is an expansion of the wave function of the three-particle system with respect to an adiabatic basis and reduction of the original Schroedinger equation to a system of ordinary differential equations. Convergence of the adiabatic expansion is ensured not only by the smallness of the ratio of the particle masses but also by the smallness of the nondiagonal matrix elements of the kinetic-energy operator of particles of the same charge. The possibilities of the method are demonstrated by the example of the calculation of the energies and wave functions of all states of the ..mu..-mesic molecules of the hydrogen isotopes and the e/sup -/e/sup -/e/sup +/ system. The method is equally suitable for calculating the ground state and the excited states of a three-particle system. This is particularly important in the calculation of the energies of the weakly bound states of the mesic molecules dd..mu.. and dt..mu.., knowledge of which is needed to describe the processes of muonic catalysis of nuclear fusion reactions.
- Research Organization:
- Joint Institute for Nuclear Research, Dubna, USSR
- OSTI ID:
- 5955418
- Journal Information:
- Sov. J. Particles Nucl. (Engl. Transl.); (United States), Journal Name: Sov. J. Particles Nucl. (Engl. Transl.); (United States) Vol. 13:6; ISSN SJPNA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
Molecular & Chemical Physics-- Positronium
Muonium
& Muonic & Mesic Atoms & Molecules
657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ADIABATIC APPROXIMATION
CATALYSIS
COULOMB FIELD
DEUTERIUM
DEUTERIUM COMPOUNDS
DEUTERIUM TRITIDES
DIFFERENTIAL EQUATIONS
ELECTRIC FIELDS
ELEMENTS
ENERGY LEVELS
EQUATIONS
FUNCTIONS
FUSION REACTIONS
HYDROGEN
HYDROGEN COMPOUNDS
HYDROGEN ISOTOPES
ISOTOPES
LABELLED COMPOUNDS
LIGHT NUCLEI
MANY-BODY PROBLEM
MECHANICS
MESIC MOLECULES
MOLECULES
MUONIC MOLECULES
NONMETALS
NUCLEAR REACTIONS
NUCLEI
ODD-ODD NUCLEI
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM MECHANICS
SCHROEDINGER EQUATION
STABLE ISOTOPES
THREE-BODY PROBLEM
TRITIUM COMPOUNDS
WAVE EQUATIONS
WAVE FUNCTIONS