Exact non-Born-Oppenheimer wave functions for three-particle Hookean systems with arbitrary masses
- Kimika Fakultatea, Euskal Herriko Unibertsitatea and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi (Spain) (Spain)
A Hookean model of a three-body problem for particles with arbitrary masses and charges where two of them interact with each other through a Coulomb potential and with the third through a harmonic potential is presented. It is shown that a condition relating the masses to the harmonic coupling constants must be satisfied in order to render this problem separable. A general exact analytic solution written in terms of the relative interparticle coordinates is given as well as general expressions for the total and binding energies of this three-body system. We apply these results to examine electronic, muonic, antiprotonic, and pionic families of non-Born-Oppenheimer Hookean systems. The first contains the atoms or atomic ions: Ps{sup -}(e{sup +}e{sup -}e{sup -}), H{sup -}(p{sup +}e{sup -}e{sup -}), D{sup -}(d{sup +}e{sup -}e{sup -}), T{sup -}(p{sup +}e{sup -}e{sup -}), {sup 4}He(he{sup +2}e{sup -}e{sup -}), and the following molecular ions: Ps{sub 2}{sup +}(e{sup -}e{sup +}e{sup +}), H{sub 2}{sup +}(e{sup -}p{sup +}p{sup +}), HD{sup +}(e{sup -}d{sup +}p{sup +}), HT{sup +}(e{sup -}t{sup +}p{sup +}), DT{sup +}(e{sup -}d{sup +}t{sup +}), D{sub 2}{sup +}(e{sup -}d{sup +}d{sup +}), T{sub 2}{sup +}(e{sup -}t{sup +}t{sup +}). The muonic and antiprotonic families are similar to the electronic ones except that the species are formed replacing e{sup -} by {mu}{sup -} or p{sup -}. The pionic family comprises exotic atoms containing at least one pion. We also apply these results to two-electron three-dimensional spherical quantum dots and for these systems we examine the effect of electronic correlation, particularly on the singlet-triplet transitions and on the collective motion of the electrons and center of mass leading to ''floppy''dynamics.
- OSTI ID:
- 20857866
- Journal Information:
- Physical Review. A, Vol. 74, Issue 4; Other Information: DOI: 10.1103/PhysRevA.74.042504; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ANALYTICAL SOLUTION
ATOMIC IONS
BINDING ENERGY
BORN-OPPENHEIMER APPROXIMATION
CORRELATIONS
COULOMB FIELD
DEUTERIUM
DEUTERIUM IONS
ELECTRONS
HADRONIC ATOMS
HARMONIC POTENTIAL
HELIUM
HELIUM 4
HELIUM IONS
HYDROGEN IONS 1 MINUS
HYDROGEN IONS 1 PLUS
HYDROGEN IONS 2 PLUS
MASS
MUONS MINUS
PIONS
POSITRONIUM
POSITRONS
POTENTIAL ENERGY
QUANTUM DOTS
THREE-BODY PROBLEM
TRITIUM
WAVE FUNCTIONS