On the validity range of the Born-Oppenheimer approximation: A semiclassical study for all-particle quantization of three-body Coulomb systems

2006 ◽  
Vol 124 (14) ◽  
pp. 144101 ◽  
Author(s):  
Satoshi Takahashi ◽  
Kazuo Takatsuka
Keyword(s):  
Coulomb Systems ◽  
Validity Range ◽  
Oppenheimer Approximation ◽  
Three Body

Three-body molecular states of the LiH2+ system in the Born-Oppenheimer approximation

2018 ◽  
Vol 118 (15) ◽  
pp. e25611 ◽  
Author(s):  
Juan M. Randazzo ◽  
Antonio Aguilar-Navarro
Keyword(s):  
Oppenheimer Approximation ◽  
Three Body

Positional correlation in laser-excited three-body Coulomb systems

1990 ◽  
Vol 64 (3) ◽  
pp. 274-277 ◽  
Author(s):  
U. Eichmann ◽  
V. Lange ◽  
W. Sandner
Keyword(s):  
Coulomb Systems ◽  
Three Body

Polarizabilities and other properties of the tdµ molecular ion

2001 ◽  
Vol 79 (9) ◽  
pp. 1149-1158
Author(s):  
A K Bhatia ◽  
R J Drachman
Keyword(s):  
Energy Levels ◽  
Molecular Ions ◽  
Muon Catalyzed Fusion ◽  
Oppenheimer Approximation ◽  
Good Energy ◽  
Cusp Conditions ◽  
Fermi Contact ◽  
Muonic System ◽  
Three Body ◽  
Contact Parameters

Wave functions of the Hylleraas type were used earlier to calculate energy levels of muonic systems. Recently, we found in the case of the molecular ions H2+, D2+, and HD+ that it was necessary to include high powers of the internuclear distance in the Hylleraas functions to localize the nuclear motion when treating the ions as three-body systems without invoking the Born–Oppenheimer approximation. We tried the same approach in a muonic system, tdµ– (triton, deuteron, and muon). Improved convergence was obtained for J = 0 and 1 states for shorter expansions when we used this type of generalized Hylleraas function, but as the expansion length increased the high powers were no longer useful. We obtained good energy values for the two lowest J = 0 and 1 states and compared them with the best earlier calculations. Expectation values were obtained for various operators, the Fermi contact parameters, and the permanent quadrupole moment. The cusp conditions were also calculated. The polarizability of the ground state was then calculated using second-order perturbation theory with intermediate J = 1 pseudostates. (It should be possible to measure the polarizability by observing Rydberg states of atoms with tdµ– acting as the nucleus.) In addition, the initial sticking probability (an essential quantity in the analysis of muon catalyzed fusion) was calculated and compared with earlier results. PACS Nos.: 30.00, 36.10-k, 02.70-c

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