Abstract
Our approach provides high precision spectroscopic calculations and general formalism for the quantum description of three-body Coulomb systems. We seek the exact solutions of the 6D Schrödinger equation. For this we propose a new algorithm for the case of nonzero total angular momentum, taking into account the overall rotation of the system which is affected indirectly by the Coriolis coupling. The robustness, efficiency, and accuracy of the adopted algorithm are studied in detail. We employ Discrete Variable Representation (DVR) and construct a special set of hyperspherical harmonics which provides much more flexibility in choosing the best basis for the needs of this particular physical problem. The method is applied to the computation of the nonrelativistic energy levels of the exotic meta-stable antiprotonic helium.
Similar content being viewed by others
REFERENCES
Abramowitz, M. and Stegun, I. A., eds. (1972).Handbook of Mathematical Functions, Dover, NY.
Aquilanti, V., Cavalli, S., and De Fazio, D. (1998). Journal of Chemical Physics 109, 3792.
Aquilanti, V., Cavalli, S., and Grossi, G. (1986). Journal of Chemical Physics 85, 1362.
Atomic spectroscopy and collisions using slow antiprotons (1997, Oct.7). CERN/SPSC/P307; (1998) CERN Courier 38, No. 8.
Avery, J. (1989). Hyperspherical Harmonics, Kluwer, Dordrecht.
Delves, L. M. (1958). Nuclear Physics B 9, 391.
Delves, L. M. (1960). Nuclear Physics B 20, 275.
Fano, U., Green, D., Bohn, J. L., and Heim, T. A. (1999).Journal of Physics B: Atomic, Molecular and Optical Physics 32, R1.
Korobov, V. I., Pusynin, I. V., and Vinitsky, S. I. (1992). MuonCatalyzed Fusion 7, 63.
Korobov, V. I. (1996). Physical Review A 54, R1749.
Korobov, V. I. and Shimamura, I. (1997). Physical Review A 56, 4587.
Lin, C. D. (1986). Advances in Atomic and Molecular Physics 22, 77.
Lin, C. D. (1995). Physics Reports 257, 1.
Lin, C. D. (1999). Journal of Chemical Physics 110, 6673.
LittleJohn, R. J. and Mitchell, K. A. (1998). Physical Review A 58, 3705.
LittleJohn, R. J. and Mitchell, K. A. (2000). Physical Review A 61, 042502.
Macek, J. (1968). Journal of Physics B: Atomic, Molecular and Optical Physics 1, 831.
Morse, P. M. and Feshbach, H. (1953). Methods of Theoretical Physics, McGraw-Hill, NY.
Smith, F. T. (1959). Journal of Chemical Physics 31, 1352.
Smith, F. T. (1962). Journal of Mathematical Physics 3, 735.
Tolstikhin, O., Watanabe, S., and Matsuzawa, M. (1995). Physical Review Letters 74, 3573.
Yamazaki, T., et al., (1993). Nature 361, 238.
Yamazaki, T. and Ohtsuki, K. (1992). Zeitschrift Für Physik Review A 45, 7782.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Machtoub, G., Zhang, C. Coriolis Coupling in Exotic Three-Body Coulomb Systems. International Journal of Theoretical Physics 41, 293–308 (2002). https://doi.org/10.1023/A:1014010923548
Issue Date:
DOI: https://doi.org/10.1023/A:1014010923548