Abstract
The hyperradial-adiabatic approach is used to study a region of localized triple-avoided crossing. A three-by-three orthogonal transformation involving a system of strongly coupled hyperradial Schrödinger equations is developed, leading to an exact coherent compensation of all peaks in the matrix elements of adiabatic corrections. In other words, the closure relation between adiabatic corrections matricesH+Q 2=0, which formally holds for a complete basis set, is nicely saturated by three strongly interacting states. One may suggest this to be a property of the hyperradial-adiabatic basis.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Landau, L. D.: Phys. Z. Sow.2, 46 (1932); Zener, C.: Proc. Roy. Soc. Lond.A137, 696 (1932); Stueckelberg, E. C. G.: Helv. Phys. Acta5, 369 (1932)
Hellmann, H., Syrkin, J. K.: Acta Physicochim. URSS2, 433 (1935); Hellmann, H.: Quantum Chemistry. Moscow-Leningrad 1937 (in Russian); Hellmann, H.: Einführung in die Quantenchemie. Wien: Deuticke 1937 (in German)
Lichten, W.: Phys. Rev.131, 229 (1963)
Smith, F. T.: Phys. Rev.179, 111 (1969)
Gabriel, H., Taulbjerg, K.: Phys. Rev.A10, 741 (1974)
Macias, A., Riera, A.: Phys. Rep.90, 299 (1982)
Matveenko, A. V.: JETP65, 2167 (1973); English Translation: Sov. Phys. JETP38, 1082 (1974)
Heil, T. G., Dalgarno, A.: J. Phys.B12, L557 (1979)
Matveenko, A. V.: Preprint E4-91-370. Dubna: JINR 1991
Matzuzawa, M., Motoyama, T., Fukuda, H., Koyama, N: Phys. Rev.A34, 1793 (1986); J. PhysB19, L333 (1986); J. Phys.B20, 2959 (1987)
Gantmacher, F. R.: The Theory of Matrices, Vol. 2, pp. 113–125. New York: Chelsea 1959; Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations (Applied Mathematical Sciences, Vol. 44). New York-Berlin-Heidelberg: Springer 1983
Matveenko, A. V., Abe, Y.: Few-Body Systems2, 127 (1987)
Hara, S., Fukuda, H., Ishihara, T., Matveenko, A. V.: Phys. Lett.A130, 22 (1988)
Johnson, B. R.: Chem. Phys. Lett27, 289 (1974)
Delos, J. B., Thorson, W. R.: J. Chem. Phys.70, 1774 (1979)
Imanishi, B., Von Oertzen, W.: Phys. Rep.155, 29 (1987)
Abe, Y., Park, J. Y.: Phys. Rev.C28, 2316 (1983)
Imanishi, B., Von Oertzen, W., Voit, H.: Phys. Rev.C35, 359 (1987)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Matveenko, A.V., Fonseca, A.C. Exact triple-avoided-crossing resolution for three-body molecular systems. Few-Body Systems 14, 81–89 (1993). https://doi.org/10.1007/BF01076307
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01076307