Abstract
The description of dynamical processes in atomic and molecular systems often leads to a set of coupled differential equations. Resonances within such species can be studied from a step by step propagation of solutions of these equations satisfying appropriate boundary conditions at both ends of the integration range. This is combined with a matching relation which plays the role of a quantization condition yielding a complex energy. Many variants are possible: the integration path can be real or complex; the addition of an optical potential is analyzed in some detail. This perturbation may, under some conditions, be completely equivalent to the use of a complex integration path. When these conditions are not fulfilled, the energy suffers a complex shift which may be eliminated through analytic continuation.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A. F. J. Siegert, Phys. Rev., 56, 750 (1939).
R. A. Bain, J. N. Bardsley, J. N. Junker and C. V.Sukumar, J. Phys. B, 7, 2189 (l974).
O. Atabek and R. Lefebvre, Phys. Rev., 22A, 1817 (1980).
C. L. Shoemaker, N. Abusalbi and D. J. Kouri, J. Phys. Chem., 87, 5389 (1983).
R. G. Gordon, J. Chem. Phys., 51, 14 (l969).
B. R. Johnson, J. Chem. Phys., 69, 4678 (l978).
D. W. Norcross and M. J. Seaton, J. Phys. B, 6, 614 (1973).
G. Bergeron, X. Chapuisat and J. M. Launay, Chem. Phys. Lett., 38, 349 (1976).
R. Lefebvre Intramolecular Dynamics, J. Jortner and B. Pullman,Eds., Reidel (1982), p. 55.
O. Atabek and R. Lefebvre, Int. J. Quant. Chem., 19, 901 (1981).
R. Lefebvre and M. Garcia-Sucre, Ann. Fond. L. de Broglie, 12, 195 (1987).
J. N. Ginocchio, Ann. Phys., 152, 203 (1984).
D. T. Colbert, R. Mayrhofer and P. R. Certain, Phys. Rev., 33A, 3560 (1986).
B. Simon, Phys. Lett., 71A, 211 (1979).
R. Guardiola and J. Ros, J. Comp. Phys., 45, 374 (1982).
D. G. Truhlar, J. Comp. Phys., 10, 123 (l972).
O. Atabek and R. Lefebvre, Chem. Phys. Lett., 84, 233 (1981).
O. Atabek, R. Lefebvre and M. Jacon, J. Phys. B, 15B, 2689 (1982).
R. Jost, Helv. Phys. Acta 20, 256 (1947).
R. Lefebvre, J. Phys. Chem. 88, 4839 (1984).
R. J. Le Roy and J. S. Carley, Adv. Chem. Phys. 42, 353 (1980).
H. Feshbach, Ann. Phys. 19, 287 (1962).
G. Jolicard and E. J. Austin, Chem. Phys. Lett. 121, 106 (1985).
M. Garcia-Sucre and R. Lefebvre, J. Chem. Phys. 85, 4753 (1986); Int. J. of Quant. Chem. 20, 541 (1986).
A. Messiah, Mécanique Quantique (Dunod, Paris, 1969), p. 197.
H. Bremmer, Physica 15, 593 (1949).
R. Lefebvre and M. Garcia-Sucre, in Stochasticity and Intermolecular Redistribution of Energy,( Eds. R. Lefebvre and S. Mukamel Reidel, 1987).
L. Schlessinger, Phys. Rev. 167, 1411 (1968).
W. P. Reinhardt, Int. J. of Quant. Chem. 21, 133 (1982).
M. Garcia-Sucre and R. Lefebvre, Mol. Phys. 60, 941 (1987.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag
About this paper
Cite this paper
Lefebvre, R. (1989). Energy shifts and widths in atomic and molecular physics: Multichannel approach. In: Brändas, E., Elander, N. (eds) Resonances The Unifying Route Towards the Formulation of Dynamical Processes Foundations and Applications in Nuclear, Atomic and Molecular Physics. Lecture Notes in Physics, vol 325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50994-1_47
Download citation
DOI: https://doi.org/10.1007/3-540-50994-1_47
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50994-3
Online ISBN: 978-3-540-46130-2
eBook Packages: Springer Book Archive