Abstract
Collision theory is briefly reviewed in the framework of the wave operator theory of quantum dynamics which emphasizes the role played by the resonances. Exact expressions of the on-shell S and T matrices are derived for an exactly solvable model which describes several resonances decaying into several channels. This model is especially relevant for investigating the physics near energy thresholds. The formalism is applied to giant resonances and to a model of laser-assisted electron-atom scattering.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
T. Y. Wu and T. Ohmura, Quantum Theory of Scattering ( Prentice-Hall, Englewood Cliffs, 1962 ).
J. R. Taylor, Scattering Theory ( Wiley, New York, 1972 ).
C. J. Joachain, Quantum Collision Theory ( North-Holland, Amsterdam, 1975 ).
H. Feshbach, Ann. Phys. 5, 357 (1958);
H. Feshbach, Annu. Rev. Nucl. Sci. 8, 49 (1958);
H. Feshbach, Ann. Phys. 19, 287 (1962).
L. Mower, Phys. Rev. 142, 799 (1965).
B. Shore, Rev. Mod. Phys. 39, 439 (1967).
M. Seaton, Rep. Prog. Phys. 46, 167 (1983).
B. A. Lippmann and J. Schwinger, Phys. Rev. 79, 479 (1950).
Ph. Durand and I. Paidarova, Phys. Rev. A 58, 1867 (1998).
J. N. Bardsley and F. Mandl, Rep. Prog. Phys. 31, 471 (1968).
P. G. Burke, Advan. At. Mol. Phys. 4, 173 (1968).
S. Buckman and C. W. Clark, Revs. Modern Phys. 66, 539 (1994).
C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions; Basic Processes and Applications (J. Wiley, New York 1992) [first edition, Inter Editions and Editions du CNRS, 1988 ].
A. Messiah Quantum Mechanics (North-Holland, Amsterdam, 1966 ), Vol. 2.
Ph. Durand, I. Paidarova, and F. X. Gadea, J. Phys. B 34, 1953 (2001).
Ph. Durand, I. Paidarova, J. Phys. B 35, 469 (2002).
R. Levine, Quantum Mechanics of Molecular Rate Processes ( Clarendon Press, Oxford 1969 ).
F. T. Smith, Phys. Rev. 118, 349 (1960).
U. Fano, Phys. Rev. 124, 1866 (1961).
R. Lefebvre, O. Atabek and V. Leon, Phys. Rev.A 65, 042726 (2002).
O. Olendski and L. Mikhailovska, Phys. Rev. B 67, 035310 (2003).
C. Mahaux and H. A. Weidenmuller, Shell Model Approach to Nuclear Reactions ( North-Holland, Amsterdam, 1969 ).
J-P. Connerade and A. M. Lane, Rep. Prog. Phys. 51, 1439 (1988).
E. Narevicius and N. Moiseyev, J. Chem. Phys. 113, 6088 (2000);
E. Narevicius and N. Moiseyev, Phys. Rev. Lett. 81, 2221 (1998).
N. J. Kylstra and C. J. Joachain, Phys. Rev. A 57, 412 (1998).
B. R. Lewis, S. T. Gibson, P. O’Keeffe, T. Ridley, K. P. Lawley and R. J. Donovan, Phys. Rev. Lett. 86, 1478 (2001).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Durand, P., Paidarová, I. (2003). Modeling Quantum Resonances: II. Overview of Collision Theory. In: Maruani, J., Lefebvre, R., Brändas, E.J. (eds) Advanced Topics in Theoretical Chemical Physics. Progress in Theoretical Chemistry and Physics, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0635-3_10
Download citation
DOI: https://doi.org/10.1007/978-94-017-0635-3_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6401-1
Online ISBN: 978-94-017-0635-3
eBook Packages: Springer Book Archive