Reprojection method for inelastic processes in atomic collisions within Born–Oppenheimer approach
DOI:
https://doi.org/10.33910/2687-153X-2022-3-1-25-36Keywords:
scattering theory, inelastic collision processes, nonadiabatic transitions, atomic dataAbstract
The paper provides a detailed description of the reprojection method for the exact solution of the nonadiabatic nuclear dynamics within the Born–Oppenheimer formalism. In particular, it discusses the asymptotic behaviour of a state-to-state transition probability when a nonadiabatic radial coupling for this transition has a nonzero asymptotic value—a fundamental feature of the Born–Oppenheimer approach. It is known that the conventional Born–Oppenheimer approach leads to divergency of inelastic cross sections and inelastic rate coefficients, while the reprojection method provides convergences. The article describes physical background of the reprojection method.
References
Bates, D. R., McCarroll, R. (1958) Electron capture in slow collisions. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 245 (1241), 175–183. https://doi.org/10.1098/rspa.1958.0075 (In English)
Belyaev, A. K. (2009) Nonadiabatic effects in inelastic collisional processes. Physica Scripta, 80 (4), article 048113. https://doi.org/10.1088/0031-8949/80/04/048113 (In English)
Belyaev, A. K. (2010) Revised Born–Oppenheimer approach and a reprojection method for inelastic collisions. Physical Review A, 82 (6), article 060701. https://doi.org/10.1103/PhysRevA.82.060701 (In English)
Belyaev, A. K. (2015) Excitation cross sections in low-energy hydrogen-helium collisions. Physical Review A, 91 (6), article 062709. https://doi.org/10.1103/PhysRevA.91.062709 (In English)
Belyaev, A. K., Dalgarno, A., McCarroll, R. (2002) The dependence of nonadiabatic couplings on the origin of electron coordinates. The Journal of Chemical Physics, 116 (13), 5395–5400. https://doi.org/10.1063/1.1457443 (In English)
Belyaev, A. K., Egorova, D., Grosser, J., Menzel, T. (2001) Electron translation and asymptotic couplings in low-energy atomic collisions. Physical Review A, 64 (5), article 052701. https://doi.org/10.1103/PhysRevA.64.052701 (In English)
Born, M., Oppenheimer, R. (1927) Zur Quantentheorie der Molekeln [On the quantum theory of molecules]. Annalen der Physik, 389 (20), 457–484. https://doi.org/10.1002/andp.19273892002 (In German)
Bransden, B. H., McDowell, M. R. C. (1992). Charge exchange and the theory of ion-atom collisions. Oxford: Clarendon Press; New York: Oxford University Press, 474 p. (In English)
Burke, V. M., Noble, C. J. (1995) FARM—A flexible asymptotic R-matrix package. Computer Physics Communications, 85 (3), 471–500. https://doi.org/10.1016/0010-4655(94)00178-5 (In English)
Faddeev, L. D. (1961) Scattering theory for a three-particle system. Soviet Physics—JETP, 12 (5), 1014–1019. (In English)
Faddeev, L. D., Merkuriev, S. P. (1993) Quantum scattering theory for several particle systems. Dordrecht: Springer Publ., 406 p. https://doi.org/10.1007/978-94-017-2832-4 (In English)
Grosser, J. (1986) Angular momentum coupling in atom-atom collisions. Zeitschrift für Physik D. Atoms, Molecules and Clusters, 3 (1), 39–58. https://doi.org/10.1007/BF01442346 (In English)
Grosser, J., Krüger, W. (1984) Hydrogen 2s and 2p excitation in low energy H, D+ He collisions. Zeitschrift für Physik A. Atoms and Nuclei, 318 (1), 25–30. (In English)
Grosser, J., Menzel, T., Belyaev, A. K. (1999) Approach to electron translation in low-energy atomic collisions. Physical Review A, 59 (2), article 1309. https://doi.org/10.1103/PhysRevA.59.1309 (In English)
Lane, A. M., Thomas, R. G. (1958) R-matrix theory of nuclear reactions. Reviews of Modern Physics, 30 (2), article 257. https://doi.org/10.1103/RevModPhys.30.257 (In English)
Light, J. C. (1979). Reactive scattering cross sections I: Theory. In: R. B. Bernstein (ed.). Atom-Molecule Collision Theory. Boston: Springer Verlag, pp. 239–257. https://doi.org/10.1007/978-1-4613-2913-8_6 (In English)
Lin, C. D. (1995) Hyperspherical coordinate approach to atomic and other Coulombic three-body systems. Physics Reports, 257 (1), 1–83. https://doi.org/10.1016/0370-1573(94)00094-J (In English)
Macek, J., Cavagnero, M., Jerjian, K., Fano, U. (1987) Bypassing translation factors in molecular dissociation and reactions. Physical Review A, 35 (9), article 3940. https://doi.org/10.1103/PhysRevA.35.3940 (In English)
Macías, A., Riera, A. (1982) Ab initio quantum chemistry in the molecular model of atomic collisions. Physics Reports, 90 (5), 299–376. https://doi.org/10.1016/0370-1573(82)90173-9 (In English)
Mott, N. F., Massey, H. S. W. (1049) The theory of atomic collisions. Oxford: Clarendon Press, 388 p. (In English)
Nikitin, E. E., Umansky, S. Ya. (1984) Theory of slow atomic collisions. Berlin: Springer Verlag, 432 p.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 Andrey K. Belyaev
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
The work is provided under the terms of the Public Offer and of Creative Commons public license Attribution-NonCommercial 4.0 International (CC BY-NC 4.0). This license allows an unlimited number of persons to reproduce and share the Licensed Material in all media and formats. Any use of the Licensed Material shall contain an identification of its Creator(s) and must be for non-commercial purposes only.