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Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 26, 1973 - Issue 5
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Original Articles

Semiclassical theory of molecular collisions : three nearly coincident classical trajectories

J.N.L. Connor Department of Chemistry, University of Manchester, Manchester, M13 9PL
Pages 1217-1231 | Received 16 Feb 1973, Published online: 23 Aug 2006

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Jakob J. Stamnes & Bjørn Spjelkavik. (1983) Evaluation of the Field near a Cusp of a Caustic. Optica Acta: International Journal of Optics 30:9, pages 1331-1358.
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J.N.L. Connor, P.R. Curtis & D. Farrelly. (1983) A differential equation method for the numerical evaluation of the Airy, Pearcey and swallowtail canonical integrals and their derivatives. Molecular Physics 48:6, pages 1305-1330.
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T. Uzer & M.S. Child. (1982) Collisions and umbilic catastrophes. Molecular Physics 46:6, pages 1371-1388.
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J.N.L. Connor. (1976) Catastrophes and molecular collisions. Molecular Physics 31:1, pages 33-55.
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M.V. Berry. (1976) Waves and Thom's theorem. Advances in Physics 25:1, pages 1-26.
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Jörn Manz. (1975) The relation of chemical potentials and reactivity studied by a state path sum. Molecular Physics 30:3, pages 899-910.
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J.N.L. Connor. (1974) Semiclassical theory of molecular collisions: Real and complex-valued classical trajectories for collinear atom Morse oscillator collisions. Molecular Physics 28:6, pages 1569-1578.
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J.N.L. Connor. (1974) Semiclassical theory of molecular collisions: Many nearly coincident classical trajectories. Molecular Physics 27:4, pages 853-866.
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J.N.L. Connor. (1973) Evaluation of multidimensional canonical integrals in semiclassical collision theory. Molecular Physics 26:6, pages 1371-1377.
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Articles from other publishers (52)

Robert Beuc, Mladen Movre & Berislav Horvatić. (2019) On the Approximate Evaluation of Some Oscillatory Integrals. Atoms 7:2, pages 47.
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J Mumford, W Kirkby & D H J O’Dell. (2017) Catastrophes in non-equilibrium many-particle wave functions: universality and critical scaling. Journal of Physics B: Atomic, Molecular and Optical Physics 50:4, pages 044005.
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Chengkui Xiahou & J. N. L. Connor. (2014) The 6Hankel asymptotic approximation for the uniform description of rainbows and glories in the angular scattering of state-to-state chemical reactions: derivation, properties and applications. Phys. Chem. Chem. Phys. 16:21, pages 10095-10111.
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Chengkui Xiahou, J. N. L. Connor & Dong H. Zhang. (2011) Rainbows and glories in the angular scattering of the state-to-state F + H2 reaction at Etrans = 0.04088 eV. Physical Chemistry Chemical Physics 13:28, pages 12981.
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C.A. Hobbs, J.N.L. Connor & N.P. Kirk. (2007) Theory and numerical evaluation of oddoids and evenoids: Oscillatory cuspoid integrals with odd and even polynomial phase functions. Journal of Computational and Applied Mathematics 207:2, pages 192-213.
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A. S. Kryukovskii, D. S. Lukin, E. A. Palkin & D. S. Rastyagaev. (2006) Wave catastrophes: Types of focusing in diffraction and propagation of electromagnetic waves. Journal of Communications Technology and Electronics 51:10, pages 1087-1125.
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Johannes Kofler & Nikita Arnold. (2006) Axially symmetric focusing as a cuspoid diffraction catastrophe: Scalar and vector cases and comparison with the theory of Mie. Physical Review B 73:23.
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Tomaž Fabčič, Jörg Main, Thomas Bartsch & Günter Wunner. (2005) Photoabsorption spectra of the diamagnetic hydrogen atom in the transition regime to chaos: closed orbit theory with bifurcating orbits. Journal of Physics B: Atomic, Molecular and Optical Physics 38:2, pages S219-S239.
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M. Leibscher, I. Sh. Averbukh, P. Rozmej & R. Arvieu. (2004) Semiclassical catastrophes and cumulative angular squeezing of a kicked quantum rotor. Physical Review A 69:3.
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Thomas Bartsch, Jörg Main & Günter Wunner. (2003) Semiclassical quantization of the hydrogen atom in crossed electric and magnetic fields. Physical Review A 67:6.
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N P Kirk, J N L Connor, P R Curtis & C A Hobbs. (2000) Theory of axially symmetric cusped focusing: numerical evaluation of a Bessoid integral by an adaptive contour algorithm. Journal of Physics A: Mathematical and General 33:26, pages 4797-4808.
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John A. Shaw & F. Robicheaux. (1998) Recurrence spectroscopy of atoms in electric fields: Scattering in the presence of bifurcations. Physical Review A 58:5, pages 3561-3566.
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John A. Shaw & F. Robicheaux. (1998) Recurrence spectroscopy of atoms in electric fields: Failure of classical scaling laws near bifurcations. Physical Review A 58:3, pages 1910-1917.
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M. Brack, S. M. Reimann & M. Sieber. (1997) Semiclassical Interpretation of the Mass Asymmetry in Nuclear Fission. Physical Review Letters 79:10, pages 1817-1820.
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A. D. Peters, C. Jaffé, J. Gao & J. B. Delos. (1997) Quantum manifestations of bifurcations of closed orbits in the photodetachment cross section of in parallel fields . Physical Review A 56:1, pages 345-355.
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Jörg Main & Günter Wunner. (1997) Hydrogen atom in a magnetic field: Ghost orbits, catastrophes, and uniform semiclassical approximations. Physical Review A 55:3, pages 1743-1759.
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Jorge Morales, Agustin Diz, E. Deumens & Yngve Öhrn. (1995) Electron nuclear dynamics of H++H2 collisions at E lab=30 eV . The Journal of Chemical Physics 103:23, pages 9968-9980.
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C. D. Schwieters & J. B. Delos. (1995) Half-cycle pulse acting on a one-dimensional Rydberg atom: Semiclassical transition amplitudes in action and angle variables. Physical Review A 51:2, pages 1030-1041.
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C. D. Schwieters & J. B. Delos. (1995) Semiclassical treatment of a half-cycle pulse acting on a one-dimensional Rydberg atom. Physical Review A 51:2, pages 1023-1029.
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R. B. Paris. (1994) A Generalization of Pearcey’s Integral. SIAM Journal on Mathematical Analysis 25:2, pages 630-645.
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J. Gao & J. B. Delos. (1994) Resonances and recurrences in the absorption spectrum of an atom in an electric field. Physical Review A 49:2, pages 869-880.
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M. W. Beims & G. Alber. (1993) Bifurcations of electronic trajectories and dynamics of electronic Rydberg wave packets. Physical Review A 48:4, pages 3123-3129.
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Efrat Shimshoni & Ady Stern. (1993) Dephasing of interference in Landau-Zener transitions. Physical Review B 47:15, pages 9523-9536.
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P. McCabe, J. N. L. Connor & K.-E. Thylwe. (1993) Complex angular momentum theory of molecular collisions: New phase rules for rotationally inelastic diffraction scattering in atom–homonuclear diatomic molecule collisions. The Journal of Chemical Physics 98:4, pages 2947-2961.
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A.G Basile & C.G Gray. (1992) A relaxation algorithm for classical paths as a function of end points: Application to the semiclassical propagator for far-from-caustic and near-caustic conditions. Journal of Computational Physics 101:1, pages 80-93.
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. (1997) The asymptotic behaviour of Pearcey’s integral for complex variables. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 432:1886, pages 391-426.
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C Jung & S Pott. (1990) Semiclassical cross section for a classically chaotic scattering system. Journal of Physics A: Mathematical and General 23:16, pages 3729-3748.
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S. H. Fricke, M. E. Brandan & K. W. McVoy. (1988) Resolution of potential ambiguities through farside angular structure: Semiclassical analysis. Physical Review C 38:2, pages 682-695.
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T. S. Wang & J. B. Delos. (1986) Electron detachment in negative-ion collisions. III. Model calculations. Physical Review A 33:6, pages 3832-3841.
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J. B. Delos. 1986. Advances in Chemical Physics. Advances in Chemical Physics 161 214 .
S. K. Knudson, J. B. Delos & B. Bloom. (1985) Semiclassical calculation of quantum-mechanical wave functions for a two-dimensional scattering system. The Journal of Chemical Physics 83:11, pages 5703-5711.
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D.M. BRINK. 1985. Semiclassical Descriptions of Atomic and Nuclear Collisions. Semiclassical Descriptions of Atomic and Nuclear Collisions 241 251 .
E.B. Ipatov, D.S. Lukin & E.A. Palkin. (1985) Numerical methods of computing special functions of wave catastrophes. USSR Computational Mathematics and Mathematical Physics 25:1, pages 144-153.
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J. N. L. Connor & P. R. Curtis. (1984) Differential equations for the cuspoid canonical integrals. Journal of Mathematical Physics 25:10, pages 2895-2902.
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J N L Connor, P R Curtis & D Farrelly. (1984) The uniform asymptotic swallowtail approximation: practical methods for oscillating integrals with four coalescing saddle points. Journal of Physics A: Mathematical and General 17:2, pages 283-310.
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J. N. L. Connor, P. R. Curtis, C. J. Edge & A. Laganà. (1984) The uniform asymptotic swallowtail approximation: Application to the collinear H+F2 chemical reaction. The Journal of Chemical Physics 80:3, pages 1362-1363.
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D.M. Brink & U. Smilansky. (1983) Multiple reflections in the path-integral approach to barrier penetration. Nuclear Physics A 405:2, pages 301-312.
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J N L Connor & P R Curtis. (1982) A method for the numerical evaluation of the oscillatory integrals associated with the cuspoid catastrophes: application to Pearcey's integral and its derivatives. Journal of Physics A: Mathematical and General 15:4, pages 1179-1190.
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J. N. L. Connor & D. Farrelly. (1981) Theory of cusped rainbows in elastic scattering: Uniform semiclassical calculations using Pearcey’s integral. The Journal of Chemical Physics 75:6, pages 2831-2846.
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J.N.L. Connor & D. Farrelly. (1981) Molecular collisions and cusp catastrophes: three methods for the calculation of pearcey's integral and its derivatives. Chemical Physics Letters 81:2, pages 306-310.
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Ian Stewart. (1981) Applications of catastrophe theory to the physical sciences. Physica D: Nonlinear Phenomena 2:2, pages 245-305.
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R. Silveira. (1981) Angular distributions of elastic and quasi elastic heavy-ion collisions. pattern analysis. Zeitschrift f�r Physik A Atoms and Nuclei 299:1, pages 79-84.
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J. N. L. Connor. 1980. Semiclassical Methods in Molecular Scattering and Spectroscopy. Semiclassical Methods in Molecular Scattering and Spectroscopy 45 107 .
J.N.L. Connor. (1979) Reactive molecular collision calculations. Computer Physics Communications 17:1-2, pages 117-143.
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Cécile DeWitt-Morette, Amar Maheshwari & Bruce Nelson. (1979) Path integration in non-relativistic quantum mechanics. Physics Reports 50:5, pages 255-372.
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M.S. Child. 1979. Advances in Atomic and Molecular Physics Volume 14. Advances in Atomic and Molecular Physics Volume 14 225 280 .
T. W. Barrett. (2008) A deterministic interpretation of the commutation and uncertainty relations of quantum theory and a redefinition of Planck’s constant as a coupling condition. Il Nuovo Cimento B 45:2, pages 297-309.
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S Levit & U Smilansky. (1977) The hamiltonian path integrals and the uniform semiclassical approximations for the propagator. Annals of Physics 108:1, pages 165-197.
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M.W. Guidry, H. Massmannt, R. Donangelo & J.O. Rasmussen. (1976) Theory of coulomb-nuclear interference for heavy-ion excitation of rotational states. Nuclear Physics A 274:1-2, pages 183-201.
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M V Berry. (1975) Cusped rainbows and incoherence effects in the rippling-mirror model for particle scattering from surfaces. Journal of Physics A: Mathematical and General 8:4, pages 566-584.
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George Starkschall & John C. Light. (1974) Semiclassical treatment of bound state systems. III. A uniform stationary phase integration for the multidimensional problem. The Journal of Chemical Physics 61:8, pages 3417-3421.
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J.N.L. Connor. (1974) Uniform evaluation of ths S matrix for elastic and inelastic collisions in semiclassical collision theory. Chemical Physics Letters 25:4, pages 611-613.
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