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Semiclassical Methods in Molecular Scattering and Spectroscopy

The ene10sed ~roeeedings of the NATO Advaneed Study Institute held in September 1979 are intended to provide a eomprehensive introduetion to the development of semie1assiea1 methods for mo1eeu1ar seattering and speetroseopy over the past twenty years. Progress in the seattering field may be taken to date from the famous paper by Ford and Wheeler in 1959, and eoineidenta1ly the RKR teehnique for diatomie speetroseopy was rediseovered at roughly t~e' same time. Subsequent developments have e~hasised the insight to be gained by eombining elassica1 and quant~ meehaniea1 ideas in a wide variety of more eOMplicated problems. Three main types of development may be recognised. First advances have oeeu~ed in mathematical teehnique, both in the development of higher order JWKB and phase integral expansions at dtscussed in chapters 1 and 3, and also in the use of uniform approximations to remove the spurious singularities inherent in the primitive JWKB approaeh. The latter are introduced in the conteat of elastic scattering in Chapter 2, and later recur in other app1ieations in ehapters 4 and 5. A second development has been to extend semie1assiea1 ideas to tunneling and curve-crossing situations. Here spectroscopic applicati. ons of this type are covered in chapter 4, and scattering situations are treated under the heading of non-adiabatic transitions in chapter 6. Finally major progress hs. s been made over the past ten years in the treatment of non-separable situations.
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Table of Contents

Semiclassical and Higher Order Approximations: Properties. Solution of Connection Problems.- 1. Introduction.- 2. First order JWKB approximation.- 3. Method for solving connection problems.- 4. Anti-Stokes' and Stokes' Lines.- 5. Properties of the JWKB Approximation in the complex plane.- 6. Bohr-Sommerfeld quantization condition.- 7. Phase shift.- 8. Normalization.- 9. Expectation values and matrix elements.- 10. Higher order approximations.- 11. Exercises.- References.- Semiclassical Theory of Elastic Scattering.- 1. Introduction.- 2. Quantum mechanical elastic scattering.- 3. Classical elastic scattering.- 4. The semiclassical phase shift.- 5. Semiclassical evaluation of f(?).- 6. Orbiting collisions and resonances.- 7. Regge pole representation of f(?).- References.- Problems.- Applications of Bohr Quantization in Diatomic Molecule Spectroscopy.- 1. Introduction.- 2. Spectroscopic properties of the potential function.- 3. RKR inversion.- 4. Near dissociation behaviour of diatomic molecules.- 5. Problems.- References.- Separable Spectroscopy Applications.- 1. Frack-Condon factors and predissociation.- 2. Tunneling and curve-crossing problems.- 3. Problems.- References.- The Classical S Matrix.- 1. Classical considerations.- 2. Derivations of the S matrix.- 3. Problems.- References.- Semiclassical Theory of Eletronically Non-Adiabatic Transitions in Molecular Collisions Processes.- 1. Introductory concepts and tools.- 2. Specific theories and dynamical models.- 3. Miller-George theory of electronic transitions.- 4. Applications of the semiclassical S matrix.- 5. Interaction with fields. Laser-enhanced collisions.- 6. Miscellaneous aspects of laser-enhanced collisions.- Problems.- References.- Correspondence-Principle Methods for Molecular Collisions.- 1. Introduction.- 2. Bound states and matrix elements.- 3. Cross sections.- 4. Collinear vibrational excitation.- 5. Rotational excitation.- 6. Rotational-vibrational excitation and rotor-rotor collisions.- 7. Conclusions.- Problems.- References.- The Determination of Bound States by Semiclassical Methods.- 1. The nature of classical trajectories.- 2. Methods for determining semiclassical eigenvalues.- 3. Quantum effects of classical ergodicity.- References.- Appendix. M. S. Child/The Airy Function.- 1. Properties.- References.- Author Index.

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