Theory of scattering

An important development in the quantum theory of scattering in the last 20 years has been the development of exact expressions which directly detennine either thennal rate constant lc(T) from the... 

Rodberg L S and Thaler R M 1967 introduction to the Quantum Theory of Scattering (New York Academic)... 

The classical theory of scattering provides us with a relatively simple selection rule for Raman activity which can be compared with that for infrared activity. 

The prindple of a LEED experiment is shown schematically in Fig. 4.26. The primary electron beam impinges on a crystal with a unit cell described by vectors ai and Uj. The (00) beam is reflected direcdy back into the electron gun and can not be observed unless the crystal is tilted. The LEED image is congruent with the reciprocal lattice described by two vectors, and 02". The kinematic theory of scattering relates the redprocal lattice vectors to the real-space lattice through the following relations... 

In the classical theory of scattering (Cohen-Tannoudji et al. 1977, James 1982), atoms are considered to scatter as dipole oscillators with definite natural frequencies. They undergo harmonic vibrations in the electromagnetic field, and emit radiation as a result of the oscillations. 

A. Kuppermann, in Theoretical Chemistry, Vol. 6, Part A, Theory of Scattering Papers in Honour of Henry Eyring, D. Henderson, ed. (Academic Press, New York, 1981), p. 79. 

There are also more limited treatments of scattering. McCartney (1976, Chaps. 4-6) confines his attention to scattering by atmospheric particles. This is also discussed by Twomey (1977, Chaps. 9-10) in his treatise on atmospheric aerosols. In Goody (1964, Chap. 7) there are discussions of absorption by gases and, in less detail, extinction by molecules and by droplets. Parts of books on electromagnetic theory or optics include the theory of scattering by a sphere, most notably Stratton (1941, pp. 563-573) and Born and Wolf (1965, pp. 633-664). The latter also derive the Ewald-Oseen extinction theorem and apply it to reflection and refraction at a plane interface (pp. 98-104). 

The fluctuation theory of scattering by molecules is treated in books by Bhagavantam (1942), Fabelinskii (1968), and Chu (1974, Chap. 3). 

As far as notation for the scattering coefficients is concerned, we have followed as much as possible van de Hulst (1957) and Kerker (1969), with the exception of the opposite sign convention for the time-harmonic factor exp( — iwt). Kerker (1969, p. 60) gives a table comparing the notation of various authors who have written on the theory of scattering by a sphere. 

Beginning with an integral equation, Acquista (1976) obtained an iterative solution to the problem of scattering by an arbitrary particle. The first iteration is just the RG expression. Agreement between approximate and exact theories of scattering by a sphere is considerably improved by a second iteration. 

In this chapter we consider theories of scattering by particles that are either inhomogeneous, anisotropic, or nonspherical. No attempt will be made to be comprehensive our choice of examples is guided solely by personal taste. First we consider a special example of inhomogeneity, a layered sphere. Then we briefly discuss anisotropic spheres, including an exactly soluble problem. Isotropic optically active particles, ones with mirror asymmetry, are then considered. Cylindrical particles are not uncommon in nature—spider webs, viruses, various fibers—and we therefore devote considerable space to scattering by a right circular cylinder. 

TABLE 5.3 Examples of the Yardsticks Lyd and the Characteristic Lengths Lch Used in Different Theories of Scattering and the Different Properties Accessed through the Theories... 

Quantum theory of scattering. The differential scattering cross section for isotropic potentials is given by the scattering phase shifts r e as... 

See, for example, T. Y. Wu and T. Ohmura, Quantum Theory of Scattering, Prentice Hall, London, 1962. 

For a two-component system (macromolecule, component 2, dissolved in pure solvent, e.g., water, component 1), application of the fluctuation theory of scattering (15, 16) shows that in a volume element of volume SV (of the order of s z at the lowest angles of measurement), the intensity of radiation scattered by the solution in excess of the solvent, I(s) = /(s)solution — I(s)solvent, is proportional to the fluctuations in the number of electrons, n ... 

Wu, T.Y. and Ohmura, T. (1962). Quantum Theory of Scattering (Englewood Cliffs, Prentice-Hall). 

D < 500 pm, Fraunhofer Diffraction Pattern Analysis (FDPA) can be employed in measuring particle size distributions (4,5). For the particles in the intermediate range, 0.7 pm < D < 10 pm, Mie theory of scattering holds and Turbidity Spectra (TS) can furnish information about particle sizes (6). 

To understand how resonances affects the molecular phase, we briefly outline the basics of the theory of scattering resonances. We consider bound states <))s) interacting with a set of continuum states denoted E, n 1), where, as for the full scattering states , n-) [see Eq. (2.66)], the states E, n 1) approach the fine asymptotic solutions at infinite time ... 

L. S. Rodberg and R. M. Thaler, Introduction to the Quantum Theory of Scattering, Academic, New York, 1967. 

Arthurs AM, Dalgarno A (1960) The theory of scattering by a rigid rotator. Proc Royal Soc (London) A 256 540-551... 

In the volumes to come, special attention will be devoted to the following subjects the quantum theory of closed states, particularly the electronic structure of atoms, molecules, and crystals the quantum theory of scattering states, dealing also with the theory of chemical reactions the quantum theory of time-dependent phenomena, including the problem of electron transfer and radiation theory molecular dynamics statistical mechanics and general quantum statistics condensed matter theory in general quantum biochemistry and quantum pharmacology the theory of numerical analysis and computational techniques. 

Assuming that the perturbation theory of scattering applies, the detailed form of the scattered EW has been derived by Gao 9 for both in-plane and out-of-plane detection. Here the results will be summarized schematically to bring out the essential factors in interpretation. The scattered EW intensity from a collection of particles is given by... 

Wu, T. Y., Ohmura, T. Quantum theory of scattering. Prentice Hall 1962. 

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