Theory of inelastic collision

M. Gryzinski, Classical theory of atomic collisions I. Theory of inelastic collisions, Phys. Rev. 138 (1965) A 336. 

At St > St the inertial impact of a particle deforms the bubble surface, creates a thin water layer between the particle and bubble and makes the particle jump back from the bubble surface. This decreases the collision efficiency which otherwise rises with the particles size. For particles of subcritical diameter the collision efficiency increases with particle diameter. The proposed theory of inelastic collision unlike other theories describes the coupling of inertial bubble-particle interaction and water drainage from the liquid interlayer. 

Delos JB, Thorson WR, Knudson SK (1972) Semiclassical theory of inelastic collisions. I. Classical picture and semiclassical formulation. Phys Rev A 6 709-720... 

The quantum theory of molecular collisions in external fields described in this chapter is based on the solutions of the time-independent Schrodinger equation. The scattering formalism considered here can be used to calculate the collision properties of molecules in the presence of static electric or magnetic fields as well as in nonresonant AC fields. In the latter case, the time-dependent problem can be reduced to the time-independent one by means of the Floquet theory, discussed in the previous section. We will consider elastic or inelastic but chemically nonreac-tive collisions of molecules in an external field. The extension of the formalism to reactive scattering problems for molecules in external fields has been described in Ref. [12]. 

In this section the derivation of the collision operators for dilute and dense suspensions are examined. Introductory the established formulas for dilute and dense gases consisting of elastic particles are outlined. Thereafter the kinetic theory of inelastic particles are considered. 

More quantitative results have been obtained by Prigogine16 and co-workers, who adopted a kinetic method of approach and who treated this problem by the modern methods of the kinetic theory of gases. The integro-differential Maxwell-Boltzmann equation was extended to the case of inelastic collisions to get the velocity distribution functions /y, in terms of which the reaction rate may be written... 

The paper Molecular collisions. VIII is a landmark in the theory of inelastic scattering of molecules because it was the first to bring together two of the most useful... 

In summary, Miller s 1970 papers [1, 2] on classical 5-matrix theory had a profound influence on the theory of molecular collisions and related topics such as photodissociation. Following earlier work on elastic scattering, they demonstrated how the results of classical mechanics can be built into a quantum mechanical framework of inelastic collisions. In my view the greatest asset of the classical 5-matrix theory is its interpretative power. The general shape of transition probabilities or collisional cross sections can be easily understood in terms of classical trajectories and their quantum mechanical interference. Exact quantum mechanical programs are like black boxes and the results are often difficult to understand without the help of classical mechanics or semiclassical analyses. The new developments such as the IVR are likely to become major tools for systems consisting of many atoms. 

J. S. Briggs and K. Taulbjerg, Theory of Inelastic Atom-Atom Collisions , in Top. Curr, Phys., ed. I. A. Sellin, Springer Verlag, Berlin, Heidelberg, New York, Vol. 5, 1978, pp. 105—153. 

This chapter deals with qnantal and semiclassical theory of heavy-particle and electron-atom collisions. Basic and nsefnl fonnnlae for cross sections, rates and associated quantities are presented. A consistent description of the mathematics and vocabnlary of scattering is provided. Topics covered inclnde collisions, rate coefficients, qnantal transition rates and cross sections. Bom cross sections, qnantal potential scattering, collisions between identical particles, qnantal inelastic heavy-particle collisions, electron-atom inelastic collisions, semiclassical inelastic scattering and long-range interactions. 

Gailitis, M. (1965). Extremal properties of approximate methods of collision theory in the presence of inelastic processes. Sov. Phys. JETP 20 107-111. 

The RRKM theory is a ubiquitous tool for studying dissociation or isomerization rates of molecules as a function of their vibrational energy. Still highly active in the theoretical field, Marcus has tackled such issues as the semiclassical theory for inelastic and reactive collisions, devising reaction coordinates, new tunneling paths, and exploring solvent dynamics effects on unim-olecular reactions in clusters. 

Resonances are common and unique features of elastic and inelastic collisions, photodissociation, unimolecular decay, autoionization problems, and related topics. Their general behavior and formal description are rather universal and identical for nuclear, electronic, atomic, or molecular scattering. Truhlar (1984) contains many examples of resonances in various fields of atomic and molecular physics. Resonances are particularly interesting if more than one degree of freedom is involved they reflect the quasi-bound states of the Hamiltonian and reveal a great deal of information about the multi-dimensional PES, the internal energy transfer, and the decay mechanism. A quantitative analysis based on time-dependent perturbation theory follows in the next section. 

When the gas-solid flow in a multiphase system is dominated by the interparticle collisions, the stresses and other dynamic properties of the solid phase can be postulated to be analogous to those of gas molecules. Thus, the kinetic theory of gases is adopted in the modeling of dense gas-solid flows. In this model, it is assumed that collision among particles is the only mechanism for the transport of mass, momentum, and energy of the particles. The energy dissipation due to inelastic collisions is included in the model despite the elastic collision condition dictated by the theory. 

When the deviation from the elastic state of the material surface is small, the Hertzian theory can estimate the force of impact, contact area, and contact duration for collisions between spherical particles and a plane surface using Eqs. (2.132), (2.133), and (2.136), respectively. To account for inelastic collisions, we may introduce r as the ratio of the reflection speed to the incoming speed, V. Therefore, we may write... 

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