Scattering statistical theory

Statistical theory of electron densities - multiple-scattering perturbation theory. Proc. Roy. Soc. London A 435, 245-255 (1991). 

W.A. Steele. The Interaction of Gases with Solid Surfaces, Pergamon Press (1974). (Thermodynamical and statistical theories for gas adsorption, molecular beam scattering from surfaces.)... 

A recent publication of Vlasov and Zaitsev reports observations of the non-linear optical activity predicted by Kididi from molecular-statistical theory and by Atkins from quantum scattering theory. 

T. Bancewiez. Molecular-statistical theory of the influence of molecular fields in liquids on the spectral distribution and intensity of Rayleigh scattered light in the approach of Racah algebra. Acta Phys. Polonica, A, 56 431-438 (1979). 

The univariate statistical theory is used, for example, for rejecting one extreme value in a set of scattered results in a given sample. For this purpose, the extreme value x is temporarily eliminated from the sample. Then, from the sample Xi, X2...Xn - Xe there are calculated m, s and the value ... 

Another utilization of statistical theory Is to decide if two specimens are the same or different when the measurements performed on each specimen generate the two samples xi, X2... x and xi, X2 ... Xk containing scattered values. For this purpose, the two averages m and m and the two standard deviations s and s are calculated. It can be shown that If the samples are large enough, the variable ... 

Several aspects of this formulation require emphasis. First, defining the SCR yields a particular statistical theory hence, a wide variety of theories are possible. Second, one should anticipate that a typical scattering event will have both direct and statistical components. Third, an analysis of the degree of statistical behavior in an exact dynamical calculation requires three sequential steps (1) the SCR must first be defined (2) the component of the scattering that does not pass through the SCR is then eliminated from consideration and (3) the product distribution associated with the component passing through the SCR is compared with the results predicted from Eq. (2.17) the latter often requires additional numerical computations. 

The coupled-channels method may be developed within the language of wave-mechanics, or more formally (and more compactly) by means of operator equations. The common feature of both approaches is that the total scattering state is expanded in internal states of reactants and products. The nature of the colliding particles and the quantum numbers of the interna] states define the reaction channel index c = a, b,. We begin with the wave-mechanical approach, some of whose features have been presented in the section on statistical theories. For the total wavefunction [pa of reactants in channel a, with relative wave vector ka, we can write... 

The most effective approach to describe the optical properties of the arrays with short-range ordering is the statistical theory of multiple scattering of waves (STMSW) [5]. This approach considers electrodynamic coupling of spatially correlated scatterers as interference summation and subsequent averaging of... 

Quantum Theory of Scattering and Unimolecnlar Breakdown.—From the theoretical viewpoint it would appear natural to compute lifetimes and cross-sections for unimolecular processes like equation (34) by one of the existing methods for the solution of the set of coupled equations of the scattering problem. There have been, however, hardly any calculations for experimental examples or at least realistic model systems. The present status of the quantum theory of unimolecular reactions is still rather in the domain of formal theories or hi y simplified models, which are not of immediate interest to the experimentalist. We shall, nevertheless, review some of the recent developments, because one may hope that in the future the detailed dynamical theories will provide a deeper understanding of unimolecular dynamics than the statistical theories presently do. 

As discussed in Section 3.3.2, scattering may be interpreted in terms of particulate or statistical theories. The particulate theories have been most useful in interpreting photographic patterns. Such theories have been used to account for scattering from spherulitic or rodlike crystalline aggregates. 

Information on the equation of state comes from two experimental sources light-scattering at low ( 1%) volume fractions via equation (20), and direct compressibility studies at high ( 10%) volume fractions. For testing statistical theories of concentrated dispersions, we therefore look towards compressibility studies on well defined systems. The available compression data on lattices show only qualitative agreement with the Monte Carlo results they are insufficiently precise to test the pairwise-additivity assumption employed in the computer simulations. 

See also Fourier Transformation and Sampling Theory PET, Methods and Instrumentation Scattering Theory Statistical Theory of Mass Spectra. 

Classical Dynamics of Nonequilibrium Processes in Fluids Integrating the Classical Equations of Motion Control of Microworld Chemical and Physical Processes Mixed Quantum-Classical Methods Multiphoton Excitation Non-adiabatic Derivative Couplings Photochemistry Rates of Chemical Reactions Reactive Scattering of Polyatomic Molecules Spectroscopy Computational Methods State to State Reactive Scattering Statistical Adiabatic Channel Models Time-dependent Multiconfigurational Hartree Method Trajectory Simulations of Molecular Collisions Classical Treatment Transition State Theory Unimolecular Reaction Dynamics Valence Bond Curve Crossing Models Vibrational Energy Level Calculations Vibronic Dynamics in Polyatomic Molecules Wave Packets. 

Path Integral Methods Reaction Path Hamiltonian and its Use for Investigating Reaction Mechanisms Reactive Scattering of Polyatomic Molecules State to State Reactive Scattering Statistical Adiabatic Channel Models Time Correlation Functions Transition State Theory Unimolecular Reaction Dynamics. 

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