A physical picture

An illustrative example is the collision of a Na Rydberg atom with CO, and in Fig. 11.1 we show a picture of the CO passing through the Na electron cloud.6 There are three interactions  

Above we have considered collisions with CO. If we now consider collisions with N2, for example, the electron-dipole interaction is absent, and the longest 

Consider a perturber which collides with a Rydberg atom as shown in Fig. 11.2(a). Before the collision the perturber is in state j3 and has momentum K. After the collision the perturber is in state and has momentum K. The 

In Fig. 11.2(b) we show the trajectory of the Rydberg electron just before and after hitting the perturber. Prior to the collision the Rydberg atom is in state a, 

Thus Q = K — K implies that Q = k — k. In other words, Q is the momentum transfer to the electron. If we assume that there is no particular orientation of the perturber during the collision we can replace U (fi, fi, p) by the isotropic potential U(fi, fi, p). With this approximation in Eq. (11.5) we recognize the Bom approximation to the electron scattering amplitude 

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This treatment is not very mathematical it is intended to provide a physical picture for the origin of isotope effects and to show some of their uses. More detailed discussions are available in reviews by Bell, Saunders, Ritchie, Carpenter, - and Drenth and Kwart. ... 

Various statistical treatments of reaction kinetics provide a physical picture for the underlying molecular basis for Arrhenius temperature dependence. One of the most common approaches is Eyring transition state theory, which postulates a thermal equilibrium between reactants and the transition state. Applying statistical mechanical methods to this equilibrium and to the inherent rate of activated molecules transiting the barrier leads to the Eyring equation (Eq. 10.3), where k is the Boltzmann constant, h is the Planck s constant, and AG is the relative free energy of the transition state [note Eq. (10.3) ignores a transmission factor, which is normally 1, in the preexponential term]. 

A physical picture of the Fermi coupling within the exchange approximation is given in Fig. 7. 

The classical crystal growth theory goes back to Burton, Cabrera and Frank (BCF) (1951). The BCF theory presents a physical picture of the interface (Fig. 6.9c) where at kinks on a surface step - at the outcrop of a screw dislocation-adsorbed crystal constituents are sequentially incorporated into the growing lattice. 

A physical picture of refraction at an interface shows TIR to be part of a continuum, rather than a sudden new phenomenon appearing at 8 = 8C. For small 8, the light waves in the liquid are sinusoidal, with a certain characteristic period noted as one moves normally away from the surface. As 8 approaches 0,., that period becomes longer as the refracted rays propagate increasingly parallel to the surface. At exactly 8 = 0C, that period is infinite, as the wave fronts of the refracted light are normal to the surface. This situation... 

In VII.5 the dissociation of a molecule into two fragments was described by the M-equation (5.4), in which the coefficients WVfl and Pv are yet to be obtained from a physical picture of the actual mechanism. Christiansen replaced the various states v of the molecule with a reaction coordinate x representing the distance between both fragments. Kramers assumed that x undergoes Brownian motion as described by equation (VIII.7.4) in appropriate units,... 

Prof. Fleming, the expressions you are using for the nonlinear response function may be derived using the second-order cumulant expansion and do not require the use of the instantaneous normal-mode model. The relevant information (the spectral density) is related to the two-time correlation function of the electronic gap (for resonant spectroscopy) and of the electronic polarizability (for off-resonant spectroscopy). You may choose to interpret the Fourier components of the spectral density as instantaneous oscillators, but this is not necessary. The instantaneous normal mode provides a physical picture whose validity needs to be verified. Does it give new predictions beyond the second-order cumulant approach The main difficulty with this model is that the modes only exist for a time scale comparable to their frequencies. In glasses, they live much longer and the picture may be more justified than in liquids. 

According to Eq. (19), t, is the time scale for excited state solvation for a Debye solvent. In fact, it is the time scale for both excited state and ground solvation of dipolar solutes and ionic solutes, t, also plays a role in a broad range of reactive (Section III) and nonreactive charge transfer processes in solution. It is clearly worthwhile to establish a physical picture for this important variable. 

Figure 10.6 A waveguide section between two partial sections, a) Physical picture indicating traveling waves in a continuous medium whose wave impedance changes from R0 to Ri to R2. b) Digital simulation diagram for the same situation. The section propagation delay is denoted asz- T. The behavior at an impedance discontinuity is characterized by a lossless splitting of an incoming wave into transmitted and reflected components.

It was noted in Ref. 12b that such important physical characteristic exists as elasticity of the spatial H-bond network, which is usually employed [15, 16, 19] for calculations of water spectra. As is intuitively clear, this elasticity should be somehow related to the R-band spectrum, since the stretching vibration, determined by the H-bond elasticity, is believed [16, 35, 51] to present the origin of this band in water. As a basic mechanism, one could regard an additional power loss due to interaction with the a.c. field of the H-bond vibrations. However in Ref. 7, as well as in Ref. 12b, a physical picture relating the CS well to bending vibrations was not established. 

A success of this composite model allows us to clarify a physical picture of molecular motions in water and to recognize a physical meaning of the hat-curved model itself. We shall return to this question in the final section. 

A physical picture of the MCD effect is first presented by considering the simplest case of a complex having ground and excited states with angular momenta 7=1/2 (M7 = 1/2) in Figure 1.7. 

An empirical generalization used to predict which phase in an emulsion will be continuous and which dispersed. It is based on a physical picture in which emulsifiers are considered to have a wedge shape and will favour adsorbing at an interface, such that most efficient packing is obtained that is, with the narrow ends pointed toward the centres of the droplets. A useful starting point, but there are many exceptions. See also Bancroft s Rule, Hydrophile-Lipophile Balance. 

Fig. 9, from Warren s 1929 paper on the crystal structure and chemical composition of amphiboles 48>, is a physical picture of the silicon-oxygen chain in diopside. Large circles represent van der Waals-like domains of oxide ions (r = 1.40 A 2>) smaller, dashed circles represent van der Waals-like domains of silicon cations [r = 0.41 A 2>). 

It is interesting to note that the Gottingen school, who later developed matrix mechanics, followed the mathematical route, while Schrodinger linked his wave mechanics to a physical picture. Despite their mathematical equivalence as Sturm-Liouville problems, the two approaches have never been reconciled. It will be argued that Schrodinger s physical model had no room for classical particles, as later assumed in the Copenhagen interpretation of quantum mechanics. Rather than contemplate the wave alternative the Copenhagen orthodoxy preferred to disperse their point particles in a probability density and to dress up their interpretation with the uncertainty principle and a quantum measurement problem to avoid any wave structure. 

To provide a physical picture for this phenomenon, the nanoparticles may be arbitrarily separated into a core, in which the magnetization is along the grain easy magnetization direction and a shell, of thickness 5, in which the moments may deviate from the local easy axis. Thus, the remanent magnetization may be expressed as ... 

After eqn.(3.14) turned out to be obeyed by many systems in practice, a model was developed that could provide a physical picture. This so-called diachoric model [306] explains the fact that the two components of the mixed phase behave independently by demixing on a microscopic scale. Hence, the stationary phase is assumed to consist of little patches or droplets of either pure A or pure B. Obviously, such a model does explain obeyance of eqn.(3.14), while it also gives a handle to explain deviations from linearity in terms of complete mixing of the two phases. 

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