Approximation optical

According to the optical approximation, which was shown by Platzman [4] to be based on the Born-Bethe theory, a radiation chemical yield of channel G, may be estimated from optical data as shown in the following equation ... 

Figure 4.10 Backscattering by a large sphere in the geometrical optics approximation.

Figure 7.2 Absorption efficiency of a water droplet ( = 1.20 /xm) the dashed curve is the geometrical optics approximation (7.2).

This result properly accounts for single scattering effects. Equation 14 represents an optical approximation which underestimates the value of E0 because the increase of the electronic kinetic energy associated with multiple scattering effects is not taken into account. 

In the optical approximation, the radiation yield of SES for small molecules is estimated65 to be gSES — 0.6-1. Similar estimates were obtained by Bednar.57... 

Direct excitation to excited states has never been observed in radiation chemistry although it is predicted in the so called "optical approximation" 2,3) Spectroscopic evidence of direct excitation by very low energy electrons is forthcoming ( ). Radiation chemistry is often called the chemistry of ionising radiation and the popular concept is that primary energy loss is to produce ionization, the subsequent chemistry then depending on the medium and its pertinent chemistry. 

The abundance of excited states produced directly can be calculated via the optical approximation (. The optical approximation states that the energy lost to a particular electronic transition of a molecule is proportional to f/e where f is the oscillator strength for that transition and e is the energy. For the state of benzene f 1.0 and e is 6.0 eV,... 

Platzman suggested that the probability d is much less than unity and there is real formation of super-excited states. Hatano calculated the yield of the super-excited molecules and the consequent dissociation (in values of g, number of dissociations per 100 eV energy absorbed) for cyclopropane together with some other hydrocarbons. He used the optical approximation introduced by Platzman , assuming that the yield is proportional to the square of the dipole-matrix-element Mj calculated from the optical spectra (equation 4). 

Yields are computed for a number of electronic transitions in gases under alpha-particle irradiation. The results are found to be usefully insensitive to approximations in the computational procedure. Comparison with experiment permits commentary on the latter. Deviations from the predictions of the optical approximation are interpreted as departures from high-energy equivalence. 

The Optical Approximation, Primary Radiation Chemical Yields, and Structure of the Track of an Ionizing Particle... 

A survey is given of the theory of the physical stage of radiolysis. Using the optical approximation to cross sections for the interaction between fast electrons and molecules, expressions have been derived for the yield g° of primary optical activations, and for the total absorbed energy Qtot It is shown that the total yield g of primary activations is conveniently discussed as a sum g° + gs, where the first term includes the action of fast electrons, while g8 describes the action of slow electrons (kinetic energy less than about 100 e.v.) on molecules of the medium. This approach is compared with Platzmans considerations on primary yields and the differences are pointed out. Finally, theoretical results of the present approach are applied to the analysis of the initial structure of the track of a fast electron, consisting of spurs, blobs, and short tracks. 

Fast electrons with kinetic energy T > 100 e.v. excite and ionize molecules predominantly in optical collisions inducing the same type of transitions of valence electrons as does the absorption of photons. This abundant type of primary activations shows, therefore, a very close connection with the optical spectra of molecules. Thus, foundations are laid for the use of the so-called optical approximation in radiation chemistry, as suggested by Platzman (13). More explicitly, the theory of cross sections for optical collisions leads in first approximation to the following formula for the yield of a particular electronic transition n ... 

The optical yield g° caused by the fast electrons can be expressed explicitly using the optical approximation. In the differential form concerning the energy transferred between E and E -f- dE we then obtain 16, 17, 18, 19) ... 

One important point remains to be resolved, however. Platzman has recently (14) summarized his eflForts for introducing the optical approximation into the theory of radiation chemistry and suggested a formula for the overall yield g0A of primary activations ... 

This formula combines optical data such as df/dE and M2ion, which is an integral over all ionized states analogous to M2 in Equation 6, with empirical radiation-chemical data on W. Equation 9 is essentially of the form g = const X g° and thus represents an alternative to, and should be compared with our view, g = g° gs. It does, in fact, extend the optical approximation expressed by Equation 1 to the totality of primary activations in the physical stage and yields, in particular, the approximative conclusion y = y°. 

Since the optical approximation is valid for all fast electrons, and since the latter are all able to induce the entire spectrum of optical transitions, the energy distribution of spurs is the same for isolated spurs and for the spurs in blobs or short tracks. The average energy per spur is thus equal in all entities and the partition of energy between spurs, blobs, and short tracks is approximately given by the above ratios, too. This is one of the reasons why the yield gs caused by slow electrons is uniformly added to the whole area of the yield g° of spurs in Figure 1. 

In Section 2 we describe the theoretical aspects of the ray-optics approximation, divided into the geometric optics and forward diffraction parts. In Section 3 we address the accuracy of the approximation via comparisons to more exact computations. In Section 4 we outline certain scattering characteristics of pristine ice crystals and irregularly shaped ice particles, including fractal crystals and Gaussian particles. Particle orientation is the topic of Section 5, and we close the chapter through summary and conclusions in Section 6. 

Born, M. and E. Wolf, 1999 Principles of Optics. Cambridge University Press. Grynko, Y. and S. Yu, 2003 Scattering matrix calculated in geometric optics approximation for semitransparent particles faceted with various shapes. J. Quant. Spectros. Radiat. Transfer, 78, 319-340. 

Muinonen, K., T. Nousiainen, P. Fast, K. Lumme, and J. I. Peltoniemi, 1996 Light scattering by Gaussian random particles ray optics approximation. J. Quant. Spectros. Radial. Transfer, 55, 577—601. 

Nousiainen, T., K. Muinonen, and P. Raisanen, 2003 Scattering of hght by large saharan dust particles in a modified ray-optics approximation. J. Geophys. Res., 108(D1), 4025, doi 10.1029/2001JD001277. 

Wielaard, D. J., M. I. Mishchenko, A. Macke, and B. E. Carlson, 1997 Improved T-matrix computations for large, nonabsorbing and weakly absorbing nonspherical particles and comparison with geometric optics approximation. Appl. Opt., 36, 4305-4313. 

According to Platzman s optical approximation theory (Platzman, 1962) the probability of picking up energy between Q and Q + dQ is given by the equation... 

As described previously, the fast electrons slow down gradually losing --10-40 eV energy in each interaction. As the kinetic energy of the incident particle drops below a certain value, 100 eV (Case c), there is no more possibility of a sudden energy transfer like with a last particle (Bednar 1983). Therefore, the optical approximation loses its validity, and optically not allowed transitions may also occur in the energy transfer process there is a direct possibility for excitation to triplet excited states. 

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