Cross-section excitation

The first term in Eq. (7.7) is the in-phasc signal, which has the same phase as that of the pump, and the second term is a quadrature or out-of-phase signal, which has a 90° phase relative to that of the pump. Their respective frequency dependencies are shown in Figure 7-2. The normalized change in transmission can be related to the excitation cross-section and quantum yield of generation ... 

Turner and Hopkins [90] previously reported an unusual structure of the EEDF. They found a dip at eV in the EEDF of a N2 plasma. They interpreted the dip as the electric absorption of a N2 molecule corresponding to the resonant peak of the vibrational excitation cross section. 

The power dissipated at two different frequencies has been calculated for all reactions and compared with the energy loss to the walls. It is shown that at 65 MHz the fraction of power lost to the boundary decreases by a large amount compared to the situation at 13.56 MHz [224]. In contrast, the power dissipated by electron impact collision increases from nearly 47% to more than 71%, of which vibrational excitation increases by a factor of 2, dissociation increases by 45%, and ionization stays approximately the same, in agreement with the product of the ionization probability per electron, the electron density, and the ion flux, as shown before. The vibrational excitation energy thresholds (0.11 and 0.27 eV) are much smaller than the dissociation (8.3 eV) and ionization (13 eV) ones, and the vibrational excitation cross sections are large too. The reaction rate of processes with a low energy threshold therefore increases more than those with a high threshold. 

Xu C, Webb WW (1996) Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm. J Opt Soc Am B 13 481—491... 

Hayashi s (1989) compilation highly overestimates the total inelastic cross section below 100 eV. These are inconsistent with measured W values. Although the total cross section is reasonably well determined, uncertainties in the elastic cross section might have led Hayashi to overestimate the inelastic cross section. Figure 4.5 shows these cross sections. It is seen, however, that one theoretical calculation is consistent with W value measurement (Pimblott et al., 1990). In any case, Hayashi s values for total inelastic cross section are much greater than all major calculations, and the discrepancy is directly traceable to overestimates of excitation cross sections. 

Fio. 5. Ideal form of excitation cross-section (a) versus energy E) functions for different fundamental processes. 

The first (and still the foremost) quantum theory of stopping, attributed to Bethe [19,20], considers the observables energy and momentum transfers as fundamental in the interaction of fast charged particles with atomic electrons. Taking the simplest case of a heavy, fast, yet nonrelativistic incident projectile, the excitation cross-section is developed in the first Born approximation that is, the incident particle is represented as a plane wave and the scattered particle as a slightly perturbed wave. Representing the Coulombic interaction as a Fourier integral over momentum transfer, Bethe derives the differential Born cross-section for excitation to the nth quantum state of the atom as follows. 

A comparison, as shown in Fig. 8, between the experimental results of the collisional energy dependence of the de-excitation cross section of He(2 P) by Ar and the theoretical ones calculated from the W-K theory [140] and the K-W theory [139] makes clearly possible for the first time to compare in detail the experimental results with the theoretical ones [141]. Previous comparisons between experiments and theories have been made only for a value of the rate constant or the cross section, respectively, at a particular temperature of collisional energy, usually at room temperature. The results of temperature-... 

Figure 8 Experimental de-excitation cross sections of He(2 P) by Ar, Kr, and Xe (denoted by...

The cross sections show a decrease with increasing collisional energy, which is in marked contrast to the de-excitation cross sections of He(2 S) atoms by the same quenching atoms, as presented in Fig. 6. However, this behavior is rather similar to other quenching molecules, such as CO2 and C2H4, where the cross sections are fairly large, on the order of tens of squared angstroms. 

Figure 13 Plots of (

A little more complicated system is the de-excitation of He(2 P) by Ne, where the deexcitation is dominated by the excitation transfer and only a minor contribution from the Penning ionization is involved. The experimental cross section obtained by the pulse radiolysis method, together with the numerical calculation for the coupled-channel radial Schrodinger equation, has clearly provided the major contribution of the following excitation transfer processes to the absolute de-excitation cross sections [151] (Fig. 15) ... 

Table 5 De-excitation Cross Sections (cm) at a Mean Collisional Energy Corresponding to Room Temperature (295 K) and De-excitation Probabilities (P) of Excited Helium Atoms He (He = He(2 S), He(2 S), and He(2 P)) and polarizabilities (am) of target molecules (From Ref. 154.)...

Table 6 De-excitation Cross Sections of He(2 S) by CH4, SiH4, or GeH4 in Comparison with the Respective Cross Sections for Reaction Products (in A ) (From Refs. 123 and 152.)...

It is seen that the individual de-excitation cross sections for a particular excited atom are governed by the individual interactions. The de-excitation cross sections of He(2 S, 2 S, and 2 P) are reasonably interpreted as follows. Two important factors are readily extracted from the semiempirical formula for the Penning ionization cross section, so that the rational relation of the Penning ionization cross section is obtained ... 

Figure 18 De-excitation cross sections of Ne( P2) by M (M = CH4, SiH4, GeH4, CF4, and Sip4, Ar, Kr, Xe, H2, D2, N2, O2, CO, NO, CO2, N2O, and SFs) as a function of the polarizability of M. (From Ref 155.) The target molecules are classified by the type of their outermost molecular orbitals c-type ( ) re-type (O) and nonbonding (O).

Figure 19 Comparison of the de-excitation cross sections of excited argon atoms Ar [Ar = Pi (O) or Pi ( )] by M (M = CH4, SiH4, or GeH4) with the theoretical cross sections (

There are various modes of excitation for T > 7.4 eV. As reported experimental excitation cross sections are fragmentary, we used the compiled data of Paretzke [184] that includes all the major excitation modes. Paretzke fitted the experimental cross sections for the 10 major individual states using a model function ... 

There are no experimental data of excitation cross sections for proton and alpha particle impact for water. The proton cross sections were obtained by scaling of the electron excitation cross sections for high-energy protons >500 keV [201]. For the lower-energy regions, the semiempirical model developed by Miller and Green [202] was adopted, which is based on the electron impact excitation. They assumed an analytical function for each excited level of the form... 

For low energy electron region, namely, below 200 x Z eV, this equation will not be valid because of the limitation of Born approximation in this energy region, the calculations will be made using electron-impact ionization and excitation cross sections for gaseous targets [7]. 

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