Vibrational excitation cross sections

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. 

The maxima near the resonances on the curve representing the dependence of the vibrational excitation cross section on the energy of the electron can be very different in shape they can be wide (up to 10 eV) or of medium size (several electron volts) or very narrow. Sometimes these maxima are arranged in groups. For the most thorougly studied molecule, N2, the maxima of different structures are observed throughout the... 

The EMAP method has been used to compute elastic scattering and symmetric-stretch vibrational excitation cross sections for electron scattering by C02 [235], This is one of the first ab initio calculations of vibrational excitation for a polyatomic molecule. The results are in good agreement with experiment, which shows unusually large low-energy cross sections. The theory identifies a near-threshold... 

Abdolsalami, M. and Morrison, M.A. (1987). Calculating vibrational-excitation cross sections off the energy shell A first-order adiabatic theory, Phys. Rev. A 36, 5474-5477. 

A necessary condition for the two-term expansion of the distribution function of equation (2) to be valid is that the electron collision frequency for momentum transfer must be larger than the total electron collision frequency for excitation for all values of electron energy. Under these conditions electron-heavy particle momentum-transfer collisions are of major importance in reducing the asymmetry in the distribution function. In many cases as pointed out by Phelps in ref. 34, this condition is not met in the analysis of N2, CO, and C02 transport data primarily because of large vibrational excitation cross sections. The effect on the accuracy of the determination of distribution functions as a result is a factor still remaining to be assessed. 

Figure 1. A comparison of experimental and theoretical vibrational excitation cross sections for N2 scattering.

Figure 5 (Kurachi and Nakamura, 1990) presents a survey of electron collision cross sections of CF4. In addition to the momentum-transfer cross section q , it shows the vibrational-excitation cross sections q T, and q (for two different vibrational modes), the (total) electronic-excitation cross section q, the dissociation cross section q j , the electron-attachment cross section qg, and the (total) ionization cross section 9,. Each of the cross sections is a function of the electron kinetic energy and reflects the physics of the collision process, which is being clarified by theory. The cross sections designated as total can be discussed in greater detail in terms of different contributions, which are designated as partial cross sections.

Fig, 2. Cross-section set for C2F6 assembled by Hayashi and Niwa (1987) the vibrational excitation cross sections measured by Takagi et al. (1994) are also shown. 

The energy dependence of the vibrational excitation cross section depends on the lifetime of the intermediate ionic states (the so-called resonances). First let us consider the so-called short-lifetime resonanees (eg., H2, N2O, H2O, etc), where the lifetime of the autoionization states AB (bi) is much shorter than the period of oscillation (t 10 s). The... 

The long-lifetime resonances result in quite narrow isolated peaks (about 0.1 eV) in cross-section dependence on electron energy (see Fig. 2-22 and Table 2-15). In contrast to boomerang resonances, here the maximum value of the vibrational excitation cross section remains the same for different vibrational quantiun numbers. 

B. Vibrationally Excited Cross Sections and Rate Constants... 

We will derive here the expression for the vibrational excitation cross section of electron/molecule collision using the complex adiabatic approximation. Let us consider a scattering event where the electron represented by collides with a molecule which has N internal electrons. We... 

The T-matrix calculated according to the prescriptions above is computed in the Bom-Oppenheimer approximation and depends parametrically on the internal vibrational coordinates of the molecule. The Bom-Oppenheimer approximation decouples the nuclear and electronic degrees of freedom just as it does in the bound state case, and therefore some additional assumptions have to be made to use the fixed-nuclei quantities in approximate calculations of vibrational or rotational excitation cross sections. The simplest approximation for vibrational excitation cross sections is to take advantage of the parametric dependence of the T-matrix on the vibrational degrees of freedom of the molecule and write... 

R. J. Bartlett and M. J. Redmon, Vibrational Excitation Cross Sections for the 0( P) 4- H2O and 0( P) 4- CO2 Collisions", final report on contract no. F04611-79-C-0024, Air Force Rocket Propulsion Laboratory, October, 1980. 

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