Partial cross sections

Another automated approach to kinetic analyses is the centrifugal analyzer, a partial cross section of which is shown in Figure 13.9. In this technique the sample and reagents are placed in separate wells oriented radially around a circular transfer disk attached to the rotor of a centrifuge. As the centrifuge spins, the... 

In addition to qualitative analysis of nearly all the elements of the periodic table, EEL spectra also enable determination of the concentration of a single element which is part of the transmitted volume and hence gives rise to a corresponding ionization edge. As in all comparable spectroscopic techniques, for quantification the net edge signal, which is related to the number N of excited atoms, must be extracted from the raw data measured. The net intensity 4 of the feth ionization shell of an individual element is directly connected to this number, N, multiplied by the partial cross-section of ionization ) and the intensity Iq of the incident electron beam, i.e. ... 

I he mixture clement shown in Fig. 14.15 contains the flowing gas and solid particles. The partial densities of these two elements are pg and p. respectively. The void fraction is and this can be interpreted as the partial cross-sectional area for gas flow (see Eq. (14.13)). This means that if the pressure of the gas is p, then the pressure force per unit area of the total mixture affecting the flow of gas is (pp and the pressure force affecting the flow of solids is 1 -

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Figure 12-3B. Partial cross-section of balanced-opposed compression cylinders. (Used by permission Bui. 85084, 1992. Dresser-Rand Company. All rights reserved.)...

The partial cross-sections on the n = 3 levels are displayed in Table 4 and Fig. 6 and show a fairly good overall agreement with the experimental results of Cotte et al. [4,7] and Dijkkamp et al. [9j. From a numerical point of view, the error bar has been estimated experimentally to 30% by Cotte et al. [4,7] and to 5% by Dijkkamp et al. [9]. Theoretically, the error bar could be evaluated to about 20%., the main difficulty arising in the determination of the sharp radial couplings. 

Our calculations reproduce the variation of the partial cross-sections with the collision energy, in particular the variation of the N +(3d) + He" level which could not be inter-... 

Partial cross-sections of single-electron capture. 

Table 6. Calculated values of the partial cross-sections of capture at 60 keV. ...

Table 7. Comparison of the capture partial cross-sections with N (ls ) and N5+(1s2s)3S at 50 keV (in 10 cm ).

Fig. 4. Computed partial cross-sections in A2 for the F + HD (v = 0, j = 0) —> HF + D reaction as a function of the total angular momentum quantum number, J, up to collision energies of 3 kcal/mol.

To uniquely associate the unusual behavior of the collision observables with the existence of a reactive resonance, it is necessary to theoretically characterize the quantum state that gives rise to the Lorentzian profile in the partial cross-sections. Using the method of spectral quantization (SQ), it is possible to extract a Seigert state wavefunction from time-dependent quantum wavepackets using the Fourier relation Eq. (21). The state obtained in this way for J = 0 is shown in Fig. 7 this state is localized in the collinear F — H — D arrangement with 3-quanta of excitation in the asymmetric stretch mode, and 0-quanta of excitation in the bend and symmetric stretch modes. If the state pictured in Fig. 7 is used as an initial (prepared) state in a wavepacket calculation, one observes pure... 

Fig. 10. The partial cross-section summed over all final states in A2 for F + H2(0,0) —> H + HF for several values of the total angular momentum J. The partial cross-section shows a double peak structure which J-shift to higher energy with J, and eventually merge at about J = 10.

The relative probabilities of ionization out of the various occupied MOs, named relative partial cross-sections (cr), are determined by several factors, the most important ones being the following ... 

D. Partial Cross Sections, Product State Distributions, and Differential Cross Sections III. Reactive Scattering Theory... 

We will be interested not only in the total absorption cross section [Eqs. (4.1) and (4.2)], which gives us a measure of the total probability that the molecule will absorb light and dissociate, but also in the probability that different product quantum states will be formed. This probability is given by a partial cross section cj/( ). From Eq. (4.1) we see that this partial integral cross section may be written as... 

The partial cross section gives the probability of absorbing light and producing a particular final product quantum state. The total photodissociation cross section is clearly given by the sum over all partial photodissociation cross sections ... 

It should be emphasized that the data shown in Fig. 3 do not provide information on the fate of the excited or ionized molecule these data constitute a sum over final molecular states. Generally, measurements of excitation and ionization cross sections for fast electrons do not provide information on subsequent target relaxation modes. However, this information is often available from separate measurements that focus on state-selected partial cross sections and molecular fragmentation [19]. 

At energies higher than 10 keV, ionization cross sections were calculated using Seltzer s formula [183]. Seltzer s formula gives the partial ionization cross sections for five molecular orbitals of water. The total ionization cross sections in the energy range of 10 keV to 10 MeV were obtained by summing up all the partial cross sections (Fig. 8). 

The H2 molecule is a system for which quite recently it has been possible to measure in unprecedented detail state-selected vibrationally and rotation-ally resolved photoionization cross sections in the presence of autoionization [27-29]. The technique employed has been resonantly enhanced multiphoton ionization. The theoretical approach sketched above has been used to calculate these experiments from first principles [30], and it has thus been possible to give a purely theoretical account of a process involving a chemical transformation in a situation where a considerable number of bound levels is embedded in an ensemble of continua that are also coupled to one another. The agreement between experiment and theory is quite good, with regard to both the relative magnitudes of the partial cross sections and the spectral profiles, which are quite different depending on the final vibrational rotational state of the ion. 

Figure 10.23 Schematic illustration of the l dependence of the partial cross section for compound nucleus (CN), fusionlike (FL), deep inelastic (D), quasi-elastic (QE), Coulomb excitation (CE), and elastic (EL) processes. [From Schroeder and Huizenga (1984, p. 242).]...

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