Cross sections for reactions

The cross-sections of the various reactions observed are shown as functions of the kinetic energies in the center of mass system and in the laboratory system by Figures 4, 5, and 6. In all cases, the cross-sections for reactions between X+ and H2 or D2, respectively, are equal if one compares them at the same relative kinetic energy. According to the... 

Reactions of Complex Ions. For reactions of systems containing H2 or HD the failure to observe an E 1/2 dependence of reaction cross-section was probably the result of the failure to include all products of ion-molecule reaction in the calculation of the experimental cross-sections. For reactions of complex molecule ions where electron impact ionization probably produces a distribution of vibrationally excited states, kinetic energy transfer can readily open channels which yield products obscured by primary ionization processes. In such cases an E n dependence of cross-section may be determined frequently n = 1 has been found. 

Table II. Total Cross-Sections for Reactions of Ions with Ethylene...

The numerical results for argon are a = 0.66 X 10 22 and b = 0.4. Since b = ki2kib/knki, we must make some further assumptions to obtain values of interest. Considering the nature of Reactions 15 and 16, we conclude that 15/ 16 1 which leads to ki2/kn 0.4. Substituting this value into the equation which defines a, we obtain kn/kis 4.75 X 10 23. In a separate study (31) with a mass spectrometer for conventional ion-molecule reaction work we could determine the cross-section for Reaction 15 as Q/ = 208 X 10 16 sq. cm. at Erl = 0.55 volt, where Er is repeller field strength and l the ion path length in the ion source. 

The cross sections cr for reactions with Ar+ are determined at thermal energies of the reactants [334] the cross sections for reactions with H are determined at a kinetic energy of the reactants of 1 eV [335], (Compiled from E. A. G, Hamers, Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands, 1998.)... 

As discussed above, the solution environment provides for a set of time scales different from the gas phase environment. In solution, there are typically 1013 collisions second"1 of a solute molecule with solvent molecules. Thus, if a photolytically generated species is expected to have a large cross section for reaction with solvent and it is desired to monitor that reaction, both generation and monitoring must be done on a picosecond (psecond) or even sub-psecond timescale. That monitoring this rapid is necessary has been confirmed in an experiment on Cr(CO)6 in cyclohexane solution where psecond photolysis and monitoring was not rapid enough to detect the naked Cr(CO)5 that existed before coordination with cyclohexane (55). 

Figure 3. Variation with relative kinetic energy of cross sections for reaction of Ni+ with HD. Data from reference 24.

The total integral reactive cross section for reaction from a particular initial state to all possible final states is then given by a summation over all total angular momenta that can contribute to the reaction ... 

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.)...

Another approach has been taken, however, by Johns, Pearson, and Brown,137 which employs either a Monte Carlo computer technique, or a random distribution method. The Monte Carlo technique is based on the formation of only a dimer and a hydrate, with cross sections for reaction according to eq. (11a)... 

The existence of differential reactivity for various sites suggests the possibility that energy absorbed at one site on the chain may be transferred down the chain until it localizes in a site with an unusually high cross section for reaction. Shulman, Gueron, and Eisinger154 claim that energy absorbed in poly dAT at the excited singlet level is transferred to a common excimer between A and T, whence it crosses to a triplet triplet excitons have been observed in poly A with a jump time of 10"8 to 10 10 sec. 

Energy transfer along the polynucleotide chain may be one factor in the variable cross section for reaction of the sites on the chain. A poly... 

In evaluating the viability of a new experimental technique for studying ion-molecule reactions, a number of factors must be considered. Ultimately our aims are to measure relative cross sections for reactions as a function of both the internal energy of the ion and the collision energy. It is important that the collision energy can be varied down to = 10 meV where the rotational energy may be comparable with the translational energy. 

Correlation between tunneling distances for reactions of trapped electrons in vitrified solutions and the cross-sections for reactions of solvated electrons in liquid solutions... 

Figure 14. Photoionization cross section of NH3 and apparent photoionization cross section for NH produced by reaction of NH3+ with NH3. Variation of reaction cross section as function of vibrational state of reactant NH3+ ion was determined by comparing relative step heights of curves for NH3+ and NH after ordinate scales of both curves were adjusted so that data points of first plateau at about 10.2 eV coincide. Ratio of a pair of corresponding step heights is then proportional to ratio of cross section for reaction of vibrationally excited NH3+ to that for NH3+ in its ground vibrational state. Step heights used to determine relative cross section for reaction of NH3+ with v = 5 are shown. Step ratio NH//NH3+ decreases with increasing e.85 ...

Figure 16. Cross section as function of ion kinetic energy for charge-transfer reaction B+(N20,B)N20+ A, cross section for reaction of B+(IS) produced from BI3 O, cross section for reaction of B+ produced from BF3 (35.3% 3P and 64.5% S ) solid line, cross section for reaction of B+(3/1) obtained by taking difference between two lower curves and correcting for appropriate abundance.7 ...

Figure 24. Apparent cross sections for collisional dissociation reaction, N2+(N2 N2,N)N+, as function of reactant kinetic energy. Both laboratory (lab) and center-of-mass (CM) energy scales are shown. Energies of ionizing electrons producing N2+ in each case are indicated. Arrows indicate upper limits on cross section for reaction when is produced by 19.2-eV electrons.36 ...

Figure 25. Kinetic-energy dependence of cross section for reaction (O ) + Ne— O+H-O + Ne.50...

Figure 6.26. PES cross section for reaction (6.41), C(1)H3 + C(2)H3OH C(I)H4 + C

An illustration of the capture process is given in Figure 8.9, which shows the positron (or electron) occupying a state in a narrow temperature or energy band in the ionic continuum. In effect the antiprotons(protons) are virtually at rest in the positron(electron) gas. This is the case, for instance, for near equi-velocity particle beams, in which the kinetic energy, Ee, of the positrons(electrons) in the rest frame of the antipro-tons(protons) is much less than the binding energy, Eo, of the lowest atomic bound state. Under these conditions the cross section for reaction... 

When reaction occurs then successful collisions are detected from the scattering patterns of products. These give an effective 6max(g), and cross section for reaction,... 

Fig. 4.1.13(a-c) shows partial cross-sections for reactions with the reactant molecules in vibrational quantum states n = 0,1,2 and rotational quantum state J = 0 and products in vibrational states n = 0,1,2, respectively, and any rotational quantum state. Note that the abscissa axis in this plot is the translational energy and not the total energy as in Fig. 4.1.12. The translational energy is found in the latter plot by subtracting the molecular energy En

Since the value of A depends on the value chosen for the cross-section, and the values are base on taking the values for non-reactive collision cross section. Hence, orientation requirement can be taken into account by replacing the collision cross section a2 in equation (2.50) by the reactive cross section o 2. A more conventional procedure takes the view that the cross section for reaction can be expressed in terms of the collisional cross section and stearic factor P such that a 2. 

Greene, Ross, and their co-workers [15,40] have found the following total reaction cross sections for reactions of K atoms with hydrogen halides ... 

Fig. 8. Cross sections for reaction of Pt+(2D5/2) with H2 as a function of kinetic energy in the center-of-mass frame (lower axis) and laboratory frame (upper axis). The best fit of Eq. (3) with parameters given in the text to the data is shown as a dashed line. The solid line shows this model convoluted over the kinetic and internal energy distributions of the reactant neutral and ion. Adapted from [97]...

As mentioned above, the processes (19.24)-(19.29) have not been studied for electronically excited states of H2. An estimate of the cross-sections for processes (19.24), (19.27)-(19.29) for N > 2 can be made by the SSH model. The available and relatively simple theoretical methods (such as the Born, Born-Rudge and impact-parameter method) can be used to calculate also the cross-section for reactions (19.26), but the difficulties of determining the higher resonant states of prevent easy estimates of cross-sections for reactions (19.25) when N > 2. 

Chemical dynamics experiments in which OH product quantum state distributions and an absolute reaction cross section for reaction (1) could be measured were reported in 1984. Subsequent experiments revealed additional details about the reaction dynamics, including nascent OH( H) spin-orbit and A-doublet rotational fine structure state distributions, Oi P) product fine structure state distributions, and OH angular momentum polarization distributions,as well as differential cross sections. The experimental results indicate that depending on the reagent collision energy... 

In all of these studies, the cross sections for reaction with 0+ were also measured. Mg and Na were found to yield no measurable cross section while cross sections exceeding 100 and 10 A were measured below ion energies of 10 eV for Ca and Fe, respectively. While accidental resonances are not surprising in the case of Fe, given the high density of ionic and... 

Taniike et al. used DFT calculations to probe NO-CO reactions on a dimer of Co atoms on a y-alumina support. These dimers had been shown to exist in previous experiments that also suggested an unusual mechanism in which NO is reduced to N2O via interaction with gas phase CO molecules. The calculations indicated that Co dimers allow the formation of an adsorbed cis-(NO)2 species that has an unusually large reactive cross section for reaction with gaseous CO via an Eley-Rideal mechanism. 

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