Charge transfer impact parameter

During slow collisions, the main contribution to the charge transfer cross-section is made by the impact parameters which exceed the size of a neutral atom. In this case, the potential barrier for tunneling is mainly formed by the electric field of the multiply charged ion in the vicinity of the neutral atom (Fig. 8). This field is equal to F = zjR2. The probability of... 

From this equation we can see that, in the problem considered, the characteristic size (in atomic units) is of the order of yfz consequently, the time of collision has the order of y/z/v, where v is the relative velocity of the colliding particles. The probability of charge transfer during the collision with the impact parameter p can be estimated if we multiply the probability of tunneling per unit time by the time of collision... 

Equating P(p) to unity, we obtain the characteristic impact parameter, p0, of charge transfer... 

Following from formula (4.54), the transfer of energy on excitation of molecules has a noticeable probability even in the case where the impact parameter is much greater than their size d. Since the intermolecular spacings in a condensed medium are of order of d, a charged particle interacts with many of its molecules. The polarization of these molecules weakens the field of the particle, which, in its turn, weakens the interaction of the particle with the molecules located far from the track. This results in that the actual ionization losses are smaller than the value we would get by simply summing the losses in collisions with individual molecules given by formula (5.1). This polarization (density) effect was first pointed out by Swann,205 while the principles of calculation of ionization losses in a dense medium were developed by Fermi.206... 

Before, however, proceeding to the results, we should discuss electronic and structural parameters of the given systems as they potentially impact the charge-transfer mechanism. 

To conclude, we can derive several criteria that we should bear in mind when designing and studying novel molecular-wire systems, especially regarding the impact of structural parameters on the charge-transfer properties ... 

Wa92a Z. Wan, J. F. Christian and S. L. Anderson, Ne -fCso Collision Energy and Impact Parameter Dependence for Endohedral Complex Formation, FVagmentation, and Charge Transfer, J. Chem. Phys. 96, 3344-3347 (1992). 

The first channel is formally endoergic charge transfer, which can occur through a variety of mechanisms. For example, in large impact parameter collisions, the time-dependent ion-induced polarization can result in electron hopping from C o to the M ion. This mechanism has been investigated for several atom-cluster ion systems [22], and is only efficient when the following condition is satisfied / AIP—hv, where AIP IP(CM) IP(Af)> v is the relative velocity of the M ion to the Cgo, and R is... 

Thus, the even orders of an Zp expansion, as included in the unitary convolution approximation (UCA), dominate the non-perturbative efifects. The present UCA results are plotted as a solid curve. This curve lies close to the average of the AO results for particles and antiparticles. Hence, although the present UCA does not include sign-of-charge efifects it perfectly describes the majority of the energy transfer processes (dominated by ionization) of fast heavy particles at small impact parameters. 

Figurel.8 (a) Probability for excitation of the 1 s j /2 state of U91 + in U92+ (y = 1.5)+U9l+ collisions as a function of the impact parameter. The solid curve is calculated with the finite-element method, the dashed curve with perturbation theory, (b) The same for charge transfer into the ground state of the projectile ion.

For the other reactant states the competition between reaction and charge transfer can be described by a simple model similar to that of North and Leventhal [22]. We restrict the discussion to collisions of N2+ (X v) + H2. The model assumes that all collisions with impact parameters less than bR give chemical reaction. Then... 

The probability ampbtude is determined by projecting the final END electronic wave function, li/r) for each impact parameter, on a particular determinant in the same basis set, and introducing the result into equation (25) for the charge transfer differential cross section. 

The major application of this technique, principally by Lindholm and co-workers (see Chapter 10), has capitalized on the above limitation in a study of charge-transfer processes, where the products may exhibit a thermal energy distribution. Even in this application, cross sections are difficult to obtain because the sampling volume is not well defined. Lindholm has been careful to quote only Q values which are estimates of the relative reaction efficiencies. There is another reason why any such cross section so measured may be unreliable. It is plausible, and indeed it has recently been demonstrated, that charge-transfer reactions may yield some products which are forward-scattered in the laboratory framework these would result from collisions with small impact parameters. To the extent that these products will not be detected in a transverse tandem machine, the measured cross section will be underestimated. 

---