Close-collision

I like to emphasize that Fig. 1 is not meant to indicate any fundamental limitation of quantum mechanics both Bohr s and Bethe s formulae invoke mathematical approximations to the underlying physical models, and Bethe s formula in particular relies on first-order perturbation theory for both distant and close collisions. 

It was seen in the previous section that the main difference between Bethe s and Bohr s descriptions lies in the dynamics of close collisions, in which electron binding is unimportant. This feature is beautifully illustrated by Bethe s sum rule [5] which expresses the mean energy transfer to a target electron at a given momentum transfer hq as... 

T Each close collision switches the orbit by a distance of the... 

Lamb dip spectroscopy provides a very sensitive tool for studying small frequency shifts and broadening of spectral lines which normally would be undetectable because they may be small compared to the doppler width. These investigations yield information about collisions at low pressures, where the effect of far distant collisions is not suppressed by the more effective close collisions. This allows the potential between the collision partners at large intermolecular distances to be examined. 

By careful inspection of the relationships of the semiclassical close collision approximations and Bethe formula, one can obtain simple and accurate information on ionization cross sections. By the method first proposed by Platzman, and used extensively by others, it is instructive to form the ratio of the differential cross sections [measured c(W,T) or calculated da(W,T)ldW)] to the Rutherford cross section. This ratio, called Y, is mathematically defined as... 

Because the semiclassical theories can be used to calculate differential cross sections with relative ease for close collisions between the incident charged particle and the bound electron, and the Bethe theory provides a straightforward method to describe low-energy electrons ejected in distant collisions, it is only natural to combine the best characteristics of the two approaches to derive a comprehensive description of electron impact ionization. 

The second subregion corresponds to large to and q and is related to close collisions (the knock-on). At very large transferred momenta (qa0> 1) the inelastic scattering by a molecule (an atom) is actually the elastic scattering by a free electron with the cross section given by Rutherford formula. In this case the function /(to, q) can be presented analytically as a delta function ... 

Formula (6.3) makes no allowance for the energy losses in close collisions with molecules, including those in which a negative intermediate ion is formed. So the conclusions of Ref. 29 are correct only if... 

There are two reasons why so much is unknown. First, at high densities three (and even four) body forces are important. This is particularly so when chemically reactive atoms are present. Then, even for two-body forces, the strongly repulsive regime is not well understood and, in addition, close in, as one approaches the united atom limit, there is considerable promotion of molecular orbitals. This is a universal mechanism for electronic excitation which means a breakdown of the Born-Oppenheimer approximation for close collisions. 

Reactions involving a close collision for the first electron transfer. They will be exemplified by the Ba + H2O system. 

It is reasonable to neglect the last term Vrecoii- By doing this transitions are excluded which are due to the interaction of the active electron with the recoiling target nucleus. This so-called recoil effect leads to insignificant contributions to total cross sections, but may be important for very close collisions (b < 10 a.u.) [33]. Before the solution of equation (3) is... 

Angular distributions of the positive ions produced by reactive ionization were found to be much broader in accord with the expectation that rather close collisions are necessary for this process. As an example, Fig. 27 shows Cohen s results on Ba + 02. 

After an approximate separation of the track into its high and low LET regions, we want to know about the energy partition between these two regions. The energy loss in the electron capture process is confined to the core by virtue of the fact that a capture may only occur in a close collision. In the electron loss process the lost electron is likely to be... 

We consider first the question of collision mechanism first, that the calculation of a close-collision cross section places no mechanistic constraints on the ensuing reaction and second, the important corollary that mechanistic statements may not be deduced from the shape of excitation functions. Next, the validity of the potential is examined,f this necessarily setting an upper bound to the energy at which the model may be applied. Various applications of the model are then considered and its success evaluated. Finally, the various explanations which have been advanced to rationalize its failure are discussed. 

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