Fast collisions

The use of the Born approximation is valid only for fast collisions. According to Ref. 144, the authors of which compared the experimental values of the cross sections for the HzO molecule with those predicted by formulas (4.38) and (4.39), the agreement is good only at electron energies exceeding 1 keV, whereas at lower energies the predicted values are greater than the actual ones. 

Vertical oxidation or reduction by fast collisions can cause excitation in the neutral intermediate. The excitation energy (Eexc) can be expressed as consisting of three terms (Eq. 3) ... 

The presence of such a process can explain the characteristics of Ma and M 3 lines these emissions behave like emission bands they are asymmetrical in the metal, clearly broader than the absorption hnes, and their position and shape vary with binding. Their broadening is due to fast collisions of the conduction or valence electrons with the 4/hole and depends on these electron distributions, explaining that the Ma and M 3 shape is different in the metal and the oxide. Lastly, the energies of Ma and M/3 are not characteristic of the atomic transition 3 4/ 3c 4/". The life-... 

This is how fast collisions occur. Now we also have to make up a little picture of the surface and adsorbed layer(s) that the collisions are involved with, as in Figure 3.8. In each layer there is a dynamic equilibrium. Consider adsorption in the first... 

The following discussion of theoretical aspects shall be restricted to fast collisions, i.e. to cases where the incident electron acts only as a momentum perturbation on the target system, which in turn responds as an isolated system. The momentum transfer is small in such a process and dipole selection rules apply for single electron excitations. 

The probability for single electron excitations depends on the kinematics of the incident electron and the transition probability (Celotta and Huebner, 1979). Within the approximation of fast collisions this transition probability is described by the dipole matrix element of the initial and final state of the target. Summing up over all possible excitations with AE the energy distribution of fast inelastically scattered electrons is obtained. 

The continuous agitation of the grinding media leads to frequent and fast collisions between the coarse heads. In the event of such a collision, the feed... 

We return to the approximate methods introduced earlier, and make use of ideas due to Reisenfeld and Watson [7.12] and Glauber [5.2], and those of the crazed maze. In a fast collision the electrons do not have time to move before the collision is over. They therefore do not sense the binding forces which hold them to the target in comparison to the strong shortlived impulse produced by the projectile. They recoil freely because they do not move far during the collision time. TMs is as true of electron-electron correlating forces as it is of the electron-target nuclear forces. 

Fast collision between trains 1.39E-02 Fast collision between trains 1.23E-04... 

D is the dynamical structural factor of the surface vibrations, and W is the Debye-Waller exponent, that for fast collisions may be written as... 

Inelastic collisions of the electrons with atomic targets are usually divided into two regimes, fast collisions and slow collisions, depending on the... 

The mechanics of atoms is often divided into "structure" and "collision" problems. I view here "collisions" as including any nonperturbative excitation process or chemical reaction, more generally any transformation of the structure of matter. The independent particle model has proved extremely successful for describing and interpreting structures in fact it is conmionly regarded as the theory of atomic systems. This model has also accounted for optical transitions and for fast collisions, which can be treated as weak perturbations of atoms. Its scope and power have been extended by configuration mixing and other procedures. 

BeUdc D (1978) A quantum theory of ionisation in fast collisions between ions and atomic systems. J Phys B At Mol Phys 11 3529. doi 10.1088/0022-3700/11/20/015... 

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