Collision cross particle transfer

Decreasing particle size means increased effort required to remove it. This rule arises from the smaller interaction cross sections for collision and momentum transfer. Furthermore, the electrostatic forces are stronger for smaller particles, and they diminish in proportion to 1/r as opposed to 1/r. Both of these factors lead to redeposition being a major source of small particles. Since mechanical action requires increasing amounts of work, chemical dissolution is more effective at removing small particles than is mechanical action. 

Despite the fact that Bohr s stopping power theory is useful for heavy charged particles such as fission fragments, Rutherford s collision cross section on which it is based is not accurate unless both the incident particle velocity and that of the ejected electron are much greater than that of the atomic electrons. The quantum mechanical theory of Bethe, with energy and momentum transfers as kinematic variables, is based on the first Born approximation and certain other approximations [1,2]. This theory also requires high incident velocity. At relatively moderate velocities certain modifications, shell corrections, can be made to extend the validity of the approximation. Other corrections for relativistic effects and polarization screening (density effects) are easily made. Nevertheless, the Bethe-Born approximation... 

Equation (4.10) defines the total collision cross-section, cr(E). between an energetic particle of energy E and the target atoms. The total cross-section gives a measure of the probability for any type of collision to occur where energy-transfers are possible, for energies up to and including the maximum value... 

That is, if one compares the cross-sections at the same kinetic energy E of the incident ion, the transfer of a H atom always occurs with a larger cross-section than the transfer of a D atom. (The cross-sections at the same relative kinetic energy are equal since the effective radial potential in which the particles move during the collision is the same for H- and D-atom transfer. The effective potential is the sum of the potentials... 

The first discussion of the thermalization of positronium appears to have been that of Sauder (1968), who derived a general (classical) expression for moderation by elastic collisions of a particle in a medium, allowing for the thermal motion of the atoms or molecules of the medium. By assuming that the momentum transfer cross section, om, is a constant he found that the time dependence of the mean positronium kinetic energy,... 

A necessary condition for the two-term expansion of the distribution function of equation (2) to be valid is that the electron collision frequency for momentum transfer must be larger than the total electron collision frequency for excitation for all values of electron energy. Under these conditions electron-heavy particle momentum-transfer collisions are of major importance in reducing the asymmetry in the distribution function. In many cases as pointed out by Phelps in ref. 34, this condition is not met in the analysis of N2, CO, and C02 transport data primarily because of large vibrational excitation cross sections. The effect on the accuracy of the determination of distribution functions as a result is a factor still remaining to be assessed. 

Transfer of energy for the different species in a plasma results from the non-radiative as well as from the radiative processes taking place. Non-radiative processes involve collisions and radiative processes involve emission, absorption and fluorescence of radiation. The efficiency of collision processes is described by the cross section This reflects the loss in impulse a particle with mass m and velocity v undergoes when it collides with a particle with mass M. It can be given by ... 

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