Collision momentum transferring

Knock-on sputtering proceeds via a sequence of individual elastic collisions (momentum transfer) occurring between atoms and/or ions as they come into close proximity to each other. How close they approach depends on the energies involved. At and below 100 keV, the distance of closest approach can be defined via the Coulombic potential as ... 

When a pure gas flows through a channel the accompanying fall in pressure is accounted for partly by acceleration of the flowing stream and partly by momentum transfer to the stationary walls. Since a porous medium may be regarded as an assembly of channels, similar considerations apply to flow through porous media, but in the diffusional situations of principal interest here accelerational pressure loss can usually be neglected. If more than one molecular species is present, we are also interested in the relative motions of the different species, so momentum transfers by collisions between different types of molecules are also important. 

Now encounters between molecules, or between a molecule and the wall are accompanied by momentuin transfer. Thus if the wall acts as a diffuse reflector, molecules colliding wlch it lose all their axial momentum on average, so such encounters directly change the axial momentum of each species. In an intermolecuLar collision there is a lateral transfer of momentum to a different location in the cross-section, but there is also a net change in total momentum for species r if the molecule encountered belongs to a different species. Furthermore, chough the total momentum of a particular species is conserved in collisions between pairs of molecules of this same species, the successive lateral transfers of momentum associated with a sequence of collisions may terminate in momentum transfer to the wall. Thus there are three mechanisms by which a given species may lose momentum in the axial direction ... 

When Che diameter of the Cube is small compared with molecular mean free path lengths in che gas mixture at Che pressure and temperature of interest, molecule-wall collisions are much more frequent Chan molecule-molecule collisions, and the partial pressure gradient of each species is entirely determined by momentum transfer to Che wall by mechanism (i). As shown by Knudsen [3] it is not difficult to estimate the rate of momentum transfer in this case, and hence deduce the flux relations. 

Despite the fact Chat there are no analogs of void fraction or pore size in the model, by varying the proportion of dust particles dispersed among the gas molecules it is possible to move from a situation where most momentum transfer occurs in collisions between pairs of gas molecules, Co one where the principal momentum transfer is between gas molecules and the dust. Thus one might hope to obtain at least a physically reasonable form for the flux relations, over the whole range from bulk diffusion to Knudsen streaming. 

Now suppose we place n molecules in a cubical box of dimension d. The pressure is fixed by the number of wall collisions per second on each square centimeter times the momentum transferred per collision ... 

The original semiclassical version of the centrifugal sudden approximation (SCS) developed by Strekalov [198, 199] consistently takes into account adiabatic corrections to IOS. Since the orbital angular momentum transfer is supposed to be small, scattering occurs in the collision plane. The body-fixed correspondence principle method (BFCP) [200] was used to write the S-matrix for f — jf Massey parameter a>xc. At low quantum numbers, when 0)zc —> 0, it reduces to the usual non-adiabatic expression, which is valid for any Though more complicated, this method is the necessary extension of the previous one adapted to account for adiabatic corrections at higher excitation... 

Inelastic collisions of swift, charged particles with matter are completely described by the distribution of generalized oscillator strengths (GOS s) characterizing the collision. These quantities, characteristic of excitation in the N-electron target (or, in fact, of a dressed projectile as well [1]) from some initial state 0) to a final state n) and concomitant momentum transfer, can be written... 

Given that a collision takes place, the nature of the momentum transfer between the cells must be specified. This should be done in such a way that the total momentum and kinetic energy on the double cell are conserved. There are many ways to do this. A multiparticle collision event may be carried out on all particles in the pair of cells. Alternatively, a hard sphere collision can be mimicked by exchanging the component of the mean velocities of the two cells along da,... 

This limit is actually nonphysical for inelastic collisions, as an excitation to a state with energy n cannot occur with zero momentum transfer. Nonetheless, it is an important limit, which serves to check on experiments on inelastic collisions (Lassettre and Francis, 1964), and it shows clearly the similarity between optical transitions and collision with fast chaiged particles for which K is small. From (4.13) and (4.14), one can write... 

The dipole oscillator strength is the dominant factor in dipole-allowed transitions, as in photoabsorption. Bethe (1930) showed that for charged-particle impact, the transition probability is proportional to the matrix elements of the operator exp(ik r), where ftk is the momentum transfer. Thus, in collision with fast charged particles where k r is small, the process is again controlled by dipole oscillator strength (see Sects. 2.3.4 and 4.5). 

At long times the excess temperature, (T) - T, decays exponentially, as can be shown from the preceding equation. The relaxation rate has independent, additive contributions from momentum transfer collisions (as in the case of rare gases) and from each pair of states connected by inelastic collision. Thus the net relaxation rate is given by... 

Symbols m, momentum transfer collision v, vibrational collision (0<- l) J (0 through 6) means rotational collision (JoJ + 2). Other processes make negligible contribution in this temperature range. 

Liquefied rare gases(LRGs) are very important both from the fundamental point of view and in application to ionization chambers. In these media, epithermal electrons are characterized by a very large mean free path for momentum transfer -10-15 nm, whereas the mean free path for energy loss by elastic collision is only -0.5 nm. This is caused by coherence in momentum transfer scattering exhibited by a small value of the structure factor at low momentum transfers... 

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