Penetration probability, particle

The penetration probability of a particle passing through the diffusion battery is given by (Busigin et al., 1980)... 

The matrix elements in angle brackets contain nuclear factors and (in the case of charged particles) the Coulomb barrier penetration probabilities or Gamow factors, originally calculated in the theory of a-decay, which can be roughly estimated as follows (Fig. 2.7). 

Fig. 2.28 Particle penetration probability in field dissociation of 4HeRh + and 3HeRh2+ from a vibrational state 300 K and 500 K above the bottom of the potential energy curve. At the same field, the particle barrier penetration probability for 3HeRh2+ is three to four orders of magnitude smaller than that for 4HeRh2+, in good agreement with the experiment.

For slow neutron-induced reactions that do not involve resonances, we know (Chapter 10) that ct ( ) °c 1 /vn so that (ctv) is a constant. For charged particle reactions, one must overcome the repulsive Coulomb force between the positively charged nuclei. For the simplest reaction, p + p, the Coulomb barrier is 550 keV. But, in a typical star such as the sun, kT is 1.3 keV, that is, the nuclear reactions that occur are subbarrier, and the resulting reactions are the result of barrier penetration. (At a proton-proton center-of-mass energy of 1 keV, the barrier penetration probability is 2 x 10-10). At these extreme subbarrier energies, the barrier penetration factor can be approximated as ... 

Due to the well known human shortcomings the probability of finding flaws using Magnetic Particle Inspection (MPI) or Liquid Penetrant Inspection (LPI) can be restricted to only 60-85% and the inspection reproducablity is difficult. 

Probably the most important powder property governing the formation of atomic bonds is the surface condition of the particles, especially with respect to the presence of oxide films. If heavy oxide layers are present, they must be penetrated by projections on the particles. This results in only local rather than widespread bonding. A ductile metal such as iron which has a heavy oxide layer may not form as strong or as many bonds as a less ductile metal. 

While it is inherently probable that product formation will be most readily initiated at sites of effective contact between reactants (A IB), it is improbable that this process alone is capable of permitting continued product formation at low temperature for two related reasons. Firstly (as discussed in detail in Sect. 2.1.1) the area available for chemical contact in a mixture of particles is a very small fraction of the total surface (and, indeed, this total surface constitutes only a small proportion of the reactant present). Secondly, bulk diffusion across a barrier layer is usually an activated process, so that interposition of product between the points of initial contact reduces the ease, and therefore the rate, of interaction. On completion of the first step in the reaction, the restricted zones of direct contact have undergone chemical modification and the continuation of reaction necessitates a transport process to maintain the migration of material from one solid to a reactive surface of the other. On increasing the temperature, surface migration usually becomes appreciable at temperatures significantly below those required for the onset of bulk diffusion within a product phase. It is to be expected that components of the less refractory constituent will migrate onto the surfaces of the other solid present. These ions are chemisorbed as the first step in product formation and, in a subsequent process, penetrate the outer layers of the... 

The probability current is conserved for E>V. When penetrating the barrier, E — V becomes negative and decays as g-C/ dv i2m(v(x)-E)]8x as particle moves from position x + <5x to position x. The total probability of... 

However, if the particulates or solutes accumulated on the surface can be dispersed back into the bulk fluid, these membranes can be used to great advantage since there is relatively little if any "internal-fouling" of the membrane structure. There is a high probability that a molecule or particle which penetrates the skin will not be trapped within the filter structure but will pass through into the filtrate. Schematically, the pores may be represented by ever-widening cones with no internal constrictions to restrain molecules or particles. 

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