Capture probability

It is important to note that the neutron capture probability, called the cross section a, is vasdy different for various elements. Excellent sensitivity for Au is due largely to its high cross section (a = 100 barns 1 barn = 1 x 10 cm ). Other elements, such as Pb, have low cross sections and much poorer detection limits. 

From the high inverse power dependence of CTe on v as seen from Eq. (3.5), it is clear that capture probability increases very rapidly with slowing down. The equilibrium ionic charge can be estimated at a given velocity from Eqs. (3.4) and (3.5). Since charge exchange is a nonequilibrium phenomenon,... 

The proton capture probability might be measured by the proton affinity. For H20 the latter is 182 kcal/mole while for NH3 a value of 207 kcal/mole has been proposed (13). The (ethyl) namines would probably have intermediate values, considering their pKb. The probability that Reaction 11 could go from left to right would not be too different from that of Reaction 12 going from right to left. Therefore, from Reactions 11 and 12... 

If the oppositely charged carriers are generated independently far away of each other (e.g. injected from electrodes) volume-controlled recombination (VR) takes place, the carriers are statistically independent of each other, the recombination process is kinetically bimolecular. It naturally proceeds through a Coulombically correlated electron-hole pair (e h) leading to various emitting states in the ultimate recombination step (mutual carrier capture) (Fig. 3 for more details, see Figs. 11 and 27 in Sec. 2.3). As a result, the overall recombination probability becomes a product of the probability of the pair formation, Pr(1) = (1 + Tm/Tt) , and the capture probability, PR(2) = (1 + tc/t(1)... 

Recently, the capture hypothesis has gained fresh support despite the generally known fact that the capture probability of the Moon is very low. One can, of course, always argue that, as there is only one Moon, statistical laws do not apply. 

The results of Figure 13 suggest that as the droplet size increases, the emulsion retention increases. The large droplets have a higher capture probability and fill up more of the pores faster, a result that explains why they elute later than the smaller droplets. Emulsions with small droplet size diameters elute with essentially the inlet size distributions. Two factors control permeability reduction the total volume of droplets retained and the effectiveness of these droplets in restricting fiow. For a given porous medium, a critical mean droplet size of the emulsion controls permeability reduction. Below this value, retention of oil in porous media is dominant, and above the critical mean droplet size, their obstruction ability is pronounced. This situation explains the trends shown in Figure 13 for the effect of droplet size on permeability reduction. These conclusions are valid for stable, very dilute OAV emulsions and are based on a few experiments. 

The form of (s) has not been specified, but the problem is identical to that discussed in Section III F in terms of the function A (o) of Eq. (3.47). The result is more general in that feedback by redissociation has been taken into account. The inverse transformation of p s) gives the time evolution of the capture probability. The initial rate is k[ and the steady-state rate is k" for k = 0. 

In nuclear technology, any material with a high capture probability for neutrons that may divert an undesirable number of neutrons from the fission chain reaction. 

Recalling from Eq. (36) the relationship between kf and the capture probability y, we see from Eq. (40) that for this present case of cell surface receptors, the capture probability for the entire cell is... 

To obtain the overall uncoupling rate constant, ku, we can again make use of the capture probability y [see Eq. (35)], such that kc = yk+. Recall that y quantifies the extent to which receptor/ligand association is rate-limited by the reaction step. As y approaches 0, association is severely reaction-limited, while as y nears 1, binding is almost purely diffusion-limited. ku is thus given by... 

Fig. 17. Capture probability for receptor density of 5 X 105 receptors/cell. (a) Probability of autocrine ligand capture is shown for various truncation distances Q. (b) The probability of capture at infinite dilution can be calculated by plotting the capture probability versus e Q. A linear fit to the data provides the y-intercept PJ.R).

Fig. 18. Probability of autocrine ligand capture. The capture probability is plotted as a function of the receptor density. Typical growth factor receptor densities are 104 to 106 receptors/cell.

Table 1. Thermal neutron capture probabilities for elements in rock matrices.

Elements that do not contribute >1% of the total capture probability for at least one rock type have not been tabulated. Rock composition used is from Parker (1967). 

Table 3. Neutron production, Li capture probability, and He/ He in average cmst.

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