STATISTICS OF PARTICLE DIFFUSION IN SPHERICAL GEOMETRY
The diffusion of particles from the center of a sphere of radius R is considered theoretically. An expression is obtained for the probability that a particle will be collected at a small probe within the sphere rather than at the surface. This result forms the basis for an experiment to determine the momentum transfer cross section Q/sub m/ for electrons in a gas. The only parameter which must be known in order to obtain absolute cross sections by the technique proposed is the acceptance coefficient for electrons at the probe. The probability A/sub c/ that a particle will have exactly c collisions characterized by a constant cross section Q before striking the surface of the sphere for the first time is evaluated. It is assumed that these collisions are not correlated with the diffusion process. In contrast with previous work the present method takes into account the variation of total diffusion time as well as the probability of a particular number of collisions during a given time. The probabilities A/sub 0/, A/sub 1/, and A/sub 2/ are given in terms of elementary functions and a recursion relationship is given for the other A's. The expression A/sub 0/ = y csch y (where y = RN(3QQm)/sup 1/2/ and N is the gas density) is useful in an experiment to determine the cross section for inelastic collisions between electrons and gases. The probability of more than any given number of collisions, the average number of collisions, and the mean-square deviation from this average are also evaluated. (auth)
- Research Organization:
- Minneapolis-Honeywell Research Center, Hopkins, Minn.
- NSA Number:
- NSA-17-022340
- OSTI ID:
- 4693200
- Journal Information:
- Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Vol. Vol: 130; Other Information: Orig. Receipt Date: 31-DEC-63
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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