A Closed General Solution of the Probability Distribution Function for Three-Dimensional Random Walk Processes
- 1 February 1961
- journal article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 34 (2), 535-546
- https://doi.org/10.1063/1.1700980
Abstract
A closed general solution of the probability distribution function for three‐dimensional random walk processes is derived. In addition: (1) For the particular case of equal‐length displacements, the exact solution is compared with the Gaussian approximation for n=3, 5, and 10 steps. (2) The general solution is utilized in calculating the probability distribution of gamma‐ray energies resulting in the Cl35 (n, γ) Cl36 process. (3) For five unequal steps of fractional length: 0.582, 0.135, 0.131, 0.092, and 0.060 (which is somewhat characteristic of the fractional energies of gamma rays resulting from neutron capture), the exact solution is compared with a Gaussian, a modified Gaussian, and a five equal‐step approximation. (4) There are presented the specific solutions for all possible unequal‐length random displacements involving n=2, 3, and 4 stepsKeywords
This publication has 6 references indexed in Scilit:
- Neutron-Capture Gamma Rays inPhysical Review B, 1959
- Gas Phase Reactions Activated by Nuclear ProcessesJournal of the American Chemical Society, 1957
- Radiation Chemistry and Hot Atom ChemistryAnnual Review of Physical Chemistry, 1955
- Recoil Reactions with High Intensity Slow Neutron Sources. II. The Retention of Radiobromine by Crystalline KBrO31Journal of the American Chemical Society, 1952
- Stochastic Problems in Physics and AstronomyReviews of Modern Physics, 1943
- XXXI. On the problem of random vibrations, and of random flights in one, two, or three dimensionsJournal of Computers in Education, 1919