Emergent direction cosines

If (/, m, n) and (/, m, n ) are the incident and emergent direction cosines of the neutron, respectively, collision theory) in the laboratory system of coordinates, and T the azimuthal angle which is random in the range (0, 2ti), then for anisotropic scattering in the laboratory system... 

Molecular flow occurs under conditions where Kn > 0.5 - the mean free path of the particles exceeds the smallest dimension of the flow channel. Under such conditions, with thin-walled orifices, for example, gas particles will pass through almost without collision. With pipes and ducts, however, this is not the case. Particularly for low Kn values (1-10) of the particles that enter the duct, some may reach the exit whilst the remainder return to the entrance after a number of collisions with the duct walls. What is important about such collisions is that, on collision with a wall, the particles are regarded as being immobilised for a very short time before emerging in any direction with equal probability (according to the cosine law). This describes diffuse or random scattering where no particular direction is favoured. To describe this process, the concept of transmission probability (Pr) was introduced by Clausing. 

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