Good morning boys and girls. In keeping with Th’ Gausslings weakness (sickness??) for odd and specialized information, a quantity known mainly to nuclear reactor operators and other nukkenvolk is trotted out.
Neutron lethargy, or logarithmic energy decrement, u, is a dimensionless logarithm of the ratio of the energy of source neutrons to the energy of neutrons after a collision: u = ln(Eo/E), or, u2-u1 = ln(E1/E2). So, if you plot a curve of E vs u (E = Eo*exp(-u)), you see an exponential decay of energy per unit collision showing that the greatest delta E’s of energy result from the early collisions.
Basically, it shows that in order to obtain thermal neutrons from fission decay neutrons, you have to contain them so that they can rattle around and dump energy before they fly out of the area of interest. As to the number of collisions that are needed? Well, that is a different issue.
Source- Glasstone & Edlund, The Elements of Nuclear Reactor Theory, Van Nostrand, 1952, p 146.