Diffusion of Neutrons

Diffusion of Neutrons


the dissemination of neutrons in a substance, accompanied by repeated change in their direction and rate of motion as a result of collisions with atomic nuclei. The diffusion of neutrons is analogous to diffusion in gases and conforms to the same laws. Upon diffusion, fast neutrons—that is, neutrons whose energy is many times greater than the average energy of thermal motion of the particles of the medium—transfer energy to the medium and are retarded. In weakly absorbing mediums, neutrons reach thermal equilibrium with the medium (thermal neutrons). In an infinite medium a thermal neutron diffuses until absorbed by one of the atomic nuclei. The diffusion of thermal neutrons is characterized by the diffusion coefficient D and the mean square of the distance from the point of formation of the thermal neutron to its point of absorption, which is equal to L2T = 6Dt, where t is the average lifetime of a thermal neutron in the medium.

The mean square distance L2F between the point of formation of a fast neutron (in a nuclear reaction such as a fission reaction) and its point of deceleration to thermal energy is used to characterize the diffusion of fast neutrons. The values of L2T for thermal neutrons and of L2F for neutrons emitted upon fission of uranium are presented in Table 1 for certain mediums.

Table 1. Values of L2T and L2T for some substances
 L2T (cm2)L2F (cm2)Diffusion of Neutrons
Water (H2O) ...............44 ...............186 ...............15 ...............
Heavy water (D2O)1.5 × 105750390
Beryllium (Be)2,60051656
Graphite (C)20,0001,880150

Upon diffusion in a finite medium, a neutron flies out of the medium with high probability if the half-dimension (radius) of the system is small in comparison with the quantity Diffusion of Neutrons, conversely, a neutron will be absorbed in the medium with high probability if its radius is great in comparison with this quantity.

The diffusion of neutrons plays a significant role in the operation of nuclear reactors. In connection with this, the development of nuclear reactors was accompanied by the intensive development of the theory of neutron diffusion and of methods of studying it experimentally.


Beckurts, K., and K. Wirts. Neitronnaia fizika. Moscow, 1968. (Translated from English.)
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