134 



ISOTOPIC TRACERS AND NUCLEAR RADIATIONS 



[Chap. 5 



depth. At a depth x measured along the normal to the boundary the 

 neutron density is 



n 



Q 



te + 9 



At the surface, n has the value 2Q/v inside the medium and the value zero 

 just outside. If the straight line representing n within the medium is 

 extended beyond the boundary, it goes to zero at a distance d = 0.7 IX from 

 the surface, a distance referred to as the extrapolated end point. 



The steady-state distribution of neutrons depends, as indicated by the 

 diffusion equation, on the geometry of the medium and the disposition of the 

 sources. The density distribution is, however, strongly affected also by the 

 presence of strongly absorbing materials placed within the medium and by 

 the character of material bounding the diffusing medium. Absorbing 

 materials such as indium or cadmium foils depress the neutron density in the 

 region near the absorber since they behave as sinks, absorbing all thermal 

 neutrons that enter. Most such substances, however, are nearly transparent 

 to fast neutrons. Those elements which possess large capture cross sections, 

 some of which are commonly used for neutron detectors and shields, are given 

 in Table 19. 



Table 19. Thermal Neutron Absorbers 

 (Approximate total cross section for neutrons of 0.024 ev energy) 



Neutrons that reach the bounding surface of the diffusing medium are 

 ordinarily lost. If, however, a second nonabsorbing medium is placed 

 around the first, some of the neutrons that cross the boundary are sub- 

 sequently scattered back, thus raising the neutron density. The effect of 

 a reflector, which may be any substance including the original diffusing 

 medium, is expressed in terms of its albedo 7, denned as the ratio of the num- 

 ber of neutrons that flow back in across the boundary to the number that 

 flow out. For a spherical diffusing medium of radius R, surrounded by a 

 reflector with a thickness very much greater than the mean free path of the 

 neutrons, 7 has the value 



