124 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 5 



momentum. The struck nucleus remains in other respects unchanged as a 

 result of the collision, and hence no energy is lost to excitation. The kinetic 

 energy transferred to the recoil nucleus is 



4wM sin 2 0/2 _ _, 



Em = —i 1 m2 E» = otEo mev 



[m + my 



where m = mass number of neutron 

 M = mass number of nucleus 

 E = initial energy of neutron, mev 

 = deflection angle of neutron from its initial direction with respect 

 to the center of mass 

 Similarly, the energy lost by the neutron is E n = E {\ — a). The greatest 

 amount of energy is lost in a head-on collision where = 2r. If the nucleus 

 is massive, the neutron will reverse its direction but sustain little loss of 

 energy; however, if the struck nucleus is a free proton, ra ~ Af and the 

 neutron may in a head-on collision be brought practically to rest in a single 

 collision. 



In traversing a scattering medium a fast neutron will make many collisions 

 before it is reduced to thermal velocities. The ratio of the neutron energy 

 after a collision to its initial energy is, on the average, a constant whose 

 magnitude depends on the mass of the scattering nuclei as given by the 

 expression 



E, _, 

 E, 



where £ = 1 - ^-— - — log 



2M 6 M - 1 



M+ 1 

 Ei = initial neutron energy 

 E 2 = final neutron energy 



(for heavy nuclei) 



The average number of collisions required to reduce the neutron from energy 

 E to energy E is then 



N = \ log | 



If the scatterer is a hydrogenous substance, the average residual kinetic 

 energy of the neutron after a collision with a hydrogen atom is 1/e of its 

 initial value; hence, after n collisions the residual neutron energy is just 

 E = E /e n . 



The elastic scattering cross section for nuclei must be determined from 

 experiment because of the absence of sufficiently detailed knowledge of 

 nuclear forces. The functional relation of the cross section has, however. 



