128 ISOTOPTC TRACERS AND NUCLEAR RADIATIONS [Chap. 5 



5.5. Interaction of Fast Neutrons with Nuclei. The interaction of fast 

 neutrons with nuclei involves a single nuclear energy level only when the 

 level spacing is comparable to the total neutron energy. This is sometimes 

 the case for light elements and for energies up to about 1 mev, corresponding 

 to excitation energies of the order of 5 to 8 mev. In medium and heavy nuclei 

 and in light nuclei for high neutron energies, more than one level is excited in 

 the formation of the compound nucleus and in the subsequent emission of 

 radiation (gamma, neutron, or charged particle). The one-level formula is 

 then not valid. When the levels are closely spaced, an average cross section 

 for a particular process must be obtained by summing the one-level formula 

 over all states of the final nucleus. If it can be assumed that the average 

 level spacing is small, i.e., the level density is high, instead of taking a sum of 

 the contributions the averaging can be performed by integrating over an 

 energy range large as compared to the level spacing but small compared to 

 the neutron kinetic energy. The average cross section for the capture of 

 fast neutrons and emission of a particular radiation q is then given by 



a = 7r£ 2 ! y 9 cm 2 



where R = nuclear radius 



T g = particle, radiation, or fission width 

 T = total width for all processes 

 £ = sticking probability 

 Further, the total average cross section for any and all processes, q, which 

 can occur, (n, n), (n, 7), (n, charged particle), fission, etc., is found by sum- 

 ming over the width for all processes. 



a = tR 2 £ cm 2 



The sticking probability £ as used here is defined as the probability that a 

 neutron which strikes a nucleus will stick, i.e., be absorbed to form a com- 

 pound nucleus. For high excitation energies where the nuclear level spacing 

 is small, this is roughly £ = T n /D, where r„ is the neutron width and D is 

 the average level spacing. For high-energy neutrons, and particularly in 

 medium and heavy elements, the sticking probability is nearly unity. For 

 medium energies (~ 1 mev) it appears to be of the order of 0.1 and for low 

 energies, considerably less [4]. At very high energies, therefore, the total 

 cross section is just equal to the geometric cross-sectional area of the nucleus, 

 ttR 2 (~ 10 -25 cm 2 ). This, necessarily, corresponds to energies for which the 

 neutron wavelength is less than the nuclear radius. 



Brief descriptions of the separate processes are given below. 



a. Inelastic Scattering (n, n). The emitted neutron is ejected with less 

 kinetic energy than the incident neutron. Only in the event that the 



