126 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 5 



r„ « r, and the a at exact resonance is then very much greater than off- 

 resonance values. In general, since potential scattering is the more impor- 

 tant factor, the elastic scattering cross section appears to be relatively- 

 independent of energy. 



Elastic scattering is not easily observed in most nuclei since it is usually 

 obscured by more competitive capture processes. Only in the light elements, 

 excepting Li 6 and B 10 , and a few elements of medium weight are scattering 

 cross sections greater than for capture. Hydrogen is the most important 

 scattering nucleus since it causes the greatest average reduction in energy per 

 collision and exhibits the largest elastic scattering cross section. In the 

 neutron energy range from 1 ev to about 10 kev, the scattering cross section 

 of hydrogen is nearly constant, with a value of about <r s = 21 barns. At 

 lower energies it increases rapidly (<r s « 85 barns for thermal neutrons, see 

 Figs. 35 and 36). 



5.4. Interaction of Slow Neutrons with Nuclei. The interaction of 

 neutrons with nuclei was first treated by Breit and Wigner for the case in 

 which only one nuclear resonance level was important in the process [3]. 

 This was later extended to the more general problem by Bethe and Placzek 

 [5] and others [6,7,8,9]. 



If only one level is important in the interaction process because of the wide 

 spacing of levels in the energy range to which a slow or thermal neutron can 

 excite the nucleus, then the cross section for the formation of a compound 

 nucleus and the emission of a particle (or gamma ray) of the kind q is given 

 by the one-level formula in the form 



2 V " 2i+lJ 



xx r r n r g 



cm 2 



(E - E r y + r 2 /4 



where X = De Broglie wavelength of neutron 

 A r = De Broglie wavelength at resonance 

 E = neutron energy 

 E r = resonance energy 

 r„ = neutron width of level 



T q = level width for emitted particle (or gamma ray) 

 r = total width for all processes 

 The total width T includes all possible processes summed over their 

 respective widths. This includes neutron emission, gamma-ray and charged- 

 particle emission as well as fission. Since the neutron width varies as Efi t 

 the total width can be written in the form 



r = r 



■©"♦X 



ev 



