Sec. 5.4] NEUTRONS 127 



Ordinarily, for slow neutrons only one kind of particle has a high probability 

 for emission and the contribution of other processes to T is negligible. Fur- 

 thermore, the emission of a neutron (inelastic scattering) is important only 

 when simple capture with gamma emission is unlikely and when the emission 

 of a charged particle is energetically impossible because of the potential 

 barrier. But usually, T n « T q as seen from the fact that the observed ratio 

 for these two widths is ~ 10~ 3 . The total width can, therefore, in many 

 instances be set equal to the particle width: r = T q . In individual cases, 

 the relative magnitude of the neutron width can be determined experiment- 

 ally from the cross section at exact resonance since the cross section is then 

 directly proportional to the ratio of the neutron to particle width. 



w--!( 1± stt)«t 



From the one-level formula for elastic scattering and the similar formula 

 above for capture, the ratio of the two cross sections gives the relative prob- 

 ability at resonance for elastic scattering (neglecting potential scattering) 

 with respect to a competing capture process (with particle or gamma-ray 

 emission). 



cr s T T , 



(Tn r. 



ar 



This ratio is greater than unity for most of the light elements (except Li 6 

 and B 10 ) and in general is less than unity for elements of medium atomic 

 weight (except iron, nickel, and copper). 



The emission width T g for charged particles is the product of the particle 

 width without the potential barrier, T'„, and the penetrability P of the barrier, 

 or T = T'gPq, where P q = e~ f and / is a function of the height and width of 

 the barrier. Because of the factor P, charged-particle emission in all but the 

 lightest elements and in the special case of fission is extremely improbable 

 under slow neutron bombardment. Proton emission is known only for 

 N 14 although it is energetically possible for B 10 [4]. Alpha-particle emission 

 is observed only in Li 6 and B 10 which have very large cross sections, about 

 3,000 and 900 barns, respectively. Without a more exact and detailed model 

 for the nucleus, the most probable process and its width must be determined 

 experimentally. In general, it will include any one of the processes (n, n), 

 (n, p), (n, a), (n, 7) and fission. 



If the energy of the neutron is small compared to the first resonance level, 

 or if it is small compared to the width of the first level, i.e., if £« E T or 

 E « T, then the resonance terms become unimportant and the cross section 

 for capture varies directly with X r , or as 1/v, where v is the neutron velocity. 

 This is observed most clearly in rhodium, indium and iridium for thermal 

 neutrons, and in B 10 for energies as high as ~ 0.1 mev. 



