Sec. 5.5] NEUTRONS 129 



nucleus is left in the ground state after the collision are the energies of the two 

 neutrons equal; in which case the process is indistinguishable from elastic 

 scattering. For inelastic scattering, the difference between the energies of 

 the initial and emitted neutrons is contributed to the excitation of the residual 

 nucleus and is subsequently emitted as gamma radiation. The direction 

 taken by the ejected neutron is purely random since, in effect, the nucleus 

 does not remember the original direction of incident neutron. Inelastically 

 scattered neutrons, therefore, are observed to be emitted uniformly over a 

 sphere. Also it is to be noted that the energy and momentum laws for the 

 collision of hard spherical particles do not hold since part of the energy is lost 

 to excitation. 



If the incident neutron energy is less than the lowest nuclear level, only 

 elastic scattering can occur. On the other hand, when the energy is suffi- 

 ciently high to excite many levels, a neutron may be emitted by any one of 

 many possible level transitions and the observed energy distribution of the 

 neutrons is approximately Maxwellian [8]. 



The observed (n, n) cross section for fast neutrons is found, in many 

 substances, to be a large fraction of the total cross section for all possible 

 processes. 



b. Radiative Capture (n, 7). Since inelastic scattering is known to occur 

 in most instances with an appreciable probability, if it is assumed that this 

 and radiative capture are the only possible process in a particular nucleus, 

 the cross section for (n, 7) is 



= TrRrt - ,' cm 2 



The gamma width T y does not appear to be a sensitive function of the 

 neutron energy and has a value ranging from 0.01 to 1.0 ev for slow neutrons 

 which is assumed to be roughly the same for neutrons of medium energy 

 (10 to 500 kev). Bethe [4] gives for the average capture cross section the 

 expression 



a y = 2 X 10- 22 £-'-' cm 2 



At very high energies, the radiative capture cross section becomes exceedingly 

 small and multiple-neutron and charged-particle emission becomes far more 

 probable. 



c. Multiple-neutron Emission (n, 2n), (n, 3n), .... More than one 

 neutron is emitted provided that the nucleus is left in a sufficiently excited 

 state following emission of the first neutron; i.e., if E b < E { — E ( , where E b is 

 the binding energy of second neutron in the nucleus, £; is the energy of 

 incident neutron, and E t is the energy of first emitted neutron. 



Assuming that the energy distribution of the emitted neutrons can be 



