150 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 6 



resonances are absent varies as E~ V K When, because of a high fission barrier, 

 fission can be induced only by fast neutrons, the resonance levels of the 

 nucleus are broad and closely spaced and thus lose their identity. The 

 cross section in this case decreases almost uniformly with increasing energy 

 approximately as E" 1 . 



The reaction time of nuclear processes or, more correctly, the mean life 

 of a highly excited nucleus is in general exceedingly small, < 10 -10 sec. 

 It is to be expected therefore that under conditions which make fission a 

 highly probable process compared to radiation and neutron emission the mean 

 time for fission following neutron capture should be of this order of magnitude. 

 This was demonstrated in experiments by Feather [13], indicating that 

 fission may occur in an interval at least as short as 5 X 10 -13 sec, and by 



Fig. 44. Simplified concept of deformation of liquid-drop nucleus undergoing fission. 

 The unexcited nucleus is represented as a sphere with uniform distribution of charge 

 (protons). The relative strengths of the surface tension r and electrostatic forces E are 

 indicated by lengths of vectors. Deformation of the drop induced by external forces 

 causes a reduction in r at the point of least curvature and an increase in the repulsive force 

 E due to the redistribution of charge to regions of large curvature. 



Wilson [14] who showed that less than 5 X 10 -5 of the fissions are delayed as 

 long as 10~ 8 sec. 



6.3. Stability of Heavy Nuclei. The stability of heavy nuclei against 

 fission depends on the relative magnitudes of the short-range nuclear forces 

 responsible for an effective surface tension and the repulsive electrostatic 

 field of the protons. Since the volume of the nucleus is directly proportional 

 to the number of particles, A, it contains [7], the energy associated with the 

 short-range forces maintaining a stable spherical nucleus is proportional to 

 the nuclear surface, A-kR 2 ~ A ^. Counteracting this, the uniform distribution 

 of charge eZ gives rise to an electrostatic energy proportional to Z 2 A ^ which 

 increases more rapidly with nuclear size than does the surface tension. A 

 critical value of the ratio of the two fields, expressed by Z 2 {A^/A^) = Z 2 /A, 

 is attained for increasing nuclear size when the electrostatic field exceeds the 

 nuclear binding forces and the nucleus is no longer stable against spontaneous 

 fission. A semiempirical calculation by Bohr and Wheeler [4] leads to a 

 critical value of Z 2 /A = 47.8. 



Nuclei with Z 2 /A only slightly smaller (~ 15 per cent) than the critical 

 value exhibit a marked stability against spontaneous fission when unexcited, 



