Sec. 6.4] FISSION 151 



but division becomes highly probable for small deformations in the spherical 

 form induced by external excitation. Classically, the minimum or critical 

 excitation energy required to induce fission is equivalent to the height of the 

 potential or fission barrier formed by the difference of the attractive nuclear 

 field and repulsive electrostatic field. Alternatively, it is the energy neces- 

 sary to induce a deformation of a liquid drop for which the cohesive forces 

 become smaller than the repulsive forces within the drop. The height of 

 the barrier decreases with increasing value of Z 2 /A, and when Z 2 /A = 47.8, 

 the fission barrier vanishes entirely. 



For nuclei with Z 2 /A near the limiting value, the critical excitation energy 

 for fission was calculated by Bohr and Wheeler [4] who gave the expression 



E = AttItA^ 

 where x = Z 2 /47.$A 



98 11,368 ,, u 



135 (1 ~ x) 34^25 (1 - X) + ••• J mev 



Airr 2 T =14 mev 



r = 1.47 X 10- w cm [4,8] 



When the critical energy of a nucleus is smaller than the neutron binding 

 energy, as it is for U 234 , fission can follow from the capture of thermal neu- 

 trons. When on the other hand it is greater than the binding energy, fission 

 becomes probable only when the kinetic energy of the incident neutron is 

 great enough to make up the deficit. An estimate of the neutron binding 

 energy in heavy nuclei, therefore, is important to determine the neutron 

 kinetic energy necessary to induce fission. For nuclei with masses greater 

 than A = 230, the neutron binding energy has a value between 5 and 7 mev. 

 On capture of a neutron this energy plus the neutron kinetic energy is con- 

 tributed to excitation of the compound nucleus. From the relation Mc 2 = E, 

 the binding energy Ei can be calculated from the mass difference of the initial 

 and compound nuclei 



E b = 931 (If .4 - M A+l + n) 



for which the masses M A and M A +\ may be estimated from the semiempirical 

 relation given in Sec. 1.4. 



Spontaneous fission is possible but relatively improbable in unexcited 

 nuclei and in nuclei with less than the critical excitation energy. The half- 

 life for spontaneous fission from the ground state appears to be 10 17 to 10 22 

 years for fissionable nuclei such as thorium, uranium, and plutonium. 



8.4. Fission Fragments. The mass distribution of fission fragments 

 exhibits a marked asymmetry about a value of one-half the mass of the 

 initial compound nucleus. Division into two fragments of nearly equal 

 mass occurs with little probability, ~ 0.01 per cent; instead, as shown in 



