Sec. 4.13] PROTONS, DEUTERONS, AND ALPHA PARTICLES 93 



The + sign is used if M > m, and — sign if M < m. This expression 

 obviously reduces to the preceding formula when M y>> m. 



Although particles will be scattered in all directions, the intensity drops off 

 very rapidly with increasing angle as measured from the forward direction, 

 thus in the case of alpha particles on platinum, less than 1 particle in 8,000 

 will be scattered into an angle greater than 90 deg. Backscattering in light 

 elements, consequently, is entirely negligible. In general, calculations of 

 scattering of particles by heavy elements for energies up to about 10 mev are 

 given to a high degree of accuracy by the Rutherford formulas. 



Deviations from Rutherford (coulomb field) scattering calculated from 

 the formulas above will be found for certain energies of the incident particle 

 depending upon the properties of the scattering nucleus. Anomalous scatter- 

 ing will occur if the particle possesses sufficient energy to penetrate the 

 electrostatic potential barrier and be affected by the nuclear forces or if the 

 energy of the particle plus the internal energy of the scattering nucleus equals 

 the energy of a quantum state of the compound nucleus. Anomalous 

 scattering that increases slowly with increased particle energy can usually be 

 identified with penetration of the potential barrier. Anomalous scattering 

 that increases rapidly to a maximum intensity and then decreases as the 

 energy is increased indicates resonance scattering. 



4.13. Alpha Decay. The theory of alpha decay is based on the now 

 familiar quantum mechanical problem of the penetration of charged particles 

 through potential barriers. Some assumptions must be made about the 

 shape of the potential field forming the barrier, but the theory can account 

 for the main details of alpha emission and provide estimates of its probability. 



If it is assumed that the alpha particle already exists as a separate entity 

 within the nucleus and that the only effect of the remaining particles on it is 

 to provide a potential "well" in which the alpha particle exists in some energy 

 state, the problem immediately reduces to the one-body model for alpha 

 decay [19,20]. 



Within the nucleus it is assumed that alpha particles can move with relative 

 freedom, but at the surface it is constrained from leaving by an effective 

 surface tension maintained by the unsaturated, attractive nuclear forces of 

 those particles lying at the surface. This force rises rapidly to a maximum 

 value at a distance approximately equal to the nuclear radius. Beyond the 

 radius, the nuclear potential field rapidly vanishes, and only the coulomb 

 field due to the protons remains. The height of the potential barrier above 

 the zero coulomb energy, i.e., the value approached asymptotically by the 

 coulomb field at great distances, is approximately the magnitude of the 

 coulomb field at the surface or 



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