By Heisenberg W.
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In the event of elastic scattering, the respective speeds of the particles remain unaltered before and after the collision. Both are deflected through the same angle measured with their respective original direction. Their centre of mass remains at rest throughout the collision. Each of the particles describes a hyperbola. The collision diameter, impact parameter and eccentricity of the orbit are the same for both the particles, Fig. 27. In our example, α particle traverses its hyperbolic path r1 about the centre of mass, while the carbon nucleus also traverses a similar path, r2 = r1 m1 /m2 = r1 /3, on the other side of the centre of mass.
Resulting in deflections θ1 , θ2 , . . The azimuth of the deflection will change after each collision, the subsequent azimuths being φ1 , φ2 , . . , the projected angle of deflection is given by q ΘP = θi cos φi i=1 We have to average over the parameters of the single collisions. 88) where δij is the Kronecker delta. 89) Observe that the most probable value of Θ or ΘP is zero. However, Θ and Θ 2 are necessarily positive, whereas ΘP is zero. 4 Multiple Scattering 45 Fig. 7 MeV. Solid lines indicate the distribution expected from the Moliere theory for small-and large-angle multiple scattering, with an extrapolation in the transition region: dashed lines, the distributions according to the Gaussian and single scattering theories.
The only answer to the anamolous scattering was to postulate the existence of strong short range attractive nuclear forces. For large b the angle θ will be given by pure Coulomb forces. As b decreases θ would increase, but not so rapidly as in the pure Coulomb field. This has the consequence of more particles to be scattered at small angles and fewer at large angles. As b decreases further, the attractive nuclear forces may more than compensate for the repulsive Coulomb forces. The angle of scattering may therefore decrease rather than increase, and in this case there will be a maximum angle of scattering.