Question

In the case of α − He scattering the measured scattered intensity at 45° (laboratory coordinates) is twice the classical result. Indicate how the wave mechanical theory of collisions explains this experimental result.

Answer 1

The differential cross-section for the scattering of identical particles of spin * is given by

where f is assumed to be independent of the azimuth angle ϕ. The angles refer to the CM-system. The first two terms on RHS are given by the Rutherford scattering, one for the scattered particle and the other for the target particle. In the CMS the identical particles are oppositely directed and the detector cannot tell one from the other. The third term on the RHS is due to quantum mechanical interference and does not occur in the classical formula. Now for alpha-alpha scattering * = 0 and (1) reduces to

Furthermore if the scattering at θ∗ = 90◦ is considered then obviously f(π − θ∗) = f (θ ∗) and the lab angle θ = 45◦. In that case classically σL(45◦) = 2| f(90◦)| 2CM while quantum mechanically σL (45◦ ) = 4| f(90◦ )|CM .

Thus quantum mechanics explains the experimental result