Transverse Isotropy in Identical Particle Scattering

It is pointed out that the cross section for the scattering of identical charged bosons is isotropic over a broad angular range around 90o when the Sommerfeld parameter has a critical value, which depends exclusively on the spin of the particle. A discussion of systems where this phenomenon can be observed is presented. The scattering of identical particles is a routine exercise in quantum mechanics and its discussion can be found in most text books on the subject [1]. However, in recent years, the rapid oscillation seen in the angular distribution of the Mott elastic scattering of identical charged particles such as nuclei, was utilized to test models such as QCD [2,3] and to discuss small deviations from the Coulomb force law owing to QED-related corrections such as vacuum polarization [4]. In the present work we point out a hitherto unknown feature of the Mott scattering cross-section for bosons, namely an almost isotropic angular distribution over a very wide angular range when the Sommerfeld parameter attains a critical value determined entirely by the spin, s, of the particles viz, ηC = (3s + 2) . For the purpose of completeness we first give a short account of the theory of scattering of identical particles. We then turn to