Test of quantum effect on elastic-scattering cross section of identical particles

In quantum mechanics, wave functions for identical bosons or fermions must be symmetrized or anti-symmetrized, respectively. This fundamental principle causes deviations in the cross sections of scatterings between identical particles from those of the Rutherford scattering. These deviations occur due to the interference between the direct and exchange terms in their scattering amplitudes. In order to confirm this quantum effect on identical particles, we measured scattering cross sections in different configurations: between identical particles or between different particles.

The measurement was conducted at the tandem accelerator facility in Kobe University. ¹²C and ¹³C beams accelerated up to 4.8 MeV or 6.0 MeV were injected to a ¹²C target. A proton beam at 2.8 MeV was also injected to an aramid film as a proton target. The scattered particles were detected by a Si detector at θ=16—60°, and the beam current was monitored by a hand-made Faraday cup. 

Whereas the angular distribution of the cross section for the ¹²C-¹³C scattering agreed with that of the Rutherford scattering, that of the ¹²C-¹²C scattering exhibited a prominent oscillation pattern due to the quantum effect on identical particles. However, the similar oscillation pattern was not observed in the proton-proton scattering due to its small Sommerfeld parameter despite being a scattering process between identical particles.