Alpha head on collision with a fixed gold nucleus, taking into account the relativistic rest mass variation as implied by mass-energy equivalence

Abstract

We reformulate the Rutherford scattering of alpha particle for a head on collision, taking into account the rest mass variation of the particle, as implied by the energy conservation law. Our relativistic reformulation (which includes the energy conservation) constitutes a new example for the breakdown of the Lorentz invariance. Briefly speaking, even at rest or during the whole scattering process, the distance between the alpha particle and the gold nucleus is not invariant but depends on the frame of the observer attached to either object. According to our relativistic reformulation, we also provide a new set of Lorentz transformations.