Rutherford Scattering: a comparison between Classical Mechanics, Non-Relativistic Quantum Mechanics, and Quantum Field Theory

This is a review article that investigates the three approaches to Rutherford Scattering Theory - Classical Mechanics, Non-Relativistic Quantum Mechanics, and Quantum Field Theory - and their distinctions. In the first sections, the mathematical models are demonstrated and a qualitative analysis of the main differences in each interpretation of the phenomenon is performed. Next, numerical simulations show the effects of dealing with relativistic or non-relativistic limits. The results make it clear that no theory is essentially wrong, but the newer ones are just more complete and consider more relevant parameters