Under the circumstances of shielding effect of extranuclear electron, the condition of the classics descriptions of Rutherford scattering formula is derived from the principle of uncertainty relation in the quantum mechanics.
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.