2022/11/25 by Martin Pijnenburg, Pijnenburg, Martin, Giulia Cusin +5 · 1 citation
Physics and Astronomy · #Crystallography and Radiation Phenomena #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Nuclear physics research studies #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2211.14113
openalex publication_date 2022/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quantum Rutherford scattering and scattering of classical waves off Coulomb-like potentials have similar formal structures and can be studied using the same mathematical techniques. In both contexts, the long-range nature of the interaction leads to a divergent total cross-section, which has been interpreted and regularized in various ways in the past literature. We review in detail the origin of this divergence, in both real and multipole spaces, and show that it arises from incorrectly using approximations out of their domain of validity. We also stress that although classical and quantum Rutherford scattering share the same formalism, the natures of the associated physical observables differ. We comment on the role of interference: while interference can be safely neglected in a quantum context (due to the fact that the observable quantity is a flux, and the incoming flux is collimated), in a classical context one expects to see a superposition of transmitted and scattered waves in a broad region downstream of the target, hence a cross-section is not connected to any physically observable quantity.