2014/03/22 by Tong Liu, Wen-Du Li, Wu-Sheng Dai
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Amplitude #Bessel function #Computer science #Electromagnetic Scattering and Analysis #Function (biology) #Mathematical analysis #Mathematics #Numerical methods in inverse problems #Observer (physics) #Physics #Polynomial #Precondition #Quantum mechanics #Scattering #Scattering amplitude #Scattering theory #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/jhep06(2014)087
published as JHEP06(2014)087
arxiv created 2014/03/22 · openalex publication_date 2014/06/01 · arxiv updated 2014/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In conventional scattering theory, to obtain an explicit result, one imposes a precondition that the distance between target and observer is infinite. With the help of this precondition, one can asymptotically replace the Hankel function and the Bessel function with the sine functions so that one can achieve an explicit result. Nevertheless, after such a treatment, the information of the distance between target and observer is inevitably lost. In this paper, we show that such a precondition is not necessary: without losing any information of distance, one can still obtain an explicit result of a scattering rigorously. In other words, we give an rigorous explicit scattering result which contains the information of distance between target and observer. We show that at a finite distance, a modification factor — the Bessel polynomial — appears in the scattering amplitude, and, consequently, the cross section depends on the distance, the outgoing wave-front surface is no longer a sphere, and, besides the phase shift, there is an additional phase (the argument of the Bessel polynomial) appears in the scattering wave function.