Análise do espalhamento de um bóson por um tubo magnético no espaço-tempo de uma corda cósmica

Abstract

The study of the scattering phenomenon is extremely important to understand the properties of matter. Aharonov and Bohm (1959) contributed signi cantly to this issue by showing the importance of the electromagnetic potentials in the quantum scattering phenomenon. In this regard, it is indispensable to know this phenomenon in all its reach. This study aims to contribute whith the increasing understanding of relativistic quantum scattering. In this perspective, this research presents an analysis of the scattering of a relativistic quantum particle charged with zero spin into a magnetic tube, considering three distinct models of eld in the space-time of a cosmic string. Our main objective was to determine the phase shift angle by analyzing the asymptotic behavior of the wave functions considering the three models. To this end, we have used two complementary methods : the algebraic method of di erential equations resolutions and the numerical calculation method by using a computational program. Firstly, we obtained as algebric results some solutions for the equations found, whose form referred us to the special functions of Bessel, Neuman and Whittaker. Secondly, the numerical calculation enableds us to understand the contribution of the cosmic string and the magnetic eld's tube in the phase's deviation of the scattering.