Abstract

The aim of this dissertation is to present the theory of relativistic electron-atom scattering at low energies. This work focuses on the theory of calculation of scattering length and how it can be formulated in the relativistic quantum theory. An approximate solution to the Dirac equation with polarization potential behaving as r-4 is presented as well as the formulation of the effective range theory for Dirac’s equation. Those formulas were later used to calculate the scattering lengths of argon, krypton, xenon, radon and oganesson. Values for argon, krypton and xenon coincide with the values obtained by different groups, both theoretically and experimentally. Values for radon and oganesson were obtained for the first time. In this work GRASP2018 computational package was used to calculate the bound states of an atom and the modified COWF code for obtaining the continuum states.

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