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Scattering of Quantum Particles by TimeIndependent Scalar Fields
(University of 20 August 1955 - Skikda, 2025-06-28) Nahla , Bourouis; Kamel, Khounfais
In the context of relativistic quantum mechanics, our work has been organized into two main parts. In the first part, we first proposed the formalism of the spin-s (𝑠 = 0,1/2) relativistic wave equation. Then, based on the stationary scattering states of a relativistic particle governed by the spin-s relativistic wave equation in the presence of a localized electromagnetic field 𝐴𝜇(𝑥, 𝑡) = (𝐴0(𝑥, 𝑡), 𝐴⃗(𝑥, 𝑡)), we constructed the formalism of the one-dimensional scattering matrix 𝑆̂−𝑠. In the second part, as an application, we studied the scattering of relativistic spin-s particles interacting with certain scalar potentials with some symmetry and range properties (Woods-Saxon potential, barrier potential, and periodic potential). For these potentials, the spin-s relativistic wave equation was first solved analytically. From the asymptotic behavior, we derived the scattering matrix. Then, using the scattering matrix formalism, we calculated even and odd wave phase shifts, scattering amplitudes, transmission and reflection coefficients, and the total effective cross-section