https://doi.org/10.1140/epjc/s10052-024-12894-4
Regular Article - Theoretical Physics
Fermion-soliton scattering in a modified
model
Laboratory of Applied Mathematics and Theoretical Physics, Tomsk State University of Control Systems and Radioelectronics, 634050, Tomsk, Russia
Received:
7
February
2024
Accepted:
12
May
2024
Published online:
29
May
2024
The scattering of fermions in the background field of a topological soliton of the modified -dimensional
model is studied here both analytically and numerically. Unlike the original
model, the Lagrangian of the modified model contains a potential term. Due to this, a dilatation zero mode of the topological soliton disappears, which results in stability of the fermion-soliton system. The symmetry properties of the fermion-soliton system are established, and the asymptotic forms of fermionic radial wave functions are studied. Questions related to the bound states of the fermion-soliton system are then discussed. General formulae describing the scattering of fermions are presented. The amplitudes of the fermion-soliton scattering are obtained in an analytical form within the framework of the Born approximation, and their symmetry properties and asymptotic forms are studied. The energy levels of the fermionic bound states and the partial phase shifts of fermionic scattering are obtained by numerical methods, and the ultrarelativistic limits of the partial phase shifts are found.
© The Author(s) 2024
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