Scattering and bound states of fermions in a mixed vector-scalar smooth step potential

TL;DR

This paper investigates how fermions scatter and form bound states in a smooth step potential with mixed vector-scalar Lorentz structures, revealing relativistic bound states and their relation to spin and pseudospin symmetries.

Contribution

It introduces a comprehensive analysis of fermion scattering and bound states in a mixed vector-scalar potential, highlighting the relativistic nature and symmetry conditions affecting bound state existence.

Findings

Bound states appear as poles of the transmission amplitude.

Bound states vanish near spin and pseudospin symmetry conditions.

Charge and chiral conjugation transformations are analyzed.

Abstract

The scattering of a fermion in the background of a smooth step potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling. Charge-conjugation and chiral-conjugation transformations are discussed and it is shown that a finite set of intrinsically relativistic bound-state solutions appears as poles of the transmission amplitude. It is also shown that those bound solutions disappear asymptotically as one approaches the conditions for the realization of the so-called spin and pseudospin symmetries in a four-dimensional space-time.