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

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 chiralconjugation 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.

Fermions in the background of mixed vector–scalar–pseudoscalar square potentials

“…Considering mixed scalar-vector potentials the Dirac equation in (1+1) dimensions have been investigated for a sign potential [17] and smooth step potential [18]. In the context of mixed scalar-vector-pseudoscalar potentials (the most general Lorentz structure), the bound-state solutions for fermions and antifermions in (1+1) dimensions have been studied for harmonic oscillator potential [19], Pöschl-Teller potential [20], Cornell potential [21,22] and Coulomb potential [23].…”

Fermions in a mixed vector-scalar double-step potential via continuous chiral transformation

“…In Refs. [13] and [14], it has been shown that the Dirac equation with a scalar potential plus a time component of vector potential of the same functional form is manageable if the vector coupling does not exceed the scalar coupling, and that the bound states for mixed scalar-vector potentials with the kink-like profiles sgn x and tanh x/λ are intrinsically relativistic solutions. Furthermore, it has been shown that the fermion can be confined in a highly localized region of space under a very strong field without any chance for spontaneous pair production related to Klein's paradox.…”

“…The complete set of solutions for massive fermions under the influence of a kink-like scalar potential added by the time component of a vector potential with the same functional form was considered in Refs. [13] and [14], in Ref. [13] for the background field behaving like sgn x, and in Ref.…”

“…[13] for the background field behaving like sgn x, and in Ref. [14] for the background behaving like tanh x/λ. In Refs.…”

“…However, the double-step potential does not seem to have received any attention regarding scalar and vector couplings in the Dirac equation. In what follows the mixing formalism developed in [13]- [14] is addressed to the double-step potential. We shall present a fairly complete account of the problem and show that, in contrast to the case of a sign step potential of Ref.…”