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

Abstract

The behaviour of fermions in the background of a double-step potential is analyzed with a general mixing of scalar and vector couplings via continuous chiral-conjugation transformation. Provided the vector coupling does not exceed the scalar coupling, a Sturm-Liouville approaching for the double-step potential shows that the transmission coefficient exhibits oscillations and that a finite set of intrinsically relativistic boundstate solutions might appear as poles of the transmission amplitude in a strong coupling regime. An isolated bound-state solution resulting from coupled first-order equations might also come into sight. It is also shown that all those possible bound solutions disappear asymptotically as one approaches the conditions for the realization of the socalled spin and pseudospin symmetries in a four-dimensional space-time. Furthermore, we show that due to the additional mass acquired by the fermion from the scalar background the high localization of the fermion in an extreme relativistic regime does not violate the Heisenberg uncertainty principle.

Klein’s paradox in the presence of a scalar potential

“…This could be of interest to modern physics for the reason that the experimental observation of the related particle creation has been regarded as a challenge for quantum electrodynamics. It should be noted that the scattering of relativistic particles and associated Klein paradox are discussed, in a certain way, in [20,21,22]. In the present work, we concentrate our attention to the effect of the scalar potential on the particle creation in the vicinity of the barrier by considering two approaches; a direct calculation based on relativistic quantum mechanics and rigorous treatment in the framework of quantum field theory.…”