Fermions in a mixed vector-scalar double-step potential via continuous chiral transformation
UNESP - Campus de Guaratinguetá, Departamento de Física e Química, 12516-410, Guaratinguetá SP, Brazil
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Revised: 6 January 2016
Accepted: 27 February 2016
Published online: 13 April 2016
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 approach for the double-step potential shows that the transmission coefficient exhibits oscillations and that a finite set of intrinsically relativistic bound-state 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 so-called 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.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2016