skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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 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. - Highlights: • Scattering and bound states of fermions in a kink-like potential. • No pair production despite the high localization. • No bounded solution under exact spin and pseudospin symmetries.

Authors:
;
Publication Date:
OSTI Identifier:
22314840
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 346; Journal Issue: Complete; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUND STATE; CHIRALITY; COUPLING; EFFECTIVE MASS; FERMIONS; FOUR-DIMENSIONAL CALCULATIONS; MATHEMATICAL SOLUTIONS; PAIR PRODUCTION; POTENTIALS; RELATIVISTIC RANGE; SCALARS; SCATTERING; SPACE-TIME; SPIN; SYMMETRY; TRANSFORMATIONS; VECTORS

Citation Formats

Castilho, W.M., E-mail: castilho.w@gmail.com, and Castro, A.S. de, E-mail: castro@pq.cnpq.br. Scattering and bound states of fermions in a mixed vector–scalar smooth step potential. United States: N. p., 2014. Web. doi:10.1016/J.AOP.2014.04.011.
Castilho, W.M., E-mail: castilho.w@gmail.com, & Castro, A.S. de, E-mail: castro@pq.cnpq.br. Scattering and bound states of fermions in a mixed vector–scalar smooth step potential. United States. doi:10.1016/J.AOP.2014.04.011.
Castilho, W.M., E-mail: castilho.w@gmail.com, and Castro, A.S. de, E-mail: castro@pq.cnpq.br. Tue . "Scattering and bound states of fermions in a mixed vector–scalar smooth step potential". United States. doi:10.1016/J.AOP.2014.04.011.
@article{osti_22314840,
title = {Scattering and bound states of fermions in a mixed vector–scalar smooth step potential},
author = {Castilho, W.M., E-mail: castilho.w@gmail.com and Castro, A.S. de, E-mail: castro@pq.cnpq.br},
abstractNote = {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. - Highlights: • Scattering and bound states of fermions in a kink-like potential. • No pair production despite the high localization. • No bounded solution under exact spin and pseudospin symmetries.},
doi = {10.1016/J.AOP.2014.04.011},
journal = {Annals of Physics (New York)},
number = Complete,
volume = 346,
place = {United States},
year = {Tue Jul 15 00:00:00 EDT 2014},
month = {Tue Jul 15 00:00:00 EDT 2014}
}
  • Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is mapped into the Schroedinger-like equation with an effective Rosen-Morse potential. It is shown that the scalar uniform background present subtle and trick effects for the scattering states and reveals itself a high-handed element for formation of bound states. In that process, it is shown that the problem of solving a differential equation for the eigenenergies is transmuted into the simpler and moremore » efficient problem of solving an irrational algebraic equation.« less
  • The scattering of a fermion in the background of a sign 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 under the Sturm–Liouville perspective. When the vector coupling and the scalar coupling have different magnitudes, an isolated solution shows that the fermion under a strong potential can be trapped in a highly localized region without manifestation of Klein’s paradox. It is also shown that the lonely bound-state solution disappears asymptotically as one approaches the conditions for the realization of spin and pseudospin symmetries. --more » Highlights: •Scattering of fermions in a sign potential assessed under a Sturm–Liouville perspective. •An isolated bounded solution. •No pair production despite the high localization. •No bounded solution under exact spin and pseudospin symmetries.« less
  • The problem of a fermion subject to a general mixing of vector and scalar potentials in a two-dimensional world is mapped into a Sturm-Liouville problem. Isolated bounded solutions are also searched. For the specific case of an inversely linear potential, which gives rise to an effective Kratzer potential in the Sturm-Liouville problem, exact bounded solutions are found in closed form. The case of a pure scalar potential with their isolated zero-energy solutions, already analyzed in a previous work, is obtained as a particular case. The behavior of the upper and lower components of the Dirac spinor is discussed in detailmore » and some unusual results are revealed. The nonrelativistic limit of our results adds a new support to the conclusion that even-parity solutions to the nonrelativistic one-dimensional hydrogen atom do not exist.« less
  • The behavior of fermions interacting via vector gluons in the strong-coupling limit is investigated. A suitable coupling betweeen the Dirac and the vector-gluon field gives rise to bound-state solutions. The coherent field approximation is employed to find the bound-state masses, which are further discussed by analytical and numerical methods and are found to be positive-definite in the example considered numerically. (AIP)
  • Taking into account the pionic self-energy of the baryons, the color-electrostatic and magnetostatic energies due to one-gluon exchange, and the corrections due to the center-of-mass motion, the ground-state masses of the octet baryons are calculated in a chiral symmetric potential model of independent quarks. The effective potential representing phenomenologically the nonperturbative gluon interactions, including gluon self-couplings, is chosen with equally mixed scalar and vector parts in a linear form. The physical masses of the baryons so obtained with the strong coupling constant {alpha}{sub c}=0.576 agree very well with the corresponding experimental values. {copyright} {ital 1997} {ital The American Physical Society}