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Title: Bounded solutions of neutral fermions with a screened Coulomb potential

Abstract

The intrinsically relativistic problem of a fermion subject to a pseudoscalar screened Coulomb plus a uniform background potential in two-dimensional space-time is mapped into a Sturm-Liouville. This mapping gives rise to an effective Morse-like potential and exact bounded solutions are found. It is shown that the uniform background potential determinates the number of bound-state solutions. The behaviour of the eigenenergies as well as of the upper and lower components of the Dirac spinor corresponding to bounded solutions is discussed in detail and some unusual results are revealed. An apparent paradox concerning the uncertainty principle is solved by recurring to the concepts of effective mass and effective Compton wavelength.

Authors:
 [1]
  1. UNESP-Campus de Guaratingueta, Departamento de Fisica e Quimica, Caixa Postal 205, 12516-410 Guaratingueta SP (Brazil). E-mail: castro@feg.unesp.br
Publication Date:
OSTI Identifier:
20690202
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 320; Journal Issue: 1; Other Information: DOI: 10.1016/j.aop.2005.05.003; PII: S0003-4916(05)00088-6; Copyright (c) 2005 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; COMPTON WAVELENGTH; COULOMB FIELD; DIRAC EQUATION; EFFECTIVE MASS; EXACT SOLUTIONS; FERMIONS; MAPPING; POTENTIALS; RELATIVISTIC RANGE; SPACE-TIME; TWO-DIMENSIONAL CALCULATIONS; UNCERTAINTY PRINCIPLE

Citation Formats

Castro, Antonio S. de. Bounded solutions of neutral fermions with a screened Coulomb potential. United States: N. p., 2005. Web. doi:10.1016/j.aop.2005.05.003.
Castro, Antonio S. de. Bounded solutions of neutral fermions with a screened Coulomb potential. United States. doi:10.1016/j.aop.2005.05.003.
Castro, Antonio S. de. Tue . "Bounded solutions of neutral fermions with a screened Coulomb potential". United States. doi:10.1016/j.aop.2005.05.003.
@article{osti_20690202,
title = {Bounded solutions of neutral fermions with a screened Coulomb potential},
author = {Castro, Antonio S. de},
abstractNote = {The intrinsically relativistic problem of a fermion subject to a pseudoscalar screened Coulomb plus a uniform background potential in two-dimensional space-time is mapped into a Sturm-Liouville. This mapping gives rise to an effective Morse-like potential and exact bounded solutions are found. It is shown that the uniform background potential determinates the number of bound-state solutions. The behaviour of the eigenenergies as well as of the upper and lower components of the Dirac spinor corresponding to bounded solutions is discussed in detail and some unusual results are revealed. An apparent paradox concerning the uncertainty principle is solved by recurring to the concepts of effective mass and effective Compton wavelength.},
doi = {10.1016/j.aop.2005.05.003},
journal = {Annals of Physics (New York)},
number = 1,
volume = 320,
place = {United States},
year = {Tue Nov 01 00:00:00 EST 2005},
month = {Tue Nov 01 00:00:00 EST 2005}
}
  • Logarithmic perturbation theory (PT) for screened Coulomb potential is considered. Calculation of higher PT orders of the level energy E/sub h/ is reduced to recurrence relations that are valid for any type of screening and are very convenient for computer calculations. They are employed to calculate the PT coefficient of E/sub h/ up to k = 100 for a number of physically interesting cases such as the Yukawa potential, the quarkonium potential, etc. The approach of E/sub h/ as k..-->..infinity to the asymptotic form of E/sub h/, defined by the quasiclassical approximation, is discussed. The problem of summation of themore » divergent PT series is considered. By employing the Pade approximants and the asymptotic form of E/sub h/ it is possible to determine with a high accuracy the energy level E(g) for the potentials mentioned above in a range that exceeds considerably the range of applicability of PT, including the strong coupling region.« less
  • It is shown that an eigenvalue expansion of the collision integral allows one to obtain the first term in the expansion of the collision integral for elastic scattering of fast electrons from a screened Coulomb potential eigenvalues of the scattering operator at large angles. In addition, the range of applicability of the model can be determined by comparing the spectrum of the collision integral with the spectrum of the first terms in the asymptotic expansion. (AIP)
  • An expression is obtained for the cross section for bremsstrahlung of a relativistic electron in the field of a nucleus. The screening effect of the atomic electron shell is taken into account. For calculation of the cross section we propose a method which permits good convergence in orbital angular momentum to be obtained. The cross section is calculated from the obtained formulas for nuclei with Z=13 and 79 and for initial electron energies E/sub i/=1.5 and 2 (in units of mc/sup 2/). The results of the calculations are in good agreement with the existing experimental data.