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Title: On the spin- 1/2 Aharonov–Bohm problem in conical space: Bound states, scattering and helicity nonconservation

In this work the bound state and scattering problems for a spin- 1/2 particle undergone to an Aharonov–Bohm potential in a conical space in the nonrelativistic limit are considered. The presence of a δ-function singularity, which comes from the Zeeman spin interaction with the magnetic flux tube, is addressed by the self-adjoint extension method. One of the advantages of the present approach is the determination of the self-adjoint extension parameter in terms of physics of the problem. Expressions for the energy bound states, phase-shift and S matrix are determined in terms of the self-adjoint extension parameter, which is explicitly determined in terms of the parameters of the problem. The relation between the bound state and zero modes and the failure of helicity conservation in the scattering problem and its relation with the gyromagnetic ratio g are discussed. Also, as an application, we consider the spin- 1/2 Aharonov–Bohm problem in conical space plus a two-dimensional isotropic harmonic oscillator. -- Highlights: •Planar dynamics of a spin- 1/2 neutral particle. •Bound state for Aharonov–Bohm systems. •Aharonov–Bohm scattering. •Helicity nonconservation. •Determination of the self-adjoint extension parameter.
Authors:
 [1] ;  [2] ;  [1]
  1. Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, 84030-900 Ponta Grossa-PR (Brazil)
  2. Departamento de Física, Universidade Federal do Maranhão, Campus Universitário do Bacanga, 65085-580 São Luís-MA (Brazil)
Publication Date:
OSTI Identifier:
22224269
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 339; Other Information: Copyright (c) 2013 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:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUND STATE; GYROMAGNETIC RATIO; HARMONIC OSCILLATORS; HELICITY; MAGNETIC FLUX; NEUTRAL PARTICLES; PHASE SHIFT; S MATRIX; SCATTERING; SINGULARITY; SPACE; SPIN; ZEEMAN EFFECT