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Journal of Physics A Mathematical and General

Ground state of a spin-1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electrostatic field

V V Semenov

Published May 21, 1992• 4 citations
Publisher

Abstract

It is shown that a relativistic spin-1/2 neutral particle with an anomalous magnetic moment moving in an x-y plane in a two-dimensional electrostatic field: E=(E x ( x , y ), E y ( x , y ), O) has (N-1)-fold degeneracy of the ground state. The degree of degeneracy of the ground state is defined by the value of the anomalous magnetic moment and a linear charge density of the filament creating this electrostatic field.

DOI
10.1088/0305-4470/25/10/004

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It is shown that a relativistic spin-1/2 neutral particle with an anomalous magnetic moment moving in an x-y plane in a two-dimensional electrostatic field: E=(E x ( x , y ), E y ( x , y ), O) has (N-1)-fold degeneracy of the ground state. The degree of degeneracy of the ground state is defined by the value of the anomalous magnetic moment and a linear charge density of the filament creating this electrostatic field.
The generalized Duffin–Kemmer equation for a spin 1 particle with the anomalous magnetic moment in the external uniform magnetic field is investigated. The separation of variables in the wave equation is performed on the basis of projective operator techniques. The problem is reduced to a system of differential equations for three independent functions that have been solved in terms of the confluent hypergeometric functions. Three series of the energy levels are found. To assign them the physical sense at all values of the main quantum number n = 0,1, 2, , special restrictions on anomalous magnetic moment values must be imposed – they are formulated in explicit form. Otherwise, only some part of the energy levels corresponds to the bound states. The neutral spin 1 particle is considered as well. In this case, no bound states exist in the systems. The main qualitative manifestation of the anomalous magnetic moment is the space scaling of the arguments of the wave functions in comparison with a particle without such a moment.
Analysis of strongly commuting self-adjoint operators with applications to a spin-¥frac12¥frac{1}{2}¥frac12 neutral particle with anomalous magnetic moment
The Aharonov-Bohm scattering of relativistic spin-1∕21∕21∕2 particles with an anomalous magnetic moment are studied. The scattering cross sections for unpolarized and polarized particles are obtained by solving the Dirac-Pauli equation. It is somewhat unexpected that the results are in general the same as those for particles without an anomalous magnetic moment. However, when the incident energy takes some special values, the cross section for polarized particles is dramatically changed. In these cases the helicity of scattered particles is not conserved. In particular, the helicity of particles scattered in the backward direction is all reversed. In the nonrelativistic limit, a very simple relation between the polarized directions of the incident and scattered particles is found, for both general and special incident energies. For particles without an anomalous magnetic moment this relation can be drawn from previous results but it appears to be unnoticed.
The scattering of a nonrelativistic neutral massive fermion having the anomalous magnetic moment (AMM) in an electric field of a uniformly charged long conducting thread aligned perpendicularly to the fermion motion is considered to study the so-called Aharonov–Casher (AC) effect by taking into account the particle spin. For this solution, the nonrelativistic Dirac–Pauli equation for a neutral massive fermion with AMM in (3+1) dimensions is found, which takes into account explicitly the particle spin and interaction between AMM of moving fermion and the electric field. Expressions for the scattering amplitude and the cross-section are obtained for spin-polarized massive neutral fermion scattered off the above conducting thread. We conclude that the scattering amplitude and cross-section of spin-polarized massive neutral fermions are influenced by the interaction of AMM of moving neutral fermions with the electric field as well as by the polarization of fermion beam in the initial state.