Comments on the Aharonov-Casher effect

We study the basic requirements for neutron confinement in the framework of some 3-D Aharonov-Casher configurations PACS number(s): 03.65Ge, 03.65.Bz, 12.60.J, 11.30.P. Aharonov and Casher (AC) pointed out the existence of a quantum mechanical process [1–3] wherein the behavior of an uncharged dipole is affected by the presence of an electric field. Let us imagine an electrically charged object with axial symmetry centered around the z axis. The nearly point dipoles, e.g. neutrons, are completely polarized along, say, the positive y direction. It is straightforward to see that this system can be recast in a supersymmetric form [4–6]. To study supersymmetry breaking, one solves the corresponding eigenvalue problem for the ground state of the given geometrical configuration. In this report we shall treat three cases: (1) a finite spherical charge distribution, (2) an infinite plane with uniform charge density, and (3) the standard Aharonov-Casher configuration. We conclude that, although in this circumstance there is apparently no force on the particles, slow neutrons will tend to move toward regions where the gradient of the field increases. To start with we assume connectivity in the configuration space in order to define a normalizable ground state. The problem turns out to have exact supersymmetry only under ∗E-mail: [email protected], Fax: 56-41-224520.