Binding of a Charged Particle in the Presence of an Electric Dipole and a Magnetic Field

Abstract

We formulate a variational method to obtain the binding energies of a charged particle in presence of an electric dipole and a magnetic field aligned along the dipole. First, we test the method by obtaining the critical dipole moment for a point dipole, as well as a finite dipole in the absence of a magnetic field. A few larger dipole moments supporting a zero energy bound state are also obtained. Adding a magnetic field of ~ 20 - 100 T, we show that for a rigid and stationary dipole of moment 2.54 D, the electron binding energy increases by 15% - 66%. Our approach also shows the absence of a critical dipole moment in presence of an aligned magnetic field.