CHARGED-PARTICLE WITH MAGNETIC-MOMENT IN THE AHARONOV-BOHM POTENTIAL

In this paper we will consider a charged quantum mechanical particle w ith a spin-1/2 and a gyromagnetic ratio of g not equivalent to 2 in th e held of a magnetic string. The interaction of the charge with the st ring is the well known Aharonov-Bohm effect, and the contribution of t he magnetic moment associated with the spin in the case g = 2 yields a dditional scattering and zero modes (one for each Bur quantum). The an omaly of the magnetic moment (i.e. g > 2) leads to bound states. We co nsidered two methods for treating the case g > 2. The first is the met hod of self-adjoint extension of the corresponding Hamilton operator. It yields one bound state as well as additional scattering. In the sec ond we will consider three exactly solvable models for finite flux tub es and than consider the limit of zero radius. For a finite radius, th ere are N + 1 bound states (N is the number of flux quanta in the tube ). For R --> 0 the bound state energies tend to be infinite so that th is limit is not physical. A sensible limit can be obtained by tending g --> 2 simultaneously with R --> 0. Thereby only for fluxes less than unity, the results of the method of self-adjoint extension are reprod uced whereas for larger fluxes N bound states will exist. We conclude therefore that this method is not applicable. We will discuss the phys ically interesting case of a small but finite radius whereby the natur al scare is given by the anomaly of the magnetic moment of the electro n alpha(e) = 1/2(g-2) approximate to 10(-3).