Finite correction to Aharonov-Bohm scattering by a contact potential

We study the influence of a contact (or delta) potential on the Aharonov-Bohm scattering of nonrelativistic particles. In general the contact potential has no effect on the scattering as expected. However, when the magnetic flux and the strength of the contact potential take some special values, the Aharonov-Bohm scattering cross-section is manifestly changed. It is shown that these special values correspond to the simultaneous existence of two half-bound states in two adjacent angular momentum channels. Two limiting processes are presented to deal with the singularity of the contact potential and results of the same nature are obtained. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007