  The longitudinal and transverse coupling impedances of a small discontinuity
on the accelerator chamber wall can be expressed in terms of the electric and
magnetic polarizabilities of the discontinuity. The polarizabilities are
geometrical factors and can be found by solving a static (electric or magnetic)
problem. However, they are known in the explicit analytical form only for a few
simple-shaped discontinuities, for example, for an elliptic hole in a thin
wall. In the present paper the polarizabilities of a ring-shaped cut in the
wall are obtained. The results are applied to calculate the coupling impedances
of button-type beam position monitors.
