  We study the time evolution of a three dimensional quantum particle under the
action of a time-dependent point interaction fixed at the origin. We assume
that the ``strength'' of the interaction (\alpha(t)) is a periodic function
with an arbitrary mean. Under very weak conditions on the Fourier coefficients
of (\alpha(t)), we prove that there is complete ionization as (t \to \infty),
starting from a bound state at time (t = 0). Moreover we prove also that, under
the same conditions, all the states of the system are scattering states.
