  We consider the scattering of nonrelativistic particles in three dimensions
by a contact potential $\Omega\hbar^2\delta(r)/ 2\mu r^\alpha$ which is defined
as the $a\to 0$ limit of $\Omega\hbar^2\delta(r-a)/2\mu r^\alpha$. It is
surprising that it gives a nonvanishing cross section when $\alpha=1$ and
$\Omega=-1$. When the contact potential is approached by a spherical square
well potential instead of the above spherical shell one, one obtains basically
the same result except that the parameter $\Omega$ that gives a nonvanishing
cross section is different. Similar problems in two and one dimensions are
studied and results of the same nature are obtained.
