We consider the scattering of nonrelativistic particles in three dimensions
by a contact potential Omegah(2)delta (r)/2 mur(alpha), which is defined a
s the a --> 0 limit of Omegah(2)delta (r - a)/2 mur(alpha). It is surprisin
g that it gives a nonvanishing cross section when alpha = 1 and Omega = -1.
When the contact potential is approached by a spherical square well potent
ial instead of the above spherical shell one, one obtains basically the sam
e result except that the parameter Omega that gives a nonvanishing cross se
ction is different. Similar problems in two and one dimensions are studied
and results of the same nature are obtained.