Scattering by a contact potential in three and lower dimensions

Abstract

We consider the scattering of nonrelativistic particles in three dimensions by a contact potential $\Omega {\hslash }^2\delta (r)/2\mu r^{\alpha }$ which is defined as the $a\to 0$ limit of $\Omega {\hslash }^2\delta (r-a)/2\mu r^{\alpha }$. 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.

REVTeX, 9 pages, no figure

References in corpus (2)

• Levinson theorem in two dimensions
• Levinson theorem for Dirac particles in one dimension