  We apply the Marchenko method of quantum inverse scattering to study nucleon
scattering problems. Assuming a $\beta/r^2$ type repulsive core and comparing
our results to the Reid93 phenomenological potential we estimate the constant
$\beta$, determining the singularity strength, in various spin/isospin
channels. Instead of using Bargmann type S-matrices which allows only integer
singularity strength, here we consider an analytical approach based on the
incomplete data method, which is suitable for fractional singularity strengths
as well.
