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.
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