The effective-range function in the presence of a Yukawa potential

It is shown that, in the presence of a Yukawa potential with cut-off radius R, the S-wave effective-range function y is equivalent to k cot delta has well defined values at all negative energies as R → infinity. It does not have the infinite value that appears in the work of Choudhary (1983 Phys. Rev. C27,398). Thus, the corresponding K matrix has finite values at all negative energies although the S matrix is singular for -infinity < k2 < -1/4μ2. The energy derivative of y at the energy k2 = -1/4μ2 is infinite. Nevertheless, for practical applications an energy expansion of y can be considered over a wider energy region than used hitherto. In particular, correct values of the deuteron asymptotic amplitude for the Reid and Paris potential models are obtained from a knowledge of the eigenphase-shifts up to a laboratory energy of 50 MeV. (author)