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

The authors show that, in the presence of a Yukawa potential with cut-off radius R, the S-wave effective-range function y identical to kk cot delta has well defined values at all negative energies as R to infinity . It does not have the infinite value that appears in the work of Choudhary (1983). Thus, the corresponding K matrix has finite values at all negative energies although the S matrix is singular for - infinity <k 2 <- 1 / 4 mu 2 . The energy derivative of y at the energy k 2 =- 1 / 4 mu 2 is infinite. Nevertheless, for practical applications an energy expansion of y can be considered over a wider energy region than used hitherto. In particular, the authors obtain correct values of the deuteron asymptotic amplitude for the Reid and Paris potential models from a knowledge of the eigenphase-shifts up to a laboratory energy of 50 MeV.