Description of scattering and of a bound state in the two-nucleon system on the basis of the Bargmann representation of the S matrix

For the effective-range function kcot{delta}, a pole approximation that involves a small number of parameters is derived on the basis of the Bargmann representation of the S matrix. The parameters of this representation, which have a clear physical meaning, are related to the parameters of the Bargmann S matrix by simple equations. By using a polynomial least squares fit to the function kcot{delta} at low energies, the triplet low-energy parameters of neutron-proton scattering are obtained for the latest experimental data of Arndt's group on phase shifts. The results are a{sub t}=5.4030 fm, r{sub t}=1.7494 fm, and v{sub 2}=0.163 fm{sup 3}. With allowance for the values found for the low-energy parameters and for the pole parameter, the pole approximation of the function kcot{delta} provides an excellent description of the triplet phase shift for neutron-proton scattering over a wide energy range (T{sub lab} < or approx. 1000 MeV), substantially improving the description at low energies as well. For the experimental phase shifts of Arndt's group, the triplet shape parameters v{sub n} of the effective-range expansion are obtained by using the pole approximation. It turns out that they are positive and decrease with increasing n. The description of the phase shift by means of the effective-range expansion featuring values found for the low-energy parameters of scattering proves to be fairly accurate over a broad energy region extending to energy values approximately equal to the energy at which this phase shift changes sign, this being indicative of a high accuracy and a considerable value of the effective-range expansion in describing experimental data on nucleon-nucleon scattering. The properties of the deuteron that were calculated by using various approximations of the effective-range function comply well with their experimental values.