Matrix Padé approximants of the nucleon-nucleon interaction

The matrix Padé approximants (with 16 × 16 matrices) and the scalar Padé approximants (with 4 × 4 matrices) of the nucleon-nucleon $S$-matrix elements are calculated for total angular momentum $J\le 4$ and for laboratory kinetic energy up to 425 MeV. The calculations are based on one- and two-pion exchanges of the pseudoscalar interaction. The coupling constant $g$ is the only parameter of the interaction for which a value, consistent with experimental results, $\frac{g^2}{4\pi }=15\mathrm{}$ is assumed. A simplified calculational scheme and formalism are presented. In order to interpret the results properly we give estimates in which energy regions we expect the one- and two-pion exchanges to be significant. For these energy regions we found that the matrix Padé approximants describe quite well the nucleon-nucleon interaction and give better approximations to the experimental data as compared to other methods of unitarization. The fact that in the framework of quantum field theory it is possible, even in limited energy regions, to give a reasonable description of the nucleon-nucleon scattering gives us more confidence in the pseudoscalar interaction as the fundamental interaction of nucleons and pions.