Matrix Padé Approximants for theS01andP03Partial Waves in Nucleon-Nucleon Scattering

In order to correct the threshold behavior of scalar Padé approximants in $\mathrm{NN}$ scattering, "matrix Padé approximants," which take into account the various positive- and negative-energy states, have been considered by several authors. In a recent paper by Bessis, Turchetti, and Wortman, truncated matrices based on an incomplete set of basis states were used and a qualitative description of the energy dependence of the ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ phase shift was obtained. In this work it is shown that this result is not obtained when a complete set of basis states is used. The main effect of matrix Padé approximants using a complete set of basis states is to introduce an additional attraction at higher energies. Our analysis of the fourth-order graphs is done in a way which allows the external momenta to be completely off shell so that the irreducible graphs can be used as kernels in the Bethe-Salpeter equation. This will make possible the calculation of several higher-order graphs by iterating the Bethe-Salpeter equation.