Padé phenomenology forNNscattering:S01phase shifts

Recently developed Padé approximant techniques are applied to two sets of ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\mathrm{NN}$ scattering data. In the first, the unconstrained ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\mathrm{np}$ phase shifts of MacGregor et al. are used to generate a scattering function, $F\left(k^2\right)=kcot\left({\delta }_0\right)$, which is fitted with high precision. A six-parameter [3/2] Padé fit gives four terms of the effective range expansion; the resulting Marchenko-type potential is expressible as the sum of a Yukawa one-pion-exchange potential and a shorter range part, the repulsion peaking at the origin at near 4 GeV. In a second application, Padé fits are made to the scattering function of the Reid soft-core potential. The [3/2] approximant which fits $F\left(k^2\right)$ through the wave numbers consistent with the Lambert, Corbella, and Thomé criterion, to $k=2.5\mathrm{}$ ${\mathrm{fm}}^{-1\mathrm{}}$, leads to a potential with a core height of 4.6 × ${10}^4$ GeV. In both [3/2] potentials the volume integrals are large and negative, and cannot be made positive by adjoining more repulsive high energy phase shifts. By application to the Reid soft-core potential the Padé formalism is shown to generate useful [$\frac{L}{L-1\mathrm{}}$] Padé approximants with increasing $L$. The analytic structure of $F\left(k^2\right)$ beyond $k=224\mathrm{}$ ${\mathrm{fm}}^{-1\mathrm{}}$ is used in the construction of higher Padé approximants that (a) satisfy the Lambert, Corbella, and Thomé criterion and (b) might lead to saturation.