Reconstruction of the optical potential from scattering data

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We propose a method for reconstructing the optical potential (OP) from scattering data. The algorithm is a two-step, procedure. In the first step, the real part of the potential is determined analytically via solution of the Marchenko equation. At this point, we use a rational function fit of the corresponding unitary S matrix. In the second step, the imaginary part of the potential is determined via the phase equation of the variable phase approach. We assume that the real and imaginary parts of the OP are proportional (the Lax-type interaction). We use the phase equation to calculate the proportionality coefficient. A numerical algorithm is developed for a single and for coupled partial waves. The developed procedure is applied to analyze the ${}^{1}{S}_{0}\mathit{NN},{}^{3}{\mathit{SD}}_{1}\mathit{NN}$, and $P31\phantom{\rule{0.3em}{0ex}}{\ensuremath{\pi}}^{\ensuremath{-}}N$ data. For the NN states, we constructed partial potentials with forbidden states (Moscow potential). We examine the ${\ensuremath{\pi}}^{\ensuremath{-}}N$ and NN partial-wave analysis data and demonstrate that the Lax-type interaction may be valid for these systems at the considered energies.