Energy-independent optical ${}^1{S}_{0}NN$ potential from Marchenko equation

Abstract

We present a new algebraic method for solving the inverse problem of quantum scattering theory based on the Marchenko theory. We applied a triangular wave set for the Marchenko equation kernel expansion in a separable form. The separable form allows a reduction of the Marchenko equation to a system of linear equations. For the zero orbital angular momentum, a linear expression of the kernel expansion coefficients is obtained in terms of the Fourier series coefficients of a function depending on the momentum $q$ and determined by the scattering data in the finite range of $q$. It is shown that a Fourier series on a finite momentum range ($0<q<\pi /h$) of a $q(1-S)$ function ($S$ is the scattering matrix) defines the potential function of the corresponding radial Schrödinger equation with $h$-step accuracy. A numerical algorithm is developed for the reconstruction of the optical potential from scattering data. The developed procedure is applied to analyze the ${}^1{S}_{0}NN$ data up to 3 GeV. It is shown that these data are described by optical energy-independent partial potential.

Comments: 6 pages, 4 figures. arXiv admin note: text overlap with arXiv:2102.01464