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

• URL: http://arxiv.org/abs/2104.03939v2
• Date: Fri, 16 Apr 2021 13:02:06 GMT
• Title: Energy-independent optical $^{1}S_{0}NN$ potential from Marchenko equation
• Authors: N. A. Khokhlov and L. I. Studenikina
• Abstract summary: We present a new method for solving the inverse problem of quantum scattering theory based on the Marchenko theory. A numerical algorithm is developed for the reconstruction of the optical potential from scattering data.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 Schr\"odinger 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.

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