An approximation of the $S$ matrix for solving the Marchenko equation

• URL: http://arxiv.org/abs/2410.20409v2
• Date: Tue, 29 Oct 2024 17:15:20 GMT
• Title: An approximation of the $S$ matrix for solving the Marchenko equation
• Authors: N. A. Khokhlov,
• Abstract summary: I present a new approximation of the $S$-matrix dependence on momentum $q$, formulated as a sum of a rational function and a truncated Sinc series. This approach enables pointwise determination of the $S$ matrix with specified resolution, capturing essential features such as resonance behavior with high accuracy.
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• Abstract: I present a new approximation of the $S$-matrix dependence on momentum $q$, formulated as a sum of a rational function and a truncated Sinc series. This approach enables pointwise determination of the $S$ matrix with specified resolution, capturing essential features such as resonance behavior with high accuracy. The resulting approximation provides a separable kernel for the Marchenko equation (fixed-$l$ inversion), reducing it to a system of linear equations for the expansion coefficients of the output kernel. Numerical results demonstrate good convergence of this method, applicable to both unitary and non-unitary $S$ matrices. Convergence is further validated through comparisons with an exactly solvable square-well potential model. The method is applied to analyze $S_{31}$ $\pi N$ scattering data.

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