Searcharxiv⌕ Search

arXiv subjects

N. A. Khokhlov

Publications and source records attributed to N. A. Khokhlov.

14 recordsLinked to original sources
arXiv2026

Approximating the $S$ matrix for solving the Marchenko equation: the case of channels with different thresholds

This work extends previous results on the inverse scattering problem within the framework of Marchenko theory (fixed-$l$ inversion). In particular, I approximate an $n$-channel $S$-matrix as a function of the first-channel momentum $q$ by a sum of a rational term and a truncated sinc series for each matrix element. Relativistic kinematics are taken into account through the correct momentum-energy relation, and the necessary minor generalization of Marchenko theory is given. For energies where only a subset of scattering channels is open, the analytic structure of the $S$-matrix is analyzed. I demonstrate that the submatrix corresponding to closed channels, particularly near their thresholds, can be reconstructed from the experimentally accessible submatrix of open channels.The convergence of the proposed method is verified by applying it to data generated from a direct solution of the scattering problem for a known potential, and comparing the reconstructed potential with the original one. Finally, the method is applied to the analysis of $S_{31}$ $πN$ scattering data.

quant-ph↗
arXiv2024

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

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 $S_{31}$ $πN$ scattering data.

nucl-th↗
arXiv2023

Energy-independent complex single $P$-waves $NN$ potential from Marchenko equation

We extend our previous results of solving the inverse problem of quantum scattering theory (Marchenko theory, fixed-$l$ inversion). In particular, we apply an isosceles triangular-pulse function set for the Marchenko equation input kernel expansion in a separable form. The separable form allows a reduction of the Marchenko equation to a system of linear equations for the output kernel expansion coefficients. We show that in the general case of a single partial wave, a linear expression of the input kernel is obtained in terms of the Fourier series coefficients of $q^{1-m}(1-S(q))$ functions in the finite range of the momentum $0\leq q\leqπ/h$ [$S(q)$ is the scattering matrix, $l$ is the angular orbital momentum, $m=0,1,\dots,2l$]. Thus, we show that the partial $S$--matrix on the finite interval determines a potential function with $h$-step accuracy. The calculated partial potentials describe a partial $S$--matrix with the required accuracy. The partial $S$--matrix is unitary below the threshold of inelasticity and non--unitary (absorptive) above the threshold. We developed a procedure and applied it to partial-wave analysis (PWA) data of $NN$ elastic scattering up to 3 GeV. We show that energy-independent complex partial potentials describe these data for single $P$-waves.

nucl-th↗
arXiv2021

An algebraic form of the Marchenko inversion. Partial waves with orbital momentum $l\ge 0$

We present a generalization of the algebraic method for solving the Marchenko equation (fixed-$l$ inversion) for any values of the orbital angular momentum $l$. We expand the Marchenko equation kernel in a separable form using a triangular wave set. The separable kernel allows a reduction of the equation to a system of linear equations. We obtained a linear expression of the kernel expansion coefficients in terms of the Fourier series coefficients of $q(1-S(q))$ function ($S(q)$ is the scattering matrix) depending on the momentum $q$. The linear expression is valid for any orbital angular momentum $l$. The kernel expansion coefficients are determined by the scattering data in the finite range $0\leq q\leqπ/h$. In turn, the thus defined Marchenko kernel of the equation allows one to find the potential function of the radial Schrödinger equation with $h$-step accuracy.

quant-ph↗
arXiv2021

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

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 ($0<q<π/h$) 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.

quant-ph↗
arXiv2021

An algebraic method for solving the inverse problem of quantum scattering theory

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 on the finite range of q.

quant-ph↗
arXiv2017

The neutron radiation capture process $n+p\rightarrow D+γ$ and $^1 S_0$ $np$ wave function

Cross section of the neutron capture reaction $n+p\rightarrow d+γ$ at threshold was calculated with different realistic $^{3}S_{1}$ deuteron and $^{1}S_{0}$ $np$ scattering wave functions stemming from Nijmegen-II, JISP16, Paris, Idaho and Moscow (with forbidden states) potentials. It is found that this reaction with thermal neutrons may be described without a contribution of meson exchange currents.

nucl-th↗
arXiv2016

The deuteron wave function and neutron form factors from the elastic electron deuteron scattering

A study of the deuteron structure in the framework of relativistic quantum mechanics is presented. Point-form (PF) relativistic quantum mechanics (RQM) is applied to the elastic eD scattering. The deuteron wave function and neutron form factors are fitted to the electromagnetic deuteron form factors. We also compare results obtained by different realistic deuteron wave functions stemming from Nijmegen-I, Nijmegen-II, JISP16, CD-Bonn, Paris, Argonne, Idaho and Moscow (with forbidden states) potentials. It is shown that the electromagnetic deuteron form factors may be described without exchange currents.

nucl-th↗
arXiv2015

Electromagnetic deuteron form factors in point form relativistic quantum mechanics

A study of electromagnetic structure of the deuteron in the framework of relativistic quantum mechanics is presented. The deuteron form factors dependencies on the transferred 4-momentum Q are calculated. We compare results obtained with different realistic deuteron wave functions stemming from Nijmegen-I, Nijmegen-II, JISP16, CD-Bonn, Paris and Moscow (with forbidden states) potentials. A nucleon form factor parametrization consistent with modern experimental analysis was used as an input data.

nucl-th↗
arXiv2007

Nucleon-nucleon wave function with short-range nodes and high-energy deuteron photodisintegration

We review a concept of the Moscow potential (MP) of the $NN$ interaction. On the basis of this concept we derive by quantum inversion optical partial potentials from the modern partial-wave analysis (PWA) data and deuteron properties. Point-form (PF) relativistic quantum mechanics (RQM) is applied to the two-body deuteron photodisintegration. Calculations of the cross-section angular distributions cover photon energies between 1.1 and 2.5 GeV. Good agreement between our theory and recent experimental data confirms the concept of deep attractive Moscow potential with forbidden $S$- and $P$-states.

nucl-th↗
arXiv2005

Reconstruction of the optical potential from scattering data

We propose a method for reconstruction of the optical potential 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 diagonal Padé approximant 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 the imaginary parts of the optical potential are proportional. 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 analysis of $^{1}S_{0}$ $NN$, $^{3}SD_{1}$ $NN$, $P31$ $π^{-} N$ and $S01$ $K^{+}N$ data.

quant-ph↗
arXiv2004

Reconstruction of the optical potential in the inverse quantum scattering. Application to the relativistic inelastic NN scattering

The numerical algorithm of the inverse quantum scattering is developed. This algorithm is based on the Marchenko theory, and includes three steps. The first one is the algebraic Pade approximation of the unitary S-matrix, what is realized by solving a system of linear equations. Second step is the exact solution of the Marchenko equation. The used approximant reduces it to another system of linear equations. At this step we get the real-valued potential. It is shown numerically that the developed algorithm is able not only to generate the given S-matrix dependence, but converges to the initial potential. At third step we construct the optical complex-valued potential which gives the needed S-matrix. It is shown that the modern phase shift analysis data allow to construct the nucleon-nucleon optical potentials of two kinds. These potentials describe the deuteron properties and the phase shift analysis data up to 3 GeV and they have different behavior at short distances. One is a repulsive core potential and another is a Moscow attractive potential with forbidden states.

nucl-th↗
arXiv1997

Bremsstrahlung of 350--450 MeV protons as a tool to study $NN$ interaction off-shell

The $pp\to ppγ$ bremsstrahlung cross section is calculated within the method of coordinate space representation. It is shown that in the beam energy range of 350--450~MeV a deep attractive NN-potential with forbidden states (Moscow potential) and realistic meson exchange potentials (MEP) give rise to the cross sections that differ essentially in shape: the cross sections nearly coincide in the minima but differ by a factor of 5 approximately in the maxima. Therefore, the $pp\to ppγ$ reaction at energies $\sim$350--450~Mev can be used to study $NN$ interaction off-shell and to discriminate experimentally between MEP and Moscow potential.

nucl-th↗