Inverse scattering problem for a family of phase-equivalent nonlocal potentials

Muzafarov, V. M.

doi:10.1088/0266-5611/4/1/016

Cited by 4 publications

(1 citation statement)

References 26 publications

(8 reference statements)

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“…We just list these and refer the reader to the original papers. These methods are: an alternative quasi-classical scheme related to the eikonal (Glauber) model of scattering [19]; a finite difference method of Hooshyar and Razavy [20,21]; a polynomial scheme developed by Kermode et al [22]; a quite interesting general approach of R-matrix inversion due to Zakhariev and Suzko [23,24]; a method due to Muzafarov for finding a general non-local potential [25,26]; a new technique based on the dispersion relations for the current matrix elements (straightforwardly generalizable to the relativistic case) by Troitsky and others [27,28]; a numerical inversion method utilizing a continuous analogue of Newton's wellknown minimization method [29], the generalized Darboux transformation of Schnizer and Leeb [30]; a method due to Alam and Malik [31,32], and many others. The majority of these approaches have been tested or studied with a few examples only and still await wider application.…”

Section: A Survey Of Inversion Methodsmentioning

confidence: 99%

The application of inversion to nuclear scattering

Kukulin

Mackintosh

2004

J. Phys. G: Nucl. Part. Phys.

141

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We review the application of inverse scattering in nuclear physics. We emphasize the various ways in which inversion can be used to understand nuclear interactions, and survey the results that have been obtained. We discuss S → V inversion from both theoretical and experimentally fitted S-matrices as well as a new method for direct observable →V inversion. The various alternative approaches to inverse scattering are briefly reviewed, and their range of applicability is discussed. This is not a review of formal inversion methods, but the iterative perturbative (IP) approach is described in some detail together with a discussion of the physics results which have been obtained using it and other inversion methods. The case of p+4He scattering is presented in some detail as a case study exemplifying the kind of information which can now be obtained by the application of inverse scattering techniques. It also brings out the comparative properties of different inversion methods.

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Section: A Survey Of Inversion Methodsmentioning

confidence: 99%

The application of inversion to nuclear scattering

Kukulin

Mackintosh

2004

J. Phys. G: Nucl. Part. Phys.

141

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New situation in quantum mechanics (wonderful potentials from the inverse problem)

Zakhariev

Chabanov

1997

Inverse Problems

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Every physicist interested in nonrelativistic wave mechanics can now gain a deeper insight into quantum intuition. This is possible thanks to the advance in the theories of the inverse problem and supersymmetry which provides numerous new classes of exactly solvable models and instructive and clear illustrations revealing the fundamental elements of the coupling between potentials and observables; how to change the disposition of bound states on the energy scale (to shift, create or destroy the spectral levels) and in space by a special choice of potential perturbation. This theory explains the algorithms to control scattering features and wave motion over the lattices (e.g. crystal or discrete variable numbering channels). The best of thousands of corresponding 'quantum pictures' are selected here. The predictive power of the acquired intuition allows us to go beyond the scope of the exact models used for its elaboration.

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SeparableNNpotentials from inverse scattering for nuclear matter studies

Kwong

Köhler

1997

Phys. Rev. C

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Low-rank separable potentials greatly simplify perturbation-theory based many-body computations and are especially useful in finite temperature and nonequilibrium nuclear matter studies. With local potentials such calculations become very lengthy. In this paper, we present a first version of a separable potential constructed directly from available empirical nucleon-nucleon phase shifts (E lab Ͻ1.6 GeV͒, and established deuteron properties, via nonrelativistic inverse scattering. In our approach, the on-shell and off-shell properties of the potential can be independently varied: the on-shell scattering data are exactly fitted by construction while physically motivated off-shell features can be systematically included. This advantage is illustrated by the application of the procedure in the 3 S 1 Ϫ 3 D 1 channel, where the deuteron wave function serves as off-shell input at the binding energy. The simplest potential thus constructed in this channel has rank 4. The deuteron wave function is nevertheless empirically undetermined at high momenta, prompting us to adopt as well as construct several model wave functions that all fit the low momentum deuteron data while allowing variations at high momenta. The effects of these off-shell variations on predicted nuclear matter properties are discussed. No off-shell information is included in the other channels, leading to potentials of rank either 1 or 2. With this simple model potential we perform standard Brueckner nuclear matter ground state calculations and compare the results with Machleidt's using Bonn OBEP. The agreement is good in the S channels and in the singlet D 2 channel. Other channels show larger discrepancies, the most significant of which coming from the 3 P 1 and 3 D 1 channels. These results are explained by the off-shell behavior of our model potential as compared to the Bonn OBEP. Further off-shell input, empirical and/or theoretical, will be explored in future improved versions of the model.

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Inverse scattering problem for a family of phase-equivalent nonlocal potentials

Cited by 4 publications

References 26 publications

The application of inversion to nuclear scattering

The application of inversion to nuclear scattering

New situation in quantum mechanics (wonderful potentials from the inverse problem)

SeparableNNpotentials from inverse scattering for nuclear matter studies

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