Development of a Cox–Thompson inverse scattering method to charged particles

Palmai, Tamas; Apagyi, Barnabás; Scheid, W.

doi:10.1088/0954-3899/37/2/025101

Cited by 3 publications

(6 citation statements)

References 30 publications

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“…The study shows clearly that the Cox-Thompson method with Riccati-Bessel functions for the reference functions produces the Coulomb singularity with an increasing number of phase shifts only in approximation. It is clear that the Cox-Thompson method with Coulomb wavefunctions as reference functions treats this problem with much higher precision [5].…”

Section: Discussionmentioning

confidence: 99%

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Study of the Cox–Thompson inverse scattering method with a Coulomb potential

Hilk

Scheid

Palmai

et al. 2010

J. Phys. A: Math. Theor.

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In order to learn more about the precision of the inversion by the Cox-Thompson method, we investigated the inversion of phase shifts of a singular potential, namely of a Coulomb potential. Using asymptotically Riccati-Bessel functions as reference functions, we could only approximately reproduce the singularity of the Coulomb potential at the origin. We also show uncertainties in the inverted potential due to different minima in the minimization solution of the nonlinear equations of the Cox-Thompson procedure. As a result, we conclude that one has to take much care with the inversion of experimental phase shifts suffering from measurement errors.

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Section: Discussionmentioning

confidence: 99%

“…where the functions v (ρ) = ρ • n (ρ) are irregular Riccati-Bessel functions [3] and W is the Wronski determinant W [a, b] = ab − ba . The values of the numbers L ∈ T are determined by minimizing the real quantity f min obtained from the highly nonlinear equations [2,4,5,7]:…”

Section: Equations Of the Cox-thompson Methodsmentioning

confidence: 99%

Study of the Cox–Thompson inverse scattering method with a Coulomb potential

Hilk

Scheid

Palmai

et al. 2010

J. Phys. A: Math. Theor.

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“…The inverse potential is finite at the origin starting with a zero derivative (see e.g. [15]) and possesses also a finite first moment ∞ 0 rq(r)dr < ∞. At fixed scattering energy the CT procedure is thus a particularly successful method for (re)constructing inverse potentials.…”

Section: Asymptoticsmentioning

confidence: 99%

“…Furthermore it is also possible to generalize the method to recover potentials having Coulomb tail e.g. by replacing the Riccati-Bessel function by Coulomb wave functions [15,16].…”

Section: Asymptoticsmentioning

confidence: 99%

Quantum mechanical inverse scattering problem at fixed energy: a constructive method

Palmai¹,

Apagyi²

2011

Preprint

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The inverse scattering problem of the three-dimensional Schrödinger equation is considered at fixed scattering energy with spherically symmetric potentials. The phase shifts determine the potential therefore a constructive scheme for recovering the scattering potential from a finite set of phase shifts at a fixed energy is of interest. Such a scheme is suggested by Cox and Thompson [3] and their method is revisited here. Also some new results are added arising from investigation of asymptotics of potentials and concerning statistics of colliding particles. A condition is given [2] for the construction of potentials belonging to the class L1,1 which are the physically meaningful ones. An uniqueness theorem is obtained [2] in the special case of one given phase shift by applying the previous condition. It is shown that if only one phase shift is specified for the inversion procedure the unique potential obtained by the Cox-Thompson scheme yields the one specified phase shift while the others are small in a certain sense. The case of two given phase shifts is also discussed by numerical treatment and synthetic examples are given to illustrate the results. Besides the new results this contribution provides a systematic treatment of the CT method.

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“…Another type of inverse method was developed in the 1960s [6][7][8] to recover fixed energy (or fixed-k) potentials from a set of phase shifts {δ l=0,1,...,l max } given at a particular wave number k. For practical analysis of the measured scattering angular distribution, the modified Newton-Sabatier (mNS) method proved to be a powerful procedure [9,10]. Also the Cox-Thompson method, developed in the last decade for practical problems, offers results with nice physical properties such as the non-singular behavior of the potential at the origin and demanding only a finite set of input data [11,12] to recover the potentials.…”

Section: Introductionmentioning

confidence: 99%