Semiclassical and quantal inversion of nuclear scattering at fixed energy

Fiedeldey, H.; Lipperheide, R.; Naidoo, Krishna; Sofianos, S. A.

doi:10.1103/physrevc.30.434

Cited by 26 publications

(21 citation statements)

References 33 publications

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“…The resulting potential is compared by Brandan and Satchler [26] and adjudged less physical than an alternative described in Section 7.2.1. We emphasize that this is not a criticism of LF S l → V (r) inversion except insofar as the the inversion procedure [16,17] requires that S l must be represented rather precisely in a specific multi-term rational function form.…”

Section: Newton-sabatier and Related Methodsmentioning

confidence: 99%

Inverse scattering: applications in nuclear physics

Mackintosh¹

2012

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In what follows we first set the context for inverse scattering in nuclear physics with a brief account of inverse problems in general. We then turn to inverse scattering which involves the S-matrix, which connects the interaction potential between two scattering particles with the measured scattering cross section. The term 'inverse' is a reference to the fact that instead of determining the scattering S-matrix from the interaction potential between the scattering particles, we do the inverse. That is to say, we calculate the interaction potential from the S-matrix. This review explains how this can now be done reliably, but the emphasis will be upon reasons why one should wish to do this, with an account of some of the ways this can lead to understanding concerning nuclear interactions.

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Section: Newton-sabatier and Related Methodsmentioning

confidence: 99%

Inverse scattering: applications in nuclear physics

Mackintosh¹

2012

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“…In this case, the inverse sine transform rṼ (r) coming from Eq. (2.29) is given in terms of the potential V (r) by 30) where R denotes the support of V . For negative values of r, the authors of [28] have put V (−r) = V (r).…”

Section: Inversion Scheme From Mixed Datamentioning

confidence: 99%

Construction of potentials using mixed scattering data

et al. 2008

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The long-standing problem of constructing a potential from mixed scattering data is discussed. We first consider the fixed-ℓ inverse scattering problem. We show that the zeros of the regular solution of the Schrödinger equation, r n (E) which are monotonic functions of the energy, determine a unique potential when the domain of energy is such that the r n (E)'s range from zero to infinity. The latter method is applied to the domain {E ≥ E 0 , ℓ = ℓ 0 } ∪ {E = E 0 , ℓ ≥ ℓ 0 } for which the zeros of the regular solution are monotonic in both parts of the domain and still range from zero to infinity. Our analysis suggests that a unique potential can be obtained from the mixed scattering data {δ(ℓ 0 , k), k ≥ k 0 } ∪ {δ(ℓ, k 0 ), ℓ ≥ ℓ 0 } provided that certain integrability conditions required for the fixed ℓ-problem, are fulfilled. The uniqueness is demonstrated using the JWKB approximation. *

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“…Solutions of the inverse quantal scattering problem at fixed energy are most readily obtained using a semiclassical (WKB) approximation [10,11], when applicable. The WKB approximation produced good results in the case of ' C -' C scattering at energies ranging from 360 to 2400…”

Section: Parametrizations Of Sam S Functionsmentioning

confidence: 99%

“…Since details of the inverse scattering, fixed energy problem and of the use of the WKB approximation to facilitate evaluation of inversion potentials have been presented in the literature [3,10,11], only the salient features will be given herein. The input data for inversion are the scattering phase shifts (equivalently the empirical scattering, S functions).…”

Section: In the Wkb Approximationmentioning

confidence: 99%

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Heavy-ion potentials derived from strong-absorption-model parametrizations of the scattering function

et al. 1991

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Heavy-ion interaction potentials for 360 MeV ' C-' C and 1503 MeV ' 0-" Ca are derived from solutions of the fixed energy, inverse scattering problem. A semiclassical (WKB) approximation is used to obtain those solutions when various strong-absorption-model parametrized S functions are defined from fits to the difFerential cross-section data. The extracted potentials vary significantly in their absorption components within the sensitive radial regions.

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Semiclassical and quantal inversion of nuclear scattering at fixed energy

Cited by 26 publications

References 33 publications

Inverse scattering: applications in nuclear physics

Inverse scattering: applications in nuclear physics

Construction of potentials using mixed scattering data

Heavy-ion potentials derived from strong-absorption-model parametrizations of the scattering function

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