Inverse problem for potential scattering at fixed energy

Lipperheide, R.; Fiedeldey, H.

doi:10.1007/bf01434612

Cited by 79 publications

(42 citation statements)

References 27 publications

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“…It is also always possible to make the transformation u)(r)--,gz(r)@(r ) and obtain another phase equivalent local potential [18], which then however has a behaviour similar to the TELP. It is even possible to obtain an exact /-independent ELP for a central nonlocal interaction by making use of the inverse scattering formalism of Lipperheide et al [26]. This potential would represent the exact counterpart to the Perey-Buck potential in the WKB approximation.…”

Section: Uih(e R) = ~ Dt E Ikl(l'r)t Kz(r E -(T/2r) R E T/2r)mentioning

confidence: 98%

Nonlocal potentials and their exact and approximate local and velocity-dependent equivalents

Fiedeldey

Sofianos

1983

Z Physik A

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We show that good approximations to the exact equivalent local potential (ELP) and damping factor of a nonlocal Perey-Buck potential can be calculated in the partial wave WKB approximation of Horiuchi. The exact ELP and damping factor are obtained by means of a method previously given by one of us. We also confirm that an approximate ELP proposed by Bauhoff et al. is of comparable accuracy as the Horiuchi approximation. These /-dependent ELP's exhibit reduced attraction in the interior and provide a test for higher order WKB approximations. We subsequently obtain an equivalent velocity dependent potential (EVDP) which is even exactly wave function equivalent to the original nonlocal potential. This almost local potential, unlike the trivial equivalent local potential, is smooth and well-behaved and is therefore particularly useful in nuclear reactions where the off-shell behaviour of the potential is important.

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Section: Uih(e R) = ~ Dt E Ikl(l'r)t Kz(r E -(T/2r) R E T/2r)mentioning

confidence: 98%

Nonlocal potentials and their exact and approximate local and velocity-dependent equivalents

Fiedeldey

Sofianos

1983

Z Physik A

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“…This procedure represents a full quantal inversion. However, as has been pointed out [16], only genuine Regge poles and zeros lead to reasonable potentials. False Regge poles and zeros are connected with singularities in the potential.…”

Section: Inversion Methods At Fixed Energymentioning

confidence: 87%

“…Among these the exactly solvable models of Bargmann-type [15] are well suited for application. In particular, in the special case of the (so-called) rational inversion scheme [16], the S matrix is of very simple (rational) form,…”

Section: Inversion Methods At Fixed Energymentioning

confidence: 99%

Strong absorption model and its associated potential

et al. 1992

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Using the example of ' C-Pb elastic scattering at El,b --1449 MeV it is shown that, at sufficiently high energies, a full quantum mechanical inversion of heavy-ion scattering data can be performed.Furthermore it is pointed out that the strong absorption model as parametrixed by McIntyre, Wang, and Becker is associated with a potential having strong repulsion at the origin.That repulsion is a remnant of the built-in point Coulomb S matrix. Finally, a systematic study is presented to define the necessary accuracy of experiment required to extend the knowledge of the nucleus-nucleus interaction to smaller radii. PACS number(s): 25.70.Bc, 24. 10.i

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“…The local potentials obtained by this type of inversion method, however, oscillate and ultimately diverge as the origin is approached. The inversion schemes recently introduced by some of the present authors [15] do not suffer from this last disadvantage. To demonstrate the suitability of this new inverse scattering method to determine local equivalent to nonlocal potentials in cases of physical interest, we consider e-160 scattering in the nonlocal fish bone optical model [19,20].…”

Section: Introductionmentioning

confidence: 99%

Equivalent local potential for the fish bone optical potential by inversion of its phase shifts

et al. 1985

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By inversion of the fish bone optical model phase shifts for e-160 scattering we confirm the presence of a Pauli barrier in the surface region of the corresponding equivalent local potential. In the interior the potential depth increases with decreasing energy, in agreement with the semiclassical results of Horiuchi. The advantages of the inversion method for the determination of equivalent local potentials are discussed.

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Inverse problem for potential scattering at fixed energy

Cited by 79 publications

References 27 publications

Nonlocal potentials and their exact and approximate local and velocity-dependent equivalents

Nonlocal potentials and their exact and approximate local and velocity-dependent equivalents

Strong absorption model and its associated potential

Equivalent local potential for the fish bone optical potential by inversion of its phase shifts

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