Supersymmetric transformations in coupled-channel systems

Leeb, H.; Sofianos, S. A.; Sparenberg, Jean-Marc; Baye, Daniel Jean

doi:10.1103/physrevc.62.064003

Cited by 21 publications

(29 citation statements)

References 21 publications

(49 reference statements)

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“…for the problem of phase-equivalent potentials [14,15,16,38,39], even for energy-dependent potentials [6].…”

Section: Discussionmentioning

confidence: 99%

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Generalized Levinson theorem for singular potentials in two dimensions

Sheka¹,

Иванов²,

Mertens³

2003

Phys. Rev. A

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“…for the problem of phase-equivalent potentials [14,15,16,38,39], even for energy-dependent potentials [6].…”

Section: Discussionmentioning

confidence: 99%

“…Moreover singular potentials naturally appear from regular ones under Darboux transformations [14,15,16,38]. Let us recall the principle of Darboux (supersymmetric) transformations for the 2D case [35].…”

Section: A Potentials With Inverse Square Singularitymentioning

confidence: 99%

Generalized Levinson theorem for singular potentials in two dimensions

Sheka¹,

Иванов²,

Mertens³

2003

Phys. Rev. A

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“…The singularities at the origin of the transformed potential, 35) increase by one unit, ν 0 → ν 1 = ν 0 + I N . In this case, there is thus no particular condition on ν 0 .…”

Section: Conservative and Non-conservative Transformationsmentioning

confidence: 99%

“…This paragraph summarizes results from references [34] and [35], where phase-equivalent deformations of coupled potentials were introduced with the aid of supersymmetric transformations. A pair of supersymmetric transformations with equal factorization energies may modify boundstate properties without affecting the scattering matrix of the system in analogy with the single-channel case (see §3.4.1 and §3.5.2).…”

Section: Equal Factorization Energies and Phase-equivalent Potentialsmentioning

confidence: 99%

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Single- and coupled-channel radial inverse scattering with supersymmetric transformations

Baye¹,

Sparenberg²,

Pupasov-Maksimov³

et al. 2014

J. Phys. A: Math. Theor.

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Abstract. The present status of the three-dimensional inverse-scattering method with supersymmetric transformations is reviewed for the coupled-channel case. We first revisit in a pedagogical way the single-channel case, where the supersymmetric approach is shown to provide a complete, efficient and elegant solution to the inverse-scattering problem for the radial Schrödinger equation with short-range interactions. A special emphasis is put on the differences between conservative and non-conservative transformations, i.e. transformations that do or do not conserve the behaviour of solutions of the radial Schrödinger equation at the origin. In particular, we show that for the zero initial potential, a non-conservative transformation is always equivalent to a pair of conservative transformations. These single-channel results are illustrated on the inversion of the neutron-proton triplet eigenphase shifts for the S and D waves.We then summarize and extend our previous works on the coupled-channel case, i.e. on systems of coupled radial Schrödinger equations, and stress remaining difficulties and open questions of this problem by putting it in perspective with the single-channel case. We mostly concentrate on two-channel examples to illustrate general principles while keeping mathematics as simple as possible. In particular, we discuss the important difference between the equal-threshold and different-threshold problems. For equal thresholds, conservative transformations can provide non-diagonal Jost and scattering matrices. Iterations of such transformations in the two-channel case are studied and shown to lead to practical algorithms for inversion. A convenient particular technique where the mixing parameter can be fitted without modifying the eigenphases is developed with iterations of pairs of conjugate transformations. This technique is applied to the neutron-proton triplet S-D scattering matrix, for which exactly-solvable matrix potential models are constructed. For different thresholds, conservative transformations do not seem to be able to provide a non-trivial coupling between channels. In contrast, a single non-conservative transformation can generate coupled-channel potentials starting from the zero potential and is a promising first step towards a full solution to the coupled-channel inverse problem with threshold differences.

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Pseudospin, supersymmetry and the shell structure of atomic nuclei

Typel¹

2008

Nuclear Physics A

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The evolution of single-particle energies with varying isospin asymmetry in the shell model is an important issue when predicting changes in the shell structure for exotic nuclei. In many cases pseudospin partner levels, that are almost degenerate in energy for stable nuclei, are relevant in extracting the size of the shell gaps. A breaking of the pseudospin symmetry can affect the size of these gaps and change the magic numbers accordingly. The strength of the pseudospin splitting is expected to depend in particular on isovector-dependent and tensor contributions to the effective nuclear interaction. A description employing supersymmetric quantum mechanics allows to derive a pseudospin symmetry breaking potential that is regular in contrast to the pseudospin-orbit potential in the conventional relativistic treatment. The derived perturbation potential provides a measure to quantify the symmetry breaking and it can be employed to improve mean-field calculations in order to better reproduce the experimentally observed shell evolution. General potentials with exact pseudospin symmetry are obtained that can be used in relativistic mean-field Hamiltonians.Comment: 33 pages, 1 table, 6 figures, additional references, minor corrections, note added in proof, accepted for publication in Nuclear Physics

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Supersymmetric transformations in coupled-channel systems

Cited by 21 publications

References 21 publications

Generalized Levinson theorem for singular potentials in two dimensions

Generalized Levinson theorem for singular potentials in two dimensions

Single- and coupled-channel radial inverse scattering with supersymmetric transformations

Pseudospin, supersymmetry and the shell structure of atomic nuclei

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