Single- and coupled-channel radial inverse scattering with supersymmetric transformations
| Autor: | Baye, Daniel, Sparenberg, Jean-Marc, Pupasov-Maksimov, Andrey M, Samsonov, Boris F |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | J. Phys. A: Math. Theor. 47 (2014) 243001 (75pp) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8113/47/24/243001 |
| Popis: | The present status of the coupled-channel inverse-scattering method with supersymmetric transformations is reviewed. We first revisit in a pedagogical way the single-channel case, where the supersymmetric approach is shown to provide a complete solution to the inverse-scattering problem. A special emphasis is put on the differences between conservative and non-conservative transformations. 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 and stress remaining difficulties and open questions. We mostly concentrate on two-channel examples to illustrate general principles while keeping mathematics as simple as possible. In particular, we discuss the 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 are shown to lead to practical algorithms for inversion. A convenient technique where the mixing parameter is fitted independently of the eigenphases is developed with iterations of pairs of conjugate transformations and 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. Comment: Topical review, 84 pages, 7 figures, 93 references |
| Databáze: | arXiv |
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