Exactly-solvable coupled-channel potential models of atom-atom magnetic Feshbach resonances from supersymmetric quantum mechanics
| Autor: | Pupasov, Andrey M., Samsonov, Boris F., Sparenberg, Jean-Marc |
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| Rok vydání: | 2007 |
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| Zdroj: | Phys. Rev. A 77, 012724 (2008) (reduced version) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevA.77.012724 |
| Popis: | Starting from a system of $N$ radial Schr\"odinger equations with a vanishing potential and finite threshold differences between the channels, a coupled $N \times N$ exactly-solvable potential model is obtained with the help of a single non-conservative supersymmetric transformation. The obtained potential matrix, which subsumes a result obtained in the literature, has a compact analytical form, as well as its Jost matrix. It depends on $N (N+1)/2$ unconstrained parameters and on one upper-bounded parameter, the factorization energy. A detailed study of the model is done for the $2\times 2$ case: a geometrical analysis of the zeros of the Jost-matrix determinant shows that the model has 0, 1 or 2 bound states, and 0 or 1 resonance; the potential parameters are explicitly expressed in terms of its bound-state energies, of its resonance energy and width, or of the open-channel scattering length, which solves schematic inverse problems. As a first physical application, exactly-solvable $2\times 2$ atom-atom interaction potentials are constructed, for cases where a magnetic Feshbach resonance interplays with a bound or virtual state close to threshold, which results in a large background scattering length. Comment: 19 pages, 15 figures |
| Databáze: | arXiv |
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