dorsal/arxiv
View Schema$J$-matrix and Isolated States
| Authors | A. M. Shirokov, S. A. Zaytsev |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0312065 |
| URL | https://arxiv.org/abs/quant-ph/0312065 |
Abstract
We show that a quantum system with nonlocal interaction can have bound states of unusual type -- Isolated States (IS). IS is a bound state that is not in correspondence with the $S$-matrix pole. IS can have a positive as well as a negative energy and can be treated as a generalization of the bound states embedded in continuum on the case of discrete spectrum states. The formation of IS in the spectrum of a quantum system is studied using a simple rank--2 separable potential with harmonic oscillator form factors. Some physical applications are discussed, in particular, we propose a separable $NN$ potential supporting IS that describes the deuteron binding energy and the s-wave triplet and singlet scattering phase shifts. We use this potential to examine the so-called problem of the three-body bound state collapse discussed in literature. We show that the variation of the two-body IS energy causes drastic changes of the binding energy and of the spectrum of excited states of the three-nucleon system.
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"abstract": "We show that a quantum system with nonlocal interaction can have bound states\nof unusual type -- Isolated States (IS). IS is a bound state that is not in\ncorrespondence with the $S$-matrix pole. IS can have a positive as well as a\nnegative energy and can be treated as a generalization of the bound states\nembedded in continuum on the case of discrete spectrum states. The formation of\nIS in the spectrum of a quantum system is studied using a simple rank--2\nseparable potential with harmonic oscillator form factors. Some physical\napplications are discussed, in particular, we propose a separable $NN$\npotential supporting IS that describes the deuteron binding energy and the\ns-wave triplet and singlet scattering phase shifts. We use this potential to\nexamine the so-called problem of the three-body bound state collapse discussed\nin literature. We show that the variation of the two-body IS energy causes\ndrastic changes of the binding energy and of the spectrum of excited states of\nthe three-nucleon system.",
"arxiv_id": "quant-ph/0312065",
"authors": [
"A. M. Shirokov",
"S. A. Zaytsev"
],
"categories": [
"quant-ph"
],
"title": "$J$-matrix and Isolated States",
"url": "https://arxiv.org/abs/quant-ph/0312065"
},
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