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$J$-matrix and Isolated States

A. M. Shirokov·S. A. Zaytsev
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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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A. M. Shirokov, S. A. Zaytsev. 2003-12-08. $J$-matrix and Isolated States. https://arxiv.org/abs/quant-ph/0312065

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