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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References
J. V. von Neumann and E. Wigner, Phys. Z. 30, 465 (1929).
B. Mulligan, L. G. Arnold, B. Bagchi, and T. O. Krause,Phys. Rev. C 13, 2131 (1976); B. Bagchi, T. O. Krause, and B. Mulligan, Phys. Rev. C 15, 1623 (1977).
R. G. Newton, Scattering Theory of Waves and Particles, 2nd. ed. (Springer-Verlag, New York, 1982).
L. Fonda and R. G. Newton, Ann. Phys. (NY) 10,490 (1960).
H. Friedrich and D. Wintgen, Phys. Rev. A 31, 3964 (1985); Phys. Rev. A 33, 3231 (1985).
L. S. Cederbaum, R. S. Friedman, V. M. Ryaboy, and N. Moiseyev, Phys. Rev. Lett. 90, 013001 (2003).
M. Grupp, G. Nandi, R. Walser, and W. P. Schleich,Phys. Rev. A 73, 050701 (2006).
F. Tabakin, Phys. Rev. 174, 1208 (1968).
J. E. Beam, Phys. Lett. B 30, 67 (1969).
V. A. Alessandrini and C. A. Garcia Canal, Nucl. PhysA 133, 950 (1969).
S. Sofianos, N. J. McGurk, and H. Fiedeldey, Z. Phys. A 286, 87 (1978); G. Pantis, H. Fiedeldey, and D. W. L. Sprung, Z. Phys. A 291, 367 (1979); 294, 101 (1980).
G. Rupp, L. Streit, and J. A. Tjon, Phys. Rev. C 31, 2285 (1985).
A. Delfino, S. K. Adhikari, L. Tomio, and T. Federico, Phys. Rev. C 46, 471 (1992).
A. Delfino, S. K. Adhikari, L. Tomio, and T. Federico, Phys. Rev. C 46, 1612 (1992).
S. Nakaichi-Maeda, Phys. Rev. C 51, 1633 (1995).
G. Pantis, I. E. Lagaris, and S. A. Sofianos, Phys. Rev. C 63, 044009 (2001).
L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-relativistic Theory (Pergamon Press,Oxford, New York, 1977).
L. A. Roriz and A. Delfino, Canad. J. Phys. 67, 37(1989).
H. A. Yamani and L. Fishman, J. Math. Phys. 16, 410(1975).
Yu. L. Dorodnykh, V. G. Neudatchin, and N. P. Yudin, Yad.Fiz. [Sov. J. Nucl. Phys.] 48, 1796 (1988).
B. N. Zakhariev and A. A. Suzko A.A., Direct and Inverse Problems (Springer, Heidelberg, 1990).
Yu. A. Lurie and A. M. Shirokov, Ann. Phys. (NY) 312, 284 (2004); see also contribution to this volume.
A. M. Shirokov, A. I. Mazur, S. A. Zaytsev, J. P. Vary, and T. A. Weber, Phys. Rev. C 70, 044005 (2004);see also contribution to this volume.
M. Dubovoy and J. Flores, Revista Mex. Fiz. 17, 289(1968).
L. Majling, J. Rizek, and Z. Pluhar, Bull. Acad. Sci.USSR, Phys. ser. 38, 2141 (1974).
V. I. Kukulin, V. N. Pomerantsev, Kh. D. Razikov, V. T. Voronchev,and G. G. Ryzhikh, Nucl. Phys. A 586, 151 (1995).
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Shirokov, A., Zaytsev, S. (2008). J-Matrix and Isolated States. In: Alhaidari, A.D., Yamani, H.A., Heller, E.J., Abdelmonem, M.S. (eds) The J-Matrix Method. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6073-1_6
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DOI: https://doi.org/10.1007/978-1-4020-6073-1_6
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