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Title: Complex shell model representation including antibound states

Abstract

A generalization of the complex shell model formalism is presented that includes antibound states in the basis. These states, together with bound states, Gamow states, and the continuum background, represented by properly chosen scattering waves, form a representation in which all states are treated on the same footing. Two-particle states are evaluated within this formalism, and observable two-particle resonances are defined. The formalism is illustrated in the well-known case of {sup 11}Li in its bound ground state and in {sup 70}Ca(g.s.), which is also bound. Both cases are found to have a halo structure. These halo structures are described within the generalized complex shell model. We investigated the formation of two-particle resonances in these nuclei, but no evidence of such resonances was found.

Authors:
; ; ; ;  [1];  [2];  [3];  [4];  [2]
  1. Departamento de Fisica, Facultad de Ciencias Exactas, Ingenieria Y Agrimensura, Universidad Nacional de Rosario, Avenida Pellegrini 250, 2000 Rosario (Argentina)
  2. (KTH), Alba Nova University Center, SE-10691 Stockholm (Sweden)
  3. (France)
  4. (Hungary)
Publication Date:
OSTI Identifier:
20699127
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevC.72.054322; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; BOUND STATE; CALCIUM ISOTOPES; GROUND STATES; LITHIUM 11; NUCLEAR HALOS; RESONANCE; SCATTERING; SHELL MODELS; WAVE FORMS

Citation Formats

Id Betan, R., Liotta, R.J., Sandulescu, N., Vertse, T., Wyss, R., Royal Institute of Technology, Institute of Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest-Magurele, Romania, SPhN-DAPNIA, CEA Saclay, F91191 Gif sur Yvette, Institute of Nuclear Research of the Hungarian Academy of Sciences, H-4001 Debrecen, Pf. 51, Hungary, University of Debrecen, Faculty of Information Science, H-4010 Debrecen, Pf. 12, and Royal Institute of Technology. Complex shell model representation including antibound states. United States: N. p., 2005. Web. doi:10.1103/PhysRevC.72.054322.
Id Betan, R., Liotta, R.J., Sandulescu, N., Vertse, T., Wyss, R., Royal Institute of Technology, Institute of Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest-Magurele, Romania, SPhN-DAPNIA, CEA Saclay, F91191 Gif sur Yvette, Institute of Nuclear Research of the Hungarian Academy of Sciences, H-4001 Debrecen, Pf. 51, Hungary, University of Debrecen, Faculty of Information Science, H-4010 Debrecen, Pf. 12, & Royal Institute of Technology. Complex shell model representation including antibound states. United States. doi:10.1103/PhysRevC.72.054322.
Id Betan, R., Liotta, R.J., Sandulescu, N., Vertse, T., Wyss, R., Royal Institute of Technology, Institute of Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest-Magurele, Romania, SPhN-DAPNIA, CEA Saclay, F91191 Gif sur Yvette, Institute of Nuclear Research of the Hungarian Academy of Sciences, H-4001 Debrecen, Pf. 51, Hungary, University of Debrecen, Faculty of Information Science, H-4010 Debrecen, Pf. 12, and Royal Institute of Technology. Tue . "Complex shell model representation including antibound states". United States. doi:10.1103/PhysRevC.72.054322.
@article{osti_20699127,
title = {Complex shell model representation including antibound states},
author = {Id Betan, R. and Liotta, R.J. and Sandulescu, N. and Vertse, T. and Wyss, R. and Royal Institute of Technology and Institute of Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest-Magurele, Romania, SPhN-DAPNIA, CEA Saclay, F91191 Gif sur Yvette and Institute of Nuclear Research of the Hungarian Academy of Sciences, H-4001 Debrecen, Pf. 51, Hungary, University of Debrecen, Faculty of Information Science, H-4010 Debrecen, Pf. 12 and Royal Institute of Technology},
abstractNote = {A generalization of the complex shell model formalism is presented that includes antibound states in the basis. These states, together with bound states, Gamow states, and the continuum background, represented by properly chosen scattering waves, form a representation in which all states are treated on the same footing. Two-particle states are evaluated within this formalism, and observable two-particle resonances are defined. The formalism is illustrated in the well-known case of {sup 11}Li in its bound ground state and in {sup 70}Ca(g.s.), which is also bound. Both cases are found to have a halo structure. These halo structures are described within the generalized complex shell model. We investigated the formation of two-particle resonances in these nuclei, but no evidence of such resonances was found.},
doi = {10.1103/PhysRevC.72.054322},
journal = {Physical Review. C, Nuclear Physics},
number = 5,
volume = 72,
place = {United States},
year = {Tue Nov 01 00:00:00 EST 2005},
month = {Tue Nov 01 00:00:00 EST 2005}
}
  • The generalized Berggren representation treats antibound states on an equal footing with bound states and resonances. The advantage of this approach is that the effects of the antibound poles and the complex continuum can be studied separately. In order to show the power of the method we applied it for shell model problem with two valence neutrons for drip line nuclei.In the example of 11Li nucleus we generated the bound ground state from the unbound basis elements and observed that the antibound state is very important in the building up the halo. However the huge contribution of the antibound polemore » is partly canceled by that of the complex continuum. We predicted a two-particle resonance in 11Li but for making more reliable predictions probably a more sophisticated model has to be used.« less
  • The open quantum system formulation of the nuclear shell model, the so-called Gamow shell model (GSM), is a multiconfigurational SM that employs a single-particle basis given by the Berggren ensemble consisting of Gamow states and the non-resonant continuum of scattering states. The GSM is of particular importance for weakly bound/unbound nuclear states where both many-body correlations and the coupling to decay channels are essential. In this context, we investigate the role of l=0 antibound (virtual) neutron single-particle states in the shell model description of loosely bound wave functions, such as the ground state wave function of a halo nucleus {supmore » 11}Li.« less
  • A comparative study of various representations of the shell model density of states, given its first four moments (centroid, width, skewness, and excess) is made. The Cornish-Fisher representation, which is obtained by the variable transformation method, is shown to be useful in studies using spectral distribution methods.
  • The multiparticle shell model is used to consider the effects of complex configurations on the behavior of inelastic-scattering form factors for high energy electrons; the calculations were performed for anomalous-parity states of the doubly magic /sup 40/Ca, and one examines not only the behavior of the form factors in the usual particle-hole model, but also the effects of the following on the trends in the form factors: states of two particle-two hole type, correlations in the ground state, and loss of nuclear rigidity in the excited state. (JFP)