Symmetry in exotic nuclei
Symmetries have played an important role in the elucidation of the structure of nuclei and will continue to do so for exotic nuclei. As an example, an application of pseudo-SU(4) symmetry is discussed. It can be used as a starting point for a boson model
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THE EUROPEAN PHYSICAL JOURNAL A
Symmetry in exotic nuclei P. Van Isacker 1 ,a and 0. Juillet 2 GANIL, BP 55027, F-14076 Caen Cedex 5, France LPC, Boulevard du Marechal Juin, F-14050 Caen, France
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Received: 21 March 2002 I Published online: 31 October 2002 -
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Societa Italiana di Fisica
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Springer-Verlag 2002
Abstract. Symmetries have played an important role in the elucidation of the structure of nuclei and will continue to do so for exotic nuclei. As an example, an application of pseudo-SU( 4) symmetry is discussed. It ca_n b~ used as a starting point for a boson model that includes T = 0 as well as T = 1 bosons (IBM-4); appltcatwns are presented for N = Z nuclei from 58 Cu to 70 Br. PACS. 21.60.Fw Models based on group theory
1 A brief history of symmetry in nuclei Symmetry considerations have played an important role in the development of nuclear physics. Already in 1932, at the inception of the discipline, the observed similarities between the proton and the neutron were interpreted by Heisenberg [1] in terms of an "isotopic" symmetry, the origin of which subsequently was related by Wigner [2] to the charge independence of the strong force. Since then, the use and application of symmetries in nuclear physics have gone from strength to strength. The most important developments include Wigner's SU( 4) supermultiplet model [2] which extends Heisenberg's idea to isospin and spin, Racah's SU(2) pairing model [3]leading to the concept of seniority, Elliott's SU(3) model [4] which provides an understanding of rotational band structures in the context of the spherical shell model and the U(6) interacting boson model of Arima and lachello [5] which gives a unified description of collective structures observed in nuclei. These different models, which were developed over a period of more than half a century, can be understood from a common perspective using the concept of dynamical symmetry or spectrum-generating algebra (for a recent review, see ref. [6]). This approach is formulated rigorously in terms of the theory of Lie algebras and can be characterised in words as follows. Given a system of interacting particles (bosons or fermions) a definite mathematical procedure exists to construct a set of commuting operators which supply the quantum numbers of a classification scheme. Furthermore, to each set of commuting operators there corresponds a class of many-body Hamiltonians which can be solved analytically simply by requiring that they be written in terms of these commuting operators. a
e-mail: isacker@ganil. fr
A point that should be emphasised is that this procedure is generic and equally valid for bosons and for fermions, as indeed it is for mixed systems of bosons and fermions. Thus, for example, the applications of the interacting boson model to even-even nuclei [7] could be extended naturally to odd-mass nuclei by introducing an interacting boson-fermion model [8]. The fact that bosons and fermions can be treated alike has led to the formulation of a supersymmetric model [9] which provides a simul
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