An application of the interacting boson model to the first half of the sd shell

Halse, P.; Elliott, J.P.; Evans, J.A.

doi:10.1016/0375-9474(84)90510-4

Cited by 61 publications

(19 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This was demonstrated for nuclei in the sd-shell [27,28] .,. space are feasible for nuclei just beyond ~~Ni28 but they become increasingly difficult for the heavier isotopes.…”

Section: The Isospin-invariant Boson Model Ibm-4mentioning

confidence: 81%

Symmetry in exotic nuclei

Isacker

Juillet

2003

Exotic Nuclei and Atomic Masses

View full text Add to dashboard Cite

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 A brief history of symmetry in nucleiSymmetry 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) 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 simultaneous description of "boson-like" (even-mass) and "fermion-like" (odd-mass) nuclei. Nuclear supersymmetry has been tested extensively and confirmed in a number of cases in the 1980s. Recent advances in detector resolution have made it possible to propose tests of dynamical supersymmetry in even more complicated odd-odd nuclei, and were successful in the example of the nucleus 198 Au [10] (see also ref. [ 11]) .There have also been developments over the last years in the theory of dynamical symmetries. For example, generalisations towards two different kinds of partial dynamical symmetry have been formulated [12,13]. And, very recently, a ne...

show abstract

“…This was demonstrated for nuclei in the sd-shell [27,28] .,. space are feasible for nuclei just beyond ~~Ni28 but they become increasingly difficult for the heavier isotopes.…”

Section: The Isospin-invariant Boson Model Ibm-4mentioning

confidence: 81%

Symmetry in exotic nuclei

Isacker

Juillet

2003

Exotic Nuclei and Atomic Masses

View full text Add to dashboard Cite

show abstract

“…Equation (12d) is the dynamical condition determining the i-th two-nucleon eigenstate of HSM with eigenenergy ESt. Of course, this is equivalent to demanding that the one-boson state created by (11) be an eigenstate of the boson hamiltonian (8).…”

Section: The Microscopic Boson Hamiltonianmentioning

confidence: 99%

“…Using (10), (12), (14) and the properties of the ClebschGordan coefficients, we can express (8) in the form…”

Section: The Microscopic Boson Hamiltonianmentioning

confidence: 99%

“…Two such versions, IBM-3 [5] and IBM-4 [7], have been considered so far. Their encouraging success (especially that of the IBM-4) [8] raises the important question of the microscopic foundation of the IBM in light nuclei. Although tremendous progress has been achieved in formulating the theoretical basis of the IBM in heavy nuclei [9], the same cannot as yet be said about light nuclei.…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Microscopic foundation of the interacting boson model in thes d-shell nuclei

Kuchta¹

1988

Z. Physik A - Atomic Nuclei

View full text Add to dashboard Cite

Starting from an isospin invariant shell-model hamiltonian, we describe a method for deriving microscopically the IBM-hamiltonian appropriate to light sd-shell nuclei. The key ingredients of our approach are: a) the Belyaev-Zelevinsky-Marshalek (BZM) bosonization procedure; b) two successive unitary transformations that extract the "maximally (s~, s~) and J decoupled" collective bosons with angular momenta J=0 + s~+, + + + d+~(T= 0), d+~(T= 1)).The method is applied to obtain the low-energy spec-= 2(d,~,,, d~, tra and the electron scattering form factors for the 0~-~2~-transitions in g~ and 24Mg. Good agreement with the exact shell-model results is achieved. The inclusion of proton-neutron bosons (s~+~, d~+~ (T= 1), d~+~(T=0)), as well as the renormalization of boson parameters due to the non-collective degrees of freedom, are shown to play a crucial role.

show abstract

“…The rationale behind this choice is that the two-particle isospin-spin combinations ͑TS͒ ͑10͒ and ͑01͒ are the ones favored by Wigner's SU(4) classification [11], which is known to have physical significance in light nuclei. In heavier nuclei SU(4) symmetry is increasingly broken [12] but IBM-4 may remain a valid approximation (as it does in sd-shell nuclei [13,14]) if the boson L and S are equated to the pseudo-orbital and pseudospin angular momentum quantum numbers of two fermions [15].…”

mentioning

confidence: 99%

T=0versusT=1Pairing in the Interacting Boson Model

Isacker

Warner

1997

Phys. Rev. Lett.

View full text Add to dashboard Cite

A connection is established between an interacting boson model (IBM) that includes T 1 bosons (IBM-3) and one that includes T 0 as well as T 1 bosons (IBM-4). The connection relies on an IBM-4 classification that breaks Wigner's SU(4) symmetry. The resulting generalized IBM-4 is relevant for studying the competition between T 0 and T 1 pairing in N ϳ Z nuclei. Consequences for the pair structure in self-conjugate nuclei are discussed. [S0031-9007(97)

show abstract

An application of the interacting boson model to the first half of the sd shell

Cited by 61 publications

References 22 publications

Symmetry in exotic nuclei

Symmetry in exotic nuclei

Microscopic foundation of the interacting boson model in thes d-shell nuclei

T=0versusT=1Pairing in the Interacting Boson Model

Contact Info

Product

Resources

About