Sum rules for B (M1, 01+ → 1+) strength in IBM-3 and IBM-4

P. Halse; P. Van Isacker; B. R. Barrett

doi:10.1016/0370-2693(95)01213-A

Sum rules for B (M1, 0₁⁺ → 1⁺) strength in IBM-3 and IBM-4

P. Halse, P. Van Isacker, B. R. Barrett

Physics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Sum rules for B (M1, 0₁⁺ → 1_i⁺) strength are derived for even-even nuclei in the isospin-invariant forms of the IBM, IBM-3 and IBM-4, in the cases where the respective natural internal symmetries, isospin U (3) and U (6) ⊃ SU (4), are conserved. Subsequently, the total strength is resolved into its component partial sums to the allowed isospins (and SU (4) representations in IBM-4). In cases where the usual IBM dynamical symmetries are also valid, a complete description of all B (M1, 0₁⁺ → 1_i⁺) follows. In contrast to IBM-2, there is fragmentation of the strength even in the dynamical symmetry cases, for T ≠ 0, over two states in IBM-3, and over three states in IBM-4. An application to the first half of the sd-shell reveals differences in strength between IBM-4 and the shell model which may also indicate areas for further study in IBM-2 analyses of heavier nuclei.

Original language	English (US)
Pages (from-to)	145-150
Number of pages	6
Journal	Physics Letters B
Volume	363
Issue number	3
DOIs	https://doi.org/10.1016/0370-2693(95)01213-A
State	Published - Nov 23 1995

Keywords

IBM-3 and IBM-4
Interacting boson model
M1 sum rules
Scissor mode

ASJC Scopus subject areas

Nuclear and High Energy Physics

Access to Document

10.1016/0370-2693(95)01213-A

Cite this

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title = "Sum rules for B (M1, 01+ → 1+) strength in IBM-3 and IBM-4",

abstract = "Sum rules for B (M1, 01+ → 1i+) strength are derived for even-even nuclei in the isospin-invariant forms of the IBM, IBM-3 and IBM-4, in the cases where the respective natural internal symmetries, isospin U (3) and U (6) ⊃ SU (4), are conserved. Subsequently, the total strength is resolved into its component partial sums to the allowed isospins (and SU (4) representations in IBM-4). In cases where the usual IBM dynamical symmetries are also valid, a complete description of all B (M1, 01+ → 1i+) follows. In contrast to IBM-2, there is fragmentation of the strength even in the dynamical symmetry cases, for T ≠ 0, over two states in IBM-3, and over three states in IBM-4. An application to the first half of the sd-shell reveals differences in strength between IBM-4 and the shell model which may also indicate areas for further study in IBM-2 analyses of heavier nuclei.",

keywords = "IBM-3 and IBM-4, Interacting boson model, M1 sum rules, Scissor mode",

author = "P. Halse and {Van Isacker}, P. and Barrett, {B. R.}",

note = "Funding Information: Oneo f us (B.R.B.) acknowledgeths eh ospitalityo f GANIL, wheret his work was carriedo ut, and P.V.I. thanksJo e Ginocchiof or a discussionco ncerningth is work. This researchis supportedin part by the National ScienceF oundationG, rant No. INT-9415451 andb y theC entreN ationadl eR echercheS cientifique.",

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AU - Halse, P.

AU - Van Isacker, P.

AU - Barrett, B. R.

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N2 - Sum rules for B (M1, 01+ → 1i+) strength are derived for even-even nuclei in the isospin-invariant forms of the IBM, IBM-3 and IBM-4, in the cases where the respective natural internal symmetries, isospin U (3) and U (6) ⊃ SU (4), are conserved. Subsequently, the total strength is resolved into its component partial sums to the allowed isospins (and SU (4) representations in IBM-4). In cases where the usual IBM dynamical symmetries are also valid, a complete description of all B (M1, 01+ → 1i+) follows. In contrast to IBM-2, there is fragmentation of the strength even in the dynamical symmetry cases, for T ≠ 0, over two states in IBM-3, and over three states in IBM-4. An application to the first half of the sd-shell reveals differences in strength between IBM-4 and the shell model which may also indicate areas for further study in IBM-2 analyses of heavier nuclei.

AB - Sum rules for B (M1, 01+ → 1i+) strength are derived for even-even nuclei in the isospin-invariant forms of the IBM, IBM-3 and IBM-4, in the cases where the respective natural internal symmetries, isospin U (3) and U (6) ⊃ SU (4), are conserved. Subsequently, the total strength is resolved into its component partial sums to the allowed isospins (and SU (4) representations in IBM-4). In cases where the usual IBM dynamical symmetries are also valid, a complete description of all B (M1, 01+ → 1i+) follows. In contrast to IBM-2, there is fragmentation of the strength even in the dynamical symmetry cases, for T ≠ 0, over two states in IBM-3, and over three states in IBM-4. An application to the first half of the sd-shell reveals differences in strength between IBM-4 and the shell model which may also indicate areas for further study in IBM-2 analyses of heavier nuclei.

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