Geometric shapes withg- bosons in the interacting boson model

Devi, Y. D.; Kota, V. K. B.

doi:10.1007/bf01283933

Cited by 20 publications

(31 citation statements)

References 27 publications

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“…The method was first proposed for the sd-IBM [33,34]. The extension to the sdg-IBM was carried out by Devi and Kota [35] for the simplified parameterization (3).…”

Section: Classical Limit Of the Sdg-ibmmentioning

confidence: 99%

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Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian

2015

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“…The method was first proposed for the sd-IBM [33,34]. The extension to the sdg-IBM was carried out by Devi and Kota [35] for the simplified parameterization (3).…”

Section: Classical Limit Of the Sdg-ibmmentioning

confidence: 99%

“…was used by Devi and Kota [35] to derive the geometry of the different limits of the sdg-IBM. The expression for the classical limit of the general sdg-Hamiltonian (7) with this coherent state was given in Ref.…”

Section: Classical Limit Of the Sdg-ibmmentioning

confidence: 99%

Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian

2015

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“…A spherical-to-deformed transition occurs between the limits U(5) ⊗ U(9) and SU(3) of the sdg-U(15) model [17]. Up to a scale factor, irrelevant for the subsequent discussion, a schematic Hamiltonian, transitional between the two limits, is of the formĤ…”

mentioning

confidence: 99%

Correlating Radii and Electric Monopole Transitions of Atomic Nuclei

et al. 2008

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A systematic analysis of the spherical-to-deformed shape phase transition in even-even rare-earth nuclei from 58Ce to 74W is carried out in the framework of the interacting boson model. These results are then used to calculate nuclear radii and electric monopole (E0) transitions with the same effective operator. The influence of the hexadecapole degree of freedom (g boson) on the correlation between radii and E0 transitions thus established, is discussed.PACS numbers: 21.10. Ft, 21.10.Ky, 21.60.Ev, 21.60.Fw Electric monopole (E0) transitions between nuclear levels proceed mainly by internal conversion with no transfer of angular momentum to the ejected electron. For transition energies greater than 2m e c 2 , electronpositron pair creation is also possible; two-photon emission is possible at all energies but extremely improbable. The total probability for a transition between initial and final states |i and |f can be separated into an electronic and a nuclear factor, P = Ωρ 2 , where the nuclear factorwith R = r 0 A 1/3 (r 0 = 1.2 fm) and where the summation runs over the Z protons in the nucleus. The coefficient σ depends on the assumed nuclear charge distribution but in any reasonable case it is smaller than 0.1 and can be neglected if the leading term is not too small [1]. The charge radius of a state |s is given byIt is found experimentally that the addition of neutrons produces a change in the nuclear charge distribution, an effect which can be parametrized by means of neutron and proton effective charges e n and e p in the charge radius operatorT (r 2 ). This leads to the following generalization of Eq. (2):where the sum is over all nucleons and e k = e n (e p ) if k is a neutron (proton). An obvious connection between ρ and the nuclear charge radius is established in the approximation σ = 0 (which henceforth will be made). Again because of the polarization effect of the neutrons, one introduces an E0 operator of the form [2]The ρ defined in Eq.(1) with σ = 0 is then given by ρ = f|T (E0)|i /eR 2 . The basic hypothesis of this Letter is to assume that the effective nucleon charges in the charge radius and E0 transition operators are the same. If this is so, comparison of Eqs. (3) and (4) leads to the relationAt present, a quantitative test of the correlations between radii and E0 transitions implied by (5) cannot be obtained in the context of the nuclear shell model. The main reason is that E0 transitions between states in a single harmonic-oscillator shell vanish identically [3] and a non-zero E0 matrix element is obtained only if valence nucleons are allowed to occupy at least two oscillator shells. This renders the shell-model calculation computationally challenging (if not impossible), certainly in the heavier nuclei which are considered here. We have therefore chosen to test the implied correlations in the context of a simpler approach, namely the interacting boson model (IBM) of atomic nuclei [4]. In this model low-lying collective excitations of nuclei are described in terms of N b bosons distrib...

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“…The method was first proposed for the sd-IBM [8,7,9]. The extension to the sdg-IBM was carried out by Devi and Kota [43] who established the classical limit of the various limits of U(15).…”

Section: The Classical Limitmentioning

confidence: 99%

Phase transitions in the sdg interacting boson model

2010

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Abstract. A geometric analysis of the sdg interacting boson model is performed. A coherent-state is used in terms of three types of deformation: axial quadrupole (β 2 ), axial hexadecapole (β 4 ) and triaxial (γ 2 ). The phase-transitional structure is established for a schematic sdg hamiltonian which is intermediate between four dynamical symmetries of U(15), namely the spherical U(5) ⊗ U(9), the (prolate and oblate) deformed SU ± (3) and the γ 2 -soft SO(15) limits. For realistic choices of the hamiltonian parameters the resulting phase diagram has properties close to what is obtained in the sd version of the model and, in particular, no transition towards a stable triaxial shape is found.

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Geometric shapes withg- bosons in the interacting boson model

Cited by 20 publications

References 27 publications

Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian

Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian

Correlating Radii and Electric Monopole Transitions of Atomic Nuclei

Phase transitions in the sdg interacting boson model

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