sdg Interacting boson model: hexadecupole degree of freedom in nuclear structure

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

doi:10.1007/bf02847336

Cited by 47 publications

(30 citation statements)

References 181 publications

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“…For a review of studies with the sdg-IBM we refer the reader to Devi and Kota [16]. A spherical-to-deformed transition occurs between the limits U(5) ⊗ U(9) and SU(3) of the sdg-U(15) model [17].…”

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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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Correlating Radii and Electric Monopole Transitions of Atomic Nuclei

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“…We refer the reader to the paper of Devi and Kota [42] for an excellent review of studies with the sdg-IBM. We limit ourselves here to a concise description of the hamiltonian of the model which is needed in this work.…”

Section: The General Hamiltonian Of Sdg-ibmmentioning

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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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“…When the predicted falloffs did not materialize in any of the experiments this was interpreted as due to insufficient collectivity of the sd-boson system at high-spins which could be ameliorated by including g bosons [7,8,9]. Since then, evidence for g bosons from low-spin spectra have continuosly grown with concurrent developments in the sdg-IBM calculations (see [10,11] for recent reviews). Ironically, the high-spin data, which have been the harbinger of g bosons, could not be treated in realistic sdg-IBM calculations.…”

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High-spin states in boson models with applications to actinide nuclei

Kuyucak

1995

Physics Letters B

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We use the 1/$N$ expansion formalism in a systematic study of high-spin states in the $sd$ and $sdg$ boson models with emphasis on spin dependence of moment of inertia and E2 transitions. The results are applied to the high-spin states in the actinide nuclei $^{232}$Th, $^{234-238}$U, where the need for $g$ bosons is especially acute but until now, no realistic calculation existed. We find that the $d$-boson energy plays a crucial role in description of the high-spin data.Comment: 11 pages Latex, 4 figures available upon request (to appear in Phys. Lett. B

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sdg Interacting boson model: hexadecupole degree of freedom in nuclear structure

Cited by 47 publications

References 181 publications

Correlating Radii and Electric Monopole Transitions of Atomic Nuclei

Correlating Radii and Electric Monopole Transitions of Atomic Nuclei

Phase transitions in the sdg interacting boson model

High-spin states in boson models with applications to actinide nuclei

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