Can we do without the Majorana term in the effective nuclear interaction?

Barrett, B. R.; Davis, E. D. D.; Diallo, A. F.

doi:10.1103/physrevc.50.1917

Phys. Rev. C

1994

DOI: 10.1103/physrevc.50.1917

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Can we do without the Majorana term in the effective nuclear interaction?

B. R. Barrett

E. D. D. Davis

A. F. Diallo

Abstract: Probably not, but we present phenomenological evidence that the strength of this term necessary to reproduce collective M 1-transition strength data could be significantly smaller than is conventionally assumed and therefore more in line with naive microscopic considerations. We also find that g-boson effects are important to the reproduction of the summed M1 strength.

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Cited by 4 publications

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“…The latter approach breaks F -spin symmetry [9] and could cause a significant amount of F -spin mixing into the lowenergy states if the Majorana interaction were not too strong [10]. The properties of mixed-symmetry states with F -spin quantum number F = F max − 1 are very sensitive to the strength of the Majorana interaction [11] and, thus, to the amount of F -spin mixing in the lowenergy wave functions [12].…”

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Parity assignments inYb172,174using polarized photons and theKquantum number in rare earth nuclei

et al. 2005

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The 100 % polarized photon beam at the High Intensity γ-ray Source (HIγS) at Duke University has been used to determine the parity of six dipole excitations between 2.9 and 3.6 MeV in the deformed nuclei 172,174 Yb in photon scattering ( γ, γ ′ ) experiments. The measured parities are compared with previous assignments based on the K quantum number that had been assigned in Nuclear Resonance Fluorescence (NRF) experiments by using the Alaga rules. A systematic survey of the relation between γ-decay branching ratios and parity quantum numbers is given for the rare earth nuclei.PACS numbers: 21.10. Hw, 25.20.Dc, 27.70.+y Low-lying dipole excitations in heavy nuclei have been studied extensively using the Nuclear Resonance Fluorescence (NRF) or photon scattering method, which provides a model-independent way to determine excitation energies, spins, decay widths, decay branchings, and transition probabilities [1]. The parity of a nuclear state can be determined by either scattering unpolarized γ-rays and measuring polarization in the exit channel, or using linearly polarized γ-ray beam and measuring the azimuthal angular distribution of the scattered photons. For deformed even-even nuclei the K quantum number of J = 1 states can be assigned within the validity of the Alaga rules [2] from the electromagnetic decay branching ratio In general, there is no relation between the K quantum number and the parity of a J = 1 excitation [3]. However, restricting oneself to dipole excitations that carry the largest part of the excitation strength one selects collective modes for which certain selection rules may exist. Within realistic calculations for deformed nuclei in the framework of the interacting boson model (IBM) [4] with s-and d-proton and neutron bosons (sd-IBM-2), where negative parity states are not included, all J π = 1 + levels have a branching ratio corresponding to K = 1 (e.g. the bandheads of the K = 0 octupole vibrational band). This suggests that those states with J = 1 and branching ratios corresponding to K = 0 have negative parity. Positive parity has generally been assumed in previous works for all K = 1 excitations in the energy range of the M 1 scissors mode for calculating the summed B(M 1) strength, if no direct parity assignments were available. This rule of thumb was supported by γ-ray polarization measurements analyzing Compton-scattering asymmetries of the NRF γ-ray lines in some deformed nuclei of the Nd to Er even-even isotopic sequences [1]. It was concluded that at least the strong dipole excitations in sufficiently axially-symmetrically deformed nuclei decay according to the Alaga rules for ∆K = 1 (0) for positive (negative) parity.

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Parity assignments inYb172,174using polarized photons and theKquantum number in rare earth nuclei

et al. 2005

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gboson and systematics of theM1 scissors mode

1996

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We discuss systematics of the M 1 scissors mode within the interacting boson model when the g-boson degree of freedom is included explicitly and microscopically motivated choices of model parameters are adopted. We try to relate the M 1 centroid energy to the energetics of deformation. We conclude that, with the introduction of a hexadecapole-hexadecapole interaction and a g-boson admixture in the ground state of only a few percent, we can obtain reasonable estimates of the M 1 centroid energy, without invoking a Majorana interaction. If one takes seriously variations in microscopic estimates of boson g factors, then the summed M 1 strength near midshell can be interpreted in terms of boson occupation numbers which saturate. ͓S0556-2813͑96͒05206-5͔ PACS number͑s͒: 21.10. Re, 21.30.Fe, 21.60.Fw One of the triumphs of the interacting boson model ͑IBM͒ is its ability to account for the properties of the M 1 scissors mode discovered after its introduction ͓1͔. There are, however, disquieting features: First, there is the fact that to reproduce the excitation energies of 1 ϩ scissors states the somewhat artificial Majorana interaction is apparently required ͓2͔; second, the summed strength does not appear to be consistent with the saturation of the groundstate d-boson occupation number expected near midshell ͓3͔ ͑the ''M 1 saturation'' problem͒. In this paper, we present possible resolutions to these problems. Our primary result is that, if one includes a g-boson degree of freedom ͑in addition to the usual s and d bosons͒, then one can dispense with the use of the Majorana interaction while still adhering to microscopically motivated values of the model parameters. If one takes seriously variations in microscopic estimates of boson g factors near midshell, then the summed strength does admit interpretation in terms of boson occupation numbers which saturate.In earlier work ͓4͔, we identified a deformation contribution E c def to the centroid energy arising from the dependence in the action of the ͑standard͒ quadrupole interaction ϪQ p •Q n on the neutron-proton ͑or F-spin͒ symmetry of states. The magnitude of this deformation contribution would have been inadvertantly underestimated in ͓2͔ because of the nonstandard ͑and microscopically implausible͒ F-spin scalar quadrupole interaction Ϫ(Q p ϩQ n )•(Q p ϩQ n ) adopted. For the deformed Sm isotopes, we found that E c def almost certainly could account for a substantial fraction of the centroid energy ͑80% or so for the choice of model parameters made in ͓4͔͒. In this paper, we attempt to understand the energetics of the M 1 scissors state solely in terms of the deformation contribution E c def . We believe this approach to be natural: Within the sdIBM-2, the M 1 scissors mode may be viewed in the intrinsic frame as an F-spin isovector quad-rupole excitation ͓5͔; within the sdgIBM-2 ͑which we consider below͒, the scissors mode is a superposition of F-spin isovector quadrupole and hexadecapole excitations.In most IBM studies of the M 1 scissors mode, it is customary t...

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Importance of the hexadecapole-hexadecapole interaction

Davis

Barrett

Diallo³

1999

Phys. Rev. C

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Can we do without the Majorana term in the effective nuclear interaction?

Cited by 4 publications

References 23 publications

Parity assignments inYb172,174using polarized photons and theKquantum number in rare earth nuclei

Parity assignments inYb172,174using polarized photons and theKquantum number in rare earth nuclei

gboson and systematics of theM1 scissors mode

Importance of the hexadecapole-hexadecapole interaction

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