Collective states of odd nuclei in a model with quadrupole-octupole degrees of freedom
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NUCLEI Theory
Collective States of Odd Nuclei in a Model with Quadrupole–Octupole Degrees of Freedom* N. Minkov1)** , S. B. Drenska1) , P. Yotov1), D. Bonatsos2)*** , and W. Scheid3)**** Received October 31, 2006
Abstract—We apply the collective axial quadrupole–octupole Hamiltonian to describe the rotation– vibration motion of odd nuclei with Coriolis coupling between the even–even core and the unpaired nucleon. We consider that the core oscillates coherently with respect to the quadrupole and octupole axialdeformation variables. The coupling between the core and the unpaired nucleon provides a split paritydoublet structure of the spectrum. The formalism successfully reproduces the parity-doublet splitting in a wide range of odd-A nuclei. It provides model estimations for the third angular-momentum projection K on the intrinsic symmetry axis and the related intrinsic nuclear structure. PACS numbers: 21.60.Ev, 21.10.Re, 27.90.+q DOI: 10.1134/S1063778807080248
1. INTRODUCTION The simultaneous manifestation of quadrupole and octupole degrees of freedom in atomic nuclei is associated with typical spectroscopic characteristics of nuclear collective motion [1]. In general, the spectrum contains positive- and negative-parity levels, some of them being related to enhanced electric E1 and E3 transitions [2]. In even–even nuclei, the even- and odd-angular-momentum levels appear with positive and negative parity, respectively, owing to the shape reflection asymmetry. In odd nuclei, the structure of the spectrum is determined by the coupling between the reflection asymmetric even–even core and the motion of the unpaired particle. The combination of the core intrinsic parity with that of the particle to a “total intrinsic parity” provides a split parity-doublet structure of the spectrum. The mutual disposition of the doublet counterparts up or down depends on the parity of the ground state as well as on the possible change in the intrinsic parity at some higher angular momenta. As in some cases, especially in heavy odd nuclei, the angular momentum of the ground state and/or its third projection K are not unambiguously
determined, the complicated structure of the spectrum represents a challenging subject for study from both experimental and theoretical points of view. That is why various theoretical models developed initially to explain the properties of quadrupole–octupole deformations in even–even nuclei have been extended to describe the respective properties in odd nuclei [2, 3]. Recently, a collective model for the quadrupole– octupole vibration–rotation motion in even–even nuclei was proposed [4]. It was able to reproduce some basic characteristics as energy levels, parity shift, and electric transition properties in nuclei with collective bands built on coupled quadrupole–octupole vibrations. The purpose of the present work is to extend this model approach to the case of odd nuclei and to apply it to collective spectra in the region of heavy odd nuclei. For this reason, we consider the Coriolis coupling of the “soft” qua
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