Nuclear scissors mode with pairing
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NUCLEI Theory
Nuclear Scissors Mode with Pairing* ˜ 3) E. B. Balbutsev1)** , L. A. Malov1), P. Schuck2), M. Urban2) , and X. Vinas Received June 22, 2007; in final form, October 25, 2007
Abstract—The coupled dynamics of the scissors mode and the isovector giant quadrupole resonance are studied using a generalized Wigner function moments method, taking into account pair correlations. Equations of motion for angular momentum, quadrupole moment, and other relevant collective variables are derived on the basis of the time-dependent Hartree–Fock–Bogolyubov equations. Analytical expressions for energy centroids and transition probabilities are found for the harmonic-oscillator model with the quadrupole–quadrupole residual interaction and monopole pairing force. Deformation dependences of energies and B(M 1) values are correctly reproduced. The inclusion of pair correlations leads to a drastic improvement in the description of qualitative and quantitative characteristics of the scissors mode. PACS numbers: 21.60.Ev, 21.60.Jz, 24.30.Cz DOI: 10.1134/S1063778808060057
1. INTRODUCTION An exhaustive analysis of the coupled dynamics of the scissors mode and the isovector giant quadrupole resonance (GQR) in a model of harmonic oscillator (HO) with quadrupole–quadrupole (QQ) residual interaction has been performed in [1]. The method of Wigner function moments (WFM) was applied to derive the dynamical equations for angular momentum and quadrupole moment. Analytical expressions for energies, B(M 1) and B(E2) values, sum rules, and flow patterns of both modes were found for arbitrary values of the deformation parameter. The subtle nature of the phenomenon and its peculiarities were clarified. Nevertheless, this description was not complete, because pairing was not taken into account. It is well known [2] that pairing is very important for the correct quantitative description of the scissors mode. Moreover, its role is crucial for an explanation of the empirically observed deformation dependence of Esc and B(M 1)sc . The prediction of the scissors mode was inspired by the geometrical picture of a counterrotating oscillation of the deformed proton density against the deformed neutron density [3, 4]. Thus, as is seen from ∗
The text was submitted by the authors in English. Joint Institute for Nuclear Research, Moscow oblast, 141980 Dubna, Russia. 2) Institut de Physique Nucleaire, CNRS and University ParisSud, France. 3) ´ Departament d’Estructura i Constituents de la Materia Facultat de F ´ısica, Universitat de Barcelona, Spain. ** E-mail: [email protected] 1)
its physical nature, the scissors mode can be observed only in deformed nuclei. Therefore, quite naturally, the question of the deformation dependence of its properties (for example, energy Esc and B(M 1)sc value) arises. However, during the first years after its discovery in 156 Gd [5], “nearly all experimental data were limited to nuclei of about the same deformation (δ ≈ 0.20−0.25), and the important aspect of orbital M 1-strength dependence on δ has not yet been examined
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