Nuclear scissors mode with pairing

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-Bogoliubov equations. Analytical expressions for energy centroids and 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 E sc and B(M1) 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 it is seen from 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 E sc and B(M1) 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 M1 strength dependence on δ has not yet been examined", see ref.[6].The first investigations of the δ-dependence of E sc and B(M1) sc were performed by W. Shortly afterwards it was discovered [9,10], that in even-even nuclei the total low-energy magnetic dipole strength is closely related to the collective E2 strength of the 2 + 1 state and, thus, depends quadratically on the nuclear deformation parameter.Later J. Enders et al. [11] made a theoretical analysis of experimental data on the scissors

Nuclear scissors with pairing and continuity equation

“…Nevertheless let us calculate the energies and B(M1) factors to get an idea of the order of magnitude of the discrepancy with experimental data. We will also compare our results with those of [3] in order to see the effect of the violation or non-violation of the continuity equation.…”

New type of nuclear collective motion: The spin scissors mode

“…Further developments of the Wigner Function Moments method, namely, the switch from TDHF to Time Dependent Hartree-Fock Bogoliubov (TD-HFB) equations, i.e. taking into account pair correlations, allowed us to improve considerably the quantitative description of the scissors mode [13,14]: for rare earth nuclei the energies are reproduced with ∼ 10% accuracy and B(M1) values were reduced by about a factor of two with respect to their non superfluid values. However, they remain about two times too high with respect to experiment.…”

Nuclear scissors modes and hidden angular momenta

“…We will work with the Wigner transform [20] of equations (5). The relevant mathematical details can be found in [13]. The most essential relations are outlined in Appendix B.…”