Theoretical aspects of the new collective modes in nuclei

Abstract

The interpretation of the low-energy orbital magnetic-dipole excitations of nonspherical nuclei, commonly called scissors modes, is examined. Different models are reviewed, and with the help of the fluid dynamical model and microscopic results from different groups, the relations between the models and their limitations are discussed. Contradictions between semiclassical models, algebraic models and microscopic calculations are shown to be only apparent. The emerging picture is that of a semiclassical vorticity mode which can only exist due to quantum effects but nevertheless, in the quantum limit, is spread over a number of states, each of them at most slightly collective. The mode is an example for the vorticity of nuclear currents which in this case has a direct measurable effect, namely the M1 strength itself. The importance of electric-quadrupole strengths to assess the nature of the modes is emphasized.

Nuclear scissors mode with pairing

“…The situation is changed radically when pairing is included. In this case the main contribution to the scissors mode energy comes from the pairing interaction (the term 4∆ 2 in (26)), E sc is not proportional to δ and the deformation dependence of B(M1) sc becomes quadratic in excellent agreement with QRPA calculations and experimental data [2,4,16,18,25,27,28,29].…”

“…It is known [2], that experimentally observed low lying magnetic dipole strength consists of two separated Table 1.…”

“…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 .…”

Low-energy magnetic dipole response in 56Fe from high-resolution electron scattering

“…M1 transitions are also sensitive to non-nucleonic degrees of freedom in elementary nuclear excitations [4][5][6]. Furthermore, a collective orbital magnetic dipole mode-the scissors mode-has been identified [7] at low excitation energies whose strength and location are intimately related to rotational properties of the nucleus (see, e.g., [8][9][10][11] and references therein).…”

Nuclear orbital and spin scissors with pairing

“…Its experimental discovery [5] has initiated a cascade of theoretical studies. An excellent review of their twenty years development was given by D. Zawischa [6]. The most successful in the description of the energy and excitation probability of the scissors mode turned out the sum rule method [7] and RPA [8].…”