The foundation of the local energy-density functional method to describe the nuclear ground-state properties is given. The method is used to investigate differential observables such as the odd-even mass differences and odd-even effects in charge radii. For a few isotope chains of spherical nuclei, the calculations are performed with an exact treatment of the Gor'kov equations in the coordinate-space representation. A zero-range cutoff density-dependent pairing interaction with a density-gradient term is used. The evolution of charge radii and nucleon separation energies is reproduced reasonably well including kinks at magic neutron numbers and sizes of staggering. It is shown that the density-dependent pairing may also induce sizeable staggering and kinks in the evolution of the mean energies of multipole excitations. The results are compared with the conventional mean field Skyrme-HFB and relativistic Hartree-BCS calculations. With the formulated approach, an extrapolation from the pairing properties of finite nuclei to pairing in infinite matter is considered, and the dilute limit near the critical point, at which the regime changes from weak to strong pairing, is discussed. 21.65.+f; 21.90.+f; 24.10.Cn PACS

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.

To clarify the physical nature of the orbital magnetic dipole excitations discussed widely in the past few years, a semiclassical model is presented and the nuclei a56Gd and 164Dy are investigated microscopically. The semiclassical model involves a consistent treatment of vibrational and rotational degrees of freedom; the microscopic results are obtained in quasiparticle-random-phase approximation (QRPA) with a realistic effective interaction. The results disagree with the picture of scissors modes or rotational vibrations.

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