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

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The influence of the boundary conditions used in the Wigner-Seitz (WS) approximation applied to the neutron star inner crust is examined. The generalized energy functional method which includes the neutron and proton pairing correlations is used. Predictions of two versions of the boundary conditions are compared with each other. The uncertainties in the equilibrium configuration (Z, R c ) of the crust, where Z is the proton charge and R c , the radius of the WS cell, correspond to variation of Z by 2 -6 units and of R c , by 1 -2 fm. The effect of the boundary conditions is enhanced at increasing density. These uncertainties are smaller than the variation of Z and R c coming from the pairing effects. In the case of high densities, k F > ∼ 1 fm −1 , the most important uncertainty occurs in the value of the neutron gap ∆ n . In the WS approximation, it originates from the shell effect in the neutron single-particle spectrum which is rather pronounced in the case of larger k F and, correspondingly, small R c values, but it becomes negligible at lower density near the drip point. An approximate recipe to avoid this uncertainty is suggested.

Excitation energies and transition probabilities of the first 2 + excitations in even tin and lead isotopes as well as the quadrupole moments of odd neighbors of these isotopes are calculated within the self-consistent Theory of Finite Fermi Systems based on the Energy Density Functional by Fayans et al. The effect of the density dependence of the effective pairing interaction is analyzed in detail by comparing results obtained with volume and surface pairing. The effect is found to be noticeable. For example, the 2 + -energies are systematically higher at 200-300 keV for the volume paring as compared with the surface pairing case. But on the average both models reasonably agree with the data. Quadrupole moments of odd-neutron nuclei are very sensitive to the single-particle energy of the state λ under consideration due to the Bogolyubov factor (u 2 λ − v 2 λ ). A reasonable agreement with experiment for the quadrupole moments has been obtained for the most part of odd nuclei considered. The method used gives a reliable possibility to predict quadrupole moments of unstable odd nuclei including very neutron rich ones.