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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Keywords: Structure of odd nuclei, solar neutrino capture rates.PACS numbers: 21.60, 25.30.Pt structure information involved in these calculations are discussed.capture rates for the 71 Ga and Usln-{JSF detectors. Uncertainties regarding nuclear calculated (assuming complete 17,, -> uc conversion), as well as the solar neutrino reactions. The total capture cross sections of the reactor electron antineutrinos are calculated and compared with those extracted from experimental spectra of (p, n) into account. Gamow-Teller strength functions of "Ga, usln and 19F nuclei are hole (ph) and particle-particle channel, and also the ph.-continuum are taken effect due to the odd quasiparticle, the effective N N -interactions both in the particle framework of the self-consistent finite Fermi-system theory. The pairing blockingThe charge-exchange excitations of superiuid odd-A nuclei are studied within the 1Br (-471 keV), 115In (-120 keV) which are sensitive both to low and to high energy ones are the odd-A nuclei with very low reaction thresholds: "Ga (Q]; : -236 keV), A number of nuclei were suggested for neutrino detectors. The most promising 17,, + AZ(I") -> e"` + AZ_1(I'"') .(1) Vc + Az(I") -·¤" + Az+1(I'"') » the v(17)-capture reactions, which take place due to the electroweak charge currents, antineutrino capture rates in detectors based on the inverse Bt-decay processes, i.e. onThe practical aspect of the problem concerns solar neutrino [15] and reactor taken with some care (see Refs. [13,14]).from recent shell-model analysis of the high-energy ,8-decay of 3- [Ca [8] have to be conclusions about the absence of gA /gV renormalization in nuclear medium drawn cation which is technically unavoidable for medium and heavy nuclei. Therefore the However, such shell-model approaches suffer from the sensitivity to the basis trun configurations can be included more efficiently than in the QRPA-like scheme [12].shell models are widely used [10, 11]. An advantage of these models is that complex The study of charge-exchange modes of excitations of superfluid odd-A nuclei is

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