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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.

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A system of equations is obtained for the Cooper gap in nuclei. The system takes two mechanisms of superfluidity into account in an approximation quadratic in the phonon-production amplitude: a BardeenCooper-Schrieffer ͑BCS͒-type mechanism and a quasiparticle-phonon mechanism. These equations are solved for 120 Sn in a realistic approximation. If the simple procedures proposed are used to determine the new particle-particle interaction and to estimate the average effect, then the contribution of the quasiparticle-phonon mechanism to the observed width of the pairing gap is 26% and the BCS-type contribution is 74%. This means that at least in semimagic nuclei pairing is of a mixed nature -it is due to the two indicated mechanisms, the first being mainly a surface mechanism and the second mainly a volume mechanism. © 1999 American Institute of Physics. ͓S0021-3640͑99͒00110-3͔PACS numbers: 21.60. Ϫn, 74.20.Fg, 67.20.ϩk In the microscopic theory of ordinary superconductors the É liashberg theory, 1 in which the interaction of the electrons that leads to pairing is due to the exchange of phonons, describes the mechanism of superconductivity quite well. In the weak electronphonon interaction limit g 2 Ӷ1 this mechanism reduces to the well-known BardeenCooper-Schrieffer ͑BCS͒ model.The situation is somewhat different in the microscopic theory of nuclei with pairing ͑nonmagic nuclei͒. As a rule, the width of the superfluid gap is determined experimentally or calculated using the BCS equation with a phenomenologically chosen particleparticle ͑pp͒ interaction. 2,3 This interaction and therefore the gap are energy-independent.In other words the quasiparticle-phonon interaction ͑QPI͒ in the problem of pairing in nuclei is taken into account only effectively -to the extent that the quasiparticlephonon pairing mechanism can be reduced to the indicated BCS mechanism. This would be justified if g 2 Ӷ1, where g is the phonon production amplitude, in nuclei. In nuclei with pairing, however, g 2 Ͼ1 can occur in each of the two nucleon systems because of the existence of a low-lying 2 ϩ collective level. 4 In nuclei with pairing the weak inequality g 2 Ͻ1 can occur in one of the nucleon systems ͑semimagic nuclei; see calculations in Ref. 5 for 120 Sn). Therefore the quasiparticle-phonon pairing mechanism must be examined explicitly, and it is of interest to study the realistic case g 2 Ͻ1 first.

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Within the Theory of Finite Fermi Systems (TFFS), a model is developed to describe Phonon Coupling (PC) effects in odd magic and semi-magic nuclei. It is based on the perturbation theory in , where gL is the vertex of the L-phonon creation. Among all diagrams the set is separated which depends significantly on the nucleus under consideration and the state λ of the odd nucleon. An ansatz is proposed to take into account the phonon tadpole diagram which ensures the total angular-momentum conservation. Calculations are carried out for three odd-proton chains, the odd Tl, In and Sb ones. Different PC corrections strongly cancel each other. In the result, the total PC correction to magnetic moments in magic nuclei is, as a rule, negligible. In the non-magic nuclei considered it is noticeable and improves the agreement with data.

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The electron-ion scattering experiment ELISe is part of the installations envisaged at the new experimental storage ring at the international Facility for Antiproton and Ion Research (FAIR) in Darmstadt, Germany. It offers an unique opportunity to use electrons as probe in investigations of the structure of exotic nuclei. The conceptual design and the scientific challenges of ELISe are presented.