We calculate, for the first time, the state-dependent pairing gap of a finite nucleus ( 120 Sn) diagonalizing the bare nucleon-nucleon potential (Argonne v14) in a Hartree-Fock basis (with effective k−mass m k ≈ 0.7 m), within the framework of the BCS approximation including scattering states up to 800 MeV above the Fermi energy to achieve convergence. The resulting gap accounts for about half of the experimental gap. We find that a consistent description of the low-energy nuclear spectrum requires, aside from the bare nucleon-nucleon interaction, not only the dressing of singleparticle motion through the coupling to the nuclear surface, to give the right density of levels close to the Fermi energy (and thus an effective mass m * ≈ m), but also the renormalization of collective vibrational modes through vertex and self-energy processes, processes which are also found to play an essential role in the pairing channel, leading to a long range, state dependent component of the pairing interaction. The combined effect of the bare nucleon-nucleon potential and of the induced pairing interaction arising from the exchange of low-lying surface vibrations between nucleons moving in time reversal states close to the Fermi energy accounts for the experimental gap.In the study of finite many-body systems such as the atomic nucleus with its rich variety of quantal size effects, structural properties, and fluctuations, the central problem has been to identify the appropriate degrees of freedom for describing the phenomena encountered. The complementary concepts referring to the independent motion of the individual nucleons and the collective behaviour of the nucleus as a whole provide the elementary modes of excitation needed to describe the system [1]. The unifying picture emerging from the interweaving of these degrees of freedom and described in terms of nuclear field theory (NFT) [2-6] based on the particlevibration coupling (for other related approaches, see e.g. [7][8][9][10]) and tailored upon QED [11][12], has been applied to a number of schematic models and realistic situations [13][14][15][16][17][18][19][20][21] and its validity demonstrated. It thus provides a natural framework to assess the role different degrees of freedom play in the nuclear structure.An important subject presently under intensive study concerns the characterization of an eventual long range component of the pairing interaction in nuclei [22][23][24]. In what follows we use NFT to assess the importance the exchange of vibrations between pairs of nucleons moving in time reversal states have in building up pairing correlations in nuclei, taking also into account self-energy and vertex corrections (i.e. avoiding using approximations which, in condensed matter literature are connected with the so-called Migdal theorem, cf. ref.[25] and refs. therein).To this scope, we study the quasiparticle and vibrational spectrum of odd-and even-isotopes of singleclosed-shell nuclei, where all the richness of the singleparticle and collective degrees of freedom a...

The coupling of single-particle motion and of vibrations in 4 11Be produces dressed neutrons which spend only a fraction of the time in pure single-particle states, and which weighing differently from the bare neutrons lead to parity inversion. If neutrons are progressively added to a normal nucleus, the Pauli principle forces them into states of higher momentum. When the core becomes neutron saturated the nucleus expels most of the wave function of the last neutrons outside to form a halo, which because of its large size can have lower momentum. It is an open question how nature stabilizes such a fragile system and provides the glue needed to bind the halo neutrons to the core. Here we show that this problem is similar to that of the instability of the normal state of an electron system at zero temperature solved by Cooper, solution which is on the basis of BCS theory of superconductivity. To understand the origin and the consequences of pairing correlations, it is illustrative to study the problem of two electrons interacting on top of a noninteracting Fermi sea of electrons. Thus, all but two of the electrons are assumed to be noninteracting. The background of electrons enter the problem only through the Pauli principle by blocking states below the Fermi surface from participating in the twoelectron problem.This system, first studied by Cooper [1], is unstable against the formation of a bound electron pair, regardless of how weak the interaction is, so long as it is attractive. This result is a consequence of the Fermi statistics and of the existence of the Fermi-sea background, since it is well known that binding does not ordinarily occur in the twobody problem in three dimensions until the strength of the potential exceeds a finite threshold value.Although actual superconductors differ in a fundamental way from a single bound pair model, Cooper pairs can be viewed as the building blocks of the superconductor. Furthermore, in the nuclear case, where the number of fermions participating in the condensate is small, and where the pairing problem can be studied in terms of individual quantal states, the Cooper pair problem can describe realistic situations. In fact it seems to have a concrete realization in the halo nucleus 12 Be͑ 10 Be+2n͒, which can be viewed as two weakly bound neutrons moving around the core 10 Be. By allowing these two neutrons to interact through the bare nucleon-nucleon potential, and to exchange surface vibrations of the core, one is able to provide a unified and quantitative picture of the observed properties of this system. This result, which is quite general, suggests a strategy for designing nuclei at the edges of the neutron drip line, and thus probing the limits of nuclear stability. It also provides evidence of the limits of validity of BCS theory in finite systems: a single Cooper pair.The properties of finite many-body systems are strongly influenced by spatial quantization [2] leading to marked shell structures [3]. This type of quantal size effects are, on the other hand, reno...

The induced pairing interaction arising from the exchange of low-lying collective surface vibrations among nucleons moving in time reversal states close to a Fermi energy is found to lead to values of the pairing gap which constitute a large fraction of those experimentally observed. PACS numbers: 21.30.Fe, 21.60.Jz, 27.40. + z, 27.60. + j It is well established that nucleons moving close to the Fermi energy in time reversal states have the tendency to form Cooper pairs which eventually condense [1]. This phenomenon, which parallels that which is at the basis of low-temperature superconductivity [2], modifies in an important way the nuclear properties.While in the case of low-temperature superconductivity the attraction among electrons is generated by the exchange of lattice phonons, in the nuclear case the origin of the pairing interaction is related to the 1 S 0 phase shift of the free nucleons, which is attractive at low relative momenta. Within the spirit of the BCS approximation [2] the matrix elements of the pairing interaction in nuclei are, in general, approximated by a constant inversely proportional to the mass number of the nucleus (G ഠ 25͞A MeV). The consequences of this model have been extensively studied (cf., e.g., Ref.[1] and references therein).In keeping with the fact that the free nucleon-nucleon interaction is strongly renormalized in nuclei, there exists a long tradition in the study of core polarization of the effective two-nucleon interaction (cf. Refs. [3-7] and references therein), in particular in the case of J 0, T 1 pairs (pairing correlations) where the role of exchange of high-lying quadrupole and hexadecapole modes (giant resonances) has been systematically studied (cf., e.g., Ref.[8] and references therein).In the present paper we shall show that Cooper pair formation in nuclei can particularly benefit from the exchange of low-lying collective surface vibrations (cf. Refs. [1,9,10]), a mechanism which gives rise to pairing gaps which account in most cases for 50%-70% of the experimental values. Calculations have been carried out for a number of isotopic chains: A 20 Ca, A 22 Ti, and A 50 Sn. The results provide insight into the role the induced interaction plays in neutron and proton pairing correlations in nuclei. Calculations have also been carried out for the case of 42 21 Sc and found to lead to strong proton-neutron pairing correlations.The basic ingredients needed in the calculation of the induced pairing interaction (cf. inset of Fig. 1) are the singleparticle energies e n and the corresponding wave functions f n ͑ r ! ͒, as well as the energieshv l ͑n͒ and transition probabilities B͑ ͑ ͑El; 0 ! l͑n͒͒ ͒ ͒ of the vibrational modes. The quantities e n and f n ͑ r ! ͒ were calculated assuming nucleons to move in an average field containing a spinorbit term and parametrized in terms of a Saxon-Woods potential, with values of the depth, radius, diffusivity, and spin-orbit strength taken from Ref. [11]. The vibrations were calculated by diagonalizing multipole-multipole intera...