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...

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 wavefunction 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 at the basis of BCS theory of superconductivity. By mimicking this approach using, aside from the bare nucleon-nucleon interaction, the long wavelength vibrations of the nucleus $^{11}$Li, the paradigm of halo nuclei, as tailored glues of the least bound neutrons, we are able to obtain a unified and quantitative picture of the observed properties of $^{11}$Li.Comment: 16 pages, 1 b/w figures, 2 colour figure

The bare nucleon-nucleon interaction is essential for the production of pair correlations in nuclei, but an important contribution also arises from the induced interaction resulting from the exchange of collective vibrations between nucleons moving in time reversal states close to the Fermi energy. The pairing field resulting from the summed interaction is strongly peaked at the nuclear surface. It is possible to reproduce the detailed spatial dependence of this field using either a local approximation which takes fully into account finite size effects, or a contact interaction, with parameters which are quite different from those commonly used in more phenomenological approaches. PACS numbers:where G 0 , G ′ 0 are the generalized Landau-Migdal parameters controlling the isoscalar and isovector spindependent channels, while δρ i J π Ln and δρ i J π Lp are respectively the neutron and proton contributions to the

With the help of a unified nuclear-structure-direct-reaction theory we analyze the reaction ¹H(¹¹Li,⁹Li)³H. The two halo neutrons are correlated through the bare and the induced (medium polarization) pairing interaction. By considering all dominant reaction channels leading to the population of the 1/2⁻ (2.69 MeV) first excited state of ⁹Li, namely, multistep transfer (successive, simultaneous, and nonorthogonality), breakup, and inelastic channels, it is possible to show that the experiment provides direct evidence of phonon mediated pairing.

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...