We carry out realistic coupled-channels calculations for 11 Be + 208 Pb reaction in order to discuss the effects of break-up of the projectile nucleus on sub-barrier fusion. We discretize in energy the particle continuum states, which are associated with the break-up process, and construct the coupling form factors to these states on a microscopic basis. The incoming boundary condition is employed in solving coupled-channels equations, which enables us to define the flux for complete fusion inside the Coulomb barrier. It is shown that complete fusion cross sections are significantly enhanced due to the couplings to the continuum states compared with the no coupling case at energies below the Coulomb barrier, while they are hindered at above barrier energies.Quantum tunneling in systems with many degrees of freedom [1] has attracted much interest in recent years in many fields of physics and chemistry [2]. In nuclear physics, heavy-ion fusion reactions at energies near and below the Coulomb barrier are typical examples for this phenomenon. In order for fusion processes to take place, the Coulomb barrier created by the cancellation between the repulsive Coulomb force and the attractive nuclear interaction has to be overcome. It has by now been well established that the coupling of the relative motion of the colliding nuclei to nuclear intrinsic excitations as well as to transfer reaction channels cause large enhancements of the fusion cross section at subbarrier energies over the predictions of a simple barrier penetration model [3].The effect of break-up processes on fusion, on the other hand, has not yet been understood very well, and many questions have been raised during the last few years both from the experimental [4][5][6][7][8] and theoretical [9-12] points of view. The issue has become especially relevant in recent years due to the increasing availability of radioactive beams. These often involve weakly-bound systems close to the drip lines for which the possibility of projectile dissociation prior to or at the point of contact cannot be ignored. Different theoretical approaches to the problem have led to controversial results, not only quantitatively but also qualitatively. The probability for fusion at energies below the barrier has been in fact predicted to be either reduced [9,10] or enhanced [11,12] by the coupling to the continuum states.These investigations, however, were not satisfactory in view of the rather simplified assumptions used in the treatment of both the structure and reaction aspects of the problem.

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This review presents the status of the field of two-nucleon and multi-nucleon transfer reactions induced by heavy ions. The role of the pairing interaction in nuclei as a finite quantum system is illustrated. These reactions serve as a unique tool for the study of the dynamical aspects of pairing correlations in nuclei in particular for the cases of nuclear superfluidity. The new possibilities offered by the development of experimental techniques, e.g. the large gammaray detectors combined with charged particle detectors are presented, which allows the study of the enhanced pair transfer between well selected states, and the problem of the expected quenching of pairing correlation at high spin. Further, the new possibilities offered by the advent of radioactive beam facilities are discussed.

The evolution of the dipole response in nuclei with strong neutron excess is studied in the Hartree-Fock plus random phase approximation with Skyrme forces. We find that the neutron excess increases the fragmentation of the isovector giant dipole resonance, while pushing the centroid of the distribution to lower energies beyond the mass dependence predicted by the collective models, The radial separation of proton and neutron densities associated with a large neutron excess leads to non-vanishing isoscalar transition densities to the GDR states, which are therefore predicted to be excited also by isoscalar nuclear probes. The evolution of the isoscalar compression dipole mode as a function of the neutron excess is finally studied. We find that the large neutron excess leads to a strong concentration of the strength associated with the isoscalar dipole operator Sigma(i)r(i)(3)Y(10), that mainly originates from uncorrelated excitations of the neutrons of the skin. (C) 1997 Elsevier Science B.V

The relation of the recently proposed E͑5͒ critical point symmetry with the interacting boson model is investigated. The large-N limit of the interacting boson model at the critical point in the transition from U(5) to O (6) The study of phase transitions is one of the most exciting topics in physics. Recently the concept of critical point symmetry has been proposed by Iachello [1]. These kinds of symmetries apply when a quantal system undergoes transitions between traditional dynamical symmetries. In Ref.[1] the particular case of the Bohr Hamiltonian [2] in nuclear physics was worked out. In this case, in the situation in which the potential energy surface in the ␤-␥ plane is ␥ independent and the dependence in the ␤ degree of freedom can be modeled by an infinite square well, the so-called E͑5͒ symmetry appears. This situation is expected to be realized in actual nuclei when they undergo a transition from spherical to ␥-unstable deformed shapes. The E͑5͒ symmetry is obtained within the formalism based on the Bohr Hamiltonian, but it has also been used in connection with the interacting boson model (IBM) [3]. Although this is not the form it was originally proposed [1], it has been in fact argued that moving from the spherical to the ␥-unstable deformed case within the IBM one should reobtain, at the critical point in the transition, the predictions of the E͑5͒ symmetry. This correspondence is supposed to be valid in the limit of large number N of bosons, but the calculations with the IBM should provide predictions for finite N as stated in Ref. [4]. In this paper, on one hand we calculate exactly the large-N limit of the IBM at the critical point in the transition from U(5) (spherical case) to O(6) (deformed ␥-unstable case). On the other hand, we solve the Bohr differential equation for a ␤ 4 potential. Both calculations lead to the same results and are not close to those obtained by solving the Bohr equation for an infinite square well [E͑5͒ symmetry]. We also show with two schematic examples that the corrections arising from the finite number of bosons are important. With this in mind, the IBM calculations still provide a tool for including corrections due to the finite number of bosons.In Ref.[1] the Bohr Hamiltonian is considered for the case of a ␥ independent potential, described by an infinite square well in the ␤ variable. In that case, the Hamiltonian is separable in both variables and if we set ⌿͑␤, ␥, i ͒ = f͑␤͒⌽͑␥, i ͒, ͑1͒where i stands for the three Euler angles, the Schrödinger equation can be split in two equations. [7][8][9] which allows to associate to it a geometrical shape in terms of the deformation variables ͑␤,␥͒. The basic idea of this formalism is to consider that the pure quadrupole states are globally described by a boson condensate of the form ͉g;N, ␤, ␥͘ = 1where the basic boson is given bywhich depends on the ␤ and ␥ shape variables. The energy surface is defined aswhere Ĥ is the IBM Hamiltonian. Here we are interested in the case in which the Hamiltonian undergoes a transitio...

Background: The 29 F system is located at the lower-N boundary of the "island of inversion" and is an exotic, weakly bound system. Little is known about this system beyond its two-neutron separation energy (S2n) with large uncertainties. A similar situation is found for the low-lying spectrum of its unbound binary subsystem 28 F.Purpose: To investigate the configuration mixing, matter radius and neutron-neutron correlations in the groundstate of 29 F within a three-body model, exploring the possibility of 29 F to be a two-neutron halo nucleus. Method:The 29 F ground-state wave function is built within the hyperspherical formalism by using an analytical transformed harmonic oscillator basis. The Gogny-Pires-Tourreil (GPT) nn interaction with central, spin-orbit and tensor terms is employed in the present calculations, together with different core + n potentials constrained by the available experimental information on 28 F. Results:The 29 F ground-state configuration mixing and its matter radius are computed for different choices of the 28 F structure and S2n value. The admixture of d-waves with pf components are found to play an important role, favouring the dominance of dineutron configurations in the wave function. Our computed radii show a mild sensitivity to the 27 F + n potential and S2n values. The relative increase of the matter radius with respect to the 27 F core lies in the range 0.1 -0.4 fm depending upon these choices.Conclusions: Our three-body results for 29 F indicate the presence of a moderate halo structure in its ground state, which is enhanced by larger intruder components. This finding calls for an experimental confirmation.

We study the spatial correlations between two particles (or two holes) around a closed shell core in terms of the probability distribution expressed as a function of the c.m. coordinate R of the two particles and of their relative coordinate r. We find that the mixing of configurations induced by the pairing force leads to a probability distribution centered in regions corresponding to larger values of R and smaller values of r, as compared to the case of a pure (j)02 configuration. This tendency to a "surface clustering" is mainly due to the interference of the contributions coming from levels with different parity. However, even with the inclusion of a large number of configurations, the size of the localized "cluster" is much larger than that of a free dinucleon system. NUCLEAR STRUCTURE Pairing correlations, correlation in space, two-particle transfer reactions.Two-particle transfer reactions are usually considered a typical tool for the study of particle-particle correlations in nuclei. In such reactions [we are thinking, in particular, of reactions induced by light ions, such as (p, t), (t,p), or (3He, n)] a dinucleon system with J = 0, very confined in space, is transferred on to (or from) the nuclear surface. It is, therefore, of interest to study to what extent the pairs of particles in the nucleus move closely in space toward each other, in particular in the surface region, where the Pauli principle is less effective and the probability of formation of few-nucleon correlated substructures should increase. We want to clarify the effect on this correlation in space of the particle-particle residual interaction, which is known to strongly enhance the two-particle transfer cross section. This should shed some light on the more general problem of the relation between correlations in spin, isospin, and angular momentum and clusterization in space.We consider the case of two identical particles (or two holes), coupled to angular momentum I = 0 and moving in single particle orbitals around a closed-shell core. The problem has been approached in Refs. 2 and 4 by selecting the S =0 part of the two-particle wave function and assuming the two particles at equal distance from the center of the nucleus, and then studying the behavior of the two-particle wave function as a function of the relative angle between I be the general antisymmetrized wave function describing the two-particle system. The index o. stands for the set [n I j ) of quantum numbers characterizing the single particle wave function +"t/ ( r, X) =@. ]/(r)[ I ]( f) X]/2( X)ljIn order to study the spatial correlations between the two particles we introduce the coordinates R =~r ]+ r q~/J2 and r =~r ] -r q[/v 2 associated with the center of mass and relative motion, respectively, and consider the probability distribution P(r, R) = &~' P( r ], X]', r q, Xq)~r R dr" dR dX]dXqIn the case of harmonic oscillator (HO) wave functions the coordinate transformation and the integration over the angular variables can be performed analytically and the probability di...

Giant resonances are collective excitation modes for many-body systems of fermions governed by a mean field, such as the atomic nuclei. The microscopic origin of such modes is the coherence among elementary particle-hole excitations, where a particle is promoted from an occupied state below the Fermi level (hole) to an empty one above the Fermi level (particle). The same coherence is also predicted for the particle–particle and the hole–hole excitations, because of the basic quantum symmetry between particles and holes. In nuclear physics, the giant modes have been widely reported for the particle–hole sector but, despite several attempts, there is no precedent in the particle–particle and hole–hole ones, thus making questionable the aforementioned symmetry assumption. Here we provide experimental indications of the Giant Pairing Vibration, which is the leading particle–particle giant mode. An immediate implication of it is the validation of the particle–hole symmetry.