Probing the halo and cluster structure of exotic nuclei

The Halo and cluster structure at the ground state of unstable nuclei are among the most exciting phenomena of current nuclear physics. Probing these structures requires a careful selection of reaction tools. In the past twenty years, knockout reactions have been used intensively to investigate spectroscopically the structure of unstable nuclei. In this report we have illustrated the latest development of the knockout reaction tool and have emphasized the recoiled proton tagging method. A quantitative criteria is developed to evaluate the quasi-free feature of the knockout process. The newly discovered "towing mode" reaction tool is also outlined and its applicability at transit energies is discussed.     

Probing the structure of exotic nuclei by transfer reactions

Low energy single nucleon transfer reactions are proposed as a tool to investigate the structure of nuclei far off stability. Experimental concepts and conditions are discussed, in particular high resolution γ-ray spectroscopy after single nucleon pickup reactions. Nuclear structure is described by Skyrme Hartree-Fock calculations including pairing. As representative examples, binding energies, radii and wave functions for Mg and Sn isotopes are calculated. In the neutron deficient Mg isotopes a proton skin is found. At the neutron driplines the Mg and Sn isotopes develop extended neutron skins. The nuclear structure results are used in DWBA and EFR-DWBA transfer calculations. Single nucleon transfer reactions of ^32,36Mg and exotic Sn beams on targets ranging from ²H to ²⁴Mg in inverse kinematics are explored. The one-nucleon transfer cross sections decrease strongly for high-Z targets. An impact parameter analysis shows that the transfer process is selective on the tails of the wave functions. The largest cross sections are obtained for ²H and ⁹Be targets at incident energies of E _lab = 2-5 MeV/u. The energy-momentum dependence is closely related to the special properties of wave functions of weakly bound states. Two-neutron (p,t) stripping reactions are studied for a ⁶He projectile. A strong competition of sequential and direct processes is found at low energies. Received: 1 October 1997 / Revised version: 25 November 1997     

Symmetry in exotic nuclei

Symmetries have played an important role in the elucidation of the structure of nuclei and will continue to do so for exotic nuclei. As an example, an application of pseudo-SU(4) symmetry is discussed. It can be used as a starting point for a boson model that includes T = 0 as well as T = 1 bosons (IBM-4); applications are presented for N = Z nuclei from ⁵⁸Cu to ⁷⁰Br. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: isacker@ganil.fr     

Detecting bubbles in exotic nuclei

The occurrence of a bubble, due to an inversion of s_1/2 state with the state usually located above, is investigated. Proton bubbles in neutron-rich argon isotopes are optimal candidates. Pairing effects which can play against the bubble formation are evaluated. They cannot prevent bubble formation in very neutron-rich argon isotopes such as ⁶⁸Ar. This pleads for a measurement of the charge density of neutron-rich argon isotopes in the forthcoming years, with the advent of electron scattering experiments in next generation exotic beam facilities such as FAIR or RIBF.     

Very neutron-rich exotic nuclei

A brief summary is done of the various types of experiment used in studies of the very neutron rich nuclei. Some highlights are given for the two-neutron halo and¹¹Li nucleus and for the one-neutron halo and¹¹Be nucleus.     

Mean field with tensor force and shell structure of exotic nuclei

The tensor force is implemented into the mean-field model so that the evolution of nuclear shells can be described for exotic nuclei as well as stable ones. Besides the tensor-force part simulating the meson exchange, the model is an extension of the successful Gogny model. One of the major issues of rare-isotope beam physics is a reduced spin-orbit splitting in neutron-rich exotic nuclei. It will be shown that the effect of the tensor force on this splitting is larger than or about equal to the one due to the neutron skin. We will present predictions for stable and exotic nuclei with comparisons to conventional results and experimental data.     

Proton halos in exotic light nuclei

The current study on proton halos in exotic light nuclei is reviewed and discussed. We place emphasis on the newly discovered proton halo in ²³Al. A measurement of the reaction cross section of N=10 isotones and Z=13 isotopes is performed at Lanzhou in China. An abnormal increase in the reaction cross section is observed for ²³Al. This abnormal increase, combined with other data, strongly suggests that there is a proton halo in ²³Al. The possible cause for a proton halo in ²³Al is analyzed, and it is found that deformation can be important for it. Other candidates for proton halos are predicted.     

Pairing and quartetting in exotic nuclei

A review is given of pair correlations in nuclei with an emphasis on the symmetry character of the superfluid solution which depends on (i) the isospin of the nucleus and (ii) the relative strength of the T=0 and T=1 pairing forces. The most general SO(8) model which accommodates neutrons and protons as well as T=0 and T=1 pairing, is solvable in three limits: only T=0 pairing, only T=1 pairing and equal strengths in the two channels. In these limits, the superfluid ground-state solution of N=Z nuclei exhibits a quartet structure. The competition between superfluidity and magicity is discussed with reference to integrable models. To cite this article: P. Van Isacker, C. R. Physique 4 (2003).     

Evolution of the nucleon structure in the lightest nuclei

We show that the pattern of the oscillation of the structure functions ratio r^A(x)=F₂^A/F₂^N(D) varies with A by changing the position of the cross-over point x₃ in which r^A(x)=1, unlike the pattern for nuclei with masses A>4, where only the amplitude of the oscillation changes. In particular we find that the pattern of F₂(x) modifications is controlled with the values (1−x₃)=0.32 (D/N), 0.16 (³He/D) and 0.08 (⁴He/D). The obtained results follow from the relativistic approach and allow one to define the class of modifications of the bound nucleon structure.     

Electron scattering for exotic nuclei

A brand-new electron scattering facility, the SCRIT Electron Scattering Facility, will soon start its operation at RIKEN RI Beam Factory, Japan. This is the world’s first electron scattering facility dedicated to the structure studies of short-lived nuclei. The goal of this facility is to determine the charge density distributions of short-lived exotic nuclei by elastic electron scattering. The first collision between electrons and exotic nuclei will be observed in the year 2014.     

Dissolution of shell structures in exotic nuclei

Nuclear many-body theory is used to study nuclear matter and finite nuclei at extreme isospin. In-medium interactions in asymmetric nuclear matter are obtained from (Dirac-) Brueckner theory. Neutron skin formation in Ni and Sn isotopes is investigated in relativistic DDRH theory with density dependent meson-nucleon vertices. Applications to light nuclei are discussed with special emphasis on pairing and core polarization in weakly bound nuclei. The calculations show that shell structures are dissolving when the driplines are approached.     

Reaction mechanisms with exotic nuclei

This article examines a number of reaction mechanisms for scattering initiated by an exotic projectile. Comparisons are made with recent experimental data, in order to extract information on the peculiarity of the nuclear structure under extreme conditions and to test the accuracy of the available theoretical methods. Predictions for future experiments are also made.     

Reaction dynamics with exotic nuclei

We review the new possibilities offered by the reaction dynamics of asymmetric heavy-ion collisions, using stable and unstable beams. We show that it represents a rather unique tool to probe regions of highly asymmetric nuclear matter (ANM) in compressed as well as dilute phases, and to test the in-medium isovector interaction for high-momentum nucleons. The focus is on a detailed study of the symmetry term of the nuclear equation of state (EOS) in regions far away from saturation conditions but always under laboratory controlled conditions.

Thermodynamic properties of ANM are surveyed starting from non-relativistic and relativistic effective interactions. In the relativistic case, the role of the isovector–scalar δ-meson is stressed. The qualitative new features of the liquid–gas phase transition, “diffusive” instability and isospin distillation, are discussed. The results of ab initio simulations of n-rich, n-poor, heavy-ion collisions, using stochastic isospin-dependent transport equations, are analyzed as a function of beam energy and centrality. The isospin dynamics plays an important role in all steps of the reaction, from prompt nucleon emissions to the final fragments. The isospin diffusion is also of large interest, due to the interplay of asymmetry and density gradients. In relativistic collisions, the possibility of a direct study of the covariant structure of the effective nucleon interaction is shown. Results are discussed for particle production, collective flows and isotransparency.

Perspectives of further developments of the field, in theory as well as in experiment, are presented.     

Pairing in exotic and in stable nuclei

The exchange of low-lying collective vibrations between pairs of nucleons moving in time reversal states close to the Fermi energy provides a conspicuous contribution to the nuclear pairing interaction, which accounts for 30-50% of the pairing gap in the case of nuclei along the stability valley, and to essentially all of the pairing correlations of the most loosely bound nucleons in the case of halo nuclei.Received: 30 October 2002, Published online: 23 March 2004PACS: 21.30.Fe Forces in hadronic systems and effective interactions - 21.60.Jz Hartree-Fock and random-phase approximations     

Direct mass measurements of exotic nuclei

The present status and recent results from direct mass measurements of exotic nuclei are presented. ISOL, in-flight, and combined facilities provide a wide variety of nuclides far-off stability covering a wide range of half-lives down to the sub-millisecond region. Modern direct mass measurements are carried out using frequency and time-of-flight techniques. The obtained accurate mass data point to nuclear-structure phenomena and serve as a basis for astrophysical and weak-interaction studies. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: c.scheidenberger@gsi.de     

Clustering aspects of light exotic nuclei

The discovery of light nuclei with neutron halos has opened new perspectives for nuclear structure and a possibility to study genuine few-body aspects of matter. A number of borromean systems where the system is bound but where no binary subsystems are bound, are realized by nature in the context of nuclei,¹¹Li being the nucleus which has had most recent attention. Although a large number of calculations have addressed the detailed structure of the¹¹Li neutron halo, no single model has yet explained all the data presently available. This is in part due to uncertainties in then+⁹Li interaction. For⁶He, also a borromean system, where then+core interaction is known, the best three-body and reaction models succeed in reproducing the data. In the¹¹Li case, a major uncertainty concerns the effect of possible 1s intruder states.