Four-body distorted-wave theory for halo excitations in peripheral fragmentation reactions

A microscopic approach to breakup into the low-energy continuum of Borromean two-neutron-halo nuclei is developed by quantum mechanically taking into account both Coulomb and nuclear dissociation. The crucial role of both elastic and inelastic fragmentation is demonstrated for ⁶He breakup on C and Pb targets at intermediate energies in kinematically complete experiments. For the first time, recent GSI experimental data are analyzed quantitatively, and a rich and complex interplay of reaction mechanisms and low-lying halo excitations is revealed.     

Breakup reactions of halo nuclei

Different reaction mechanisms of breakup reactions are discussed and the microscopic reaction model for two-neutron halo dissociation is presented. Some examples of halo breakup in reactions with electrons, nucleons, and nuclei are given.     

Neutron Halo Structure at the Limit of Stability Probed by Breakup Reactions

Atomic nuclei along the neutron drip line are investigated experimentally by breakup reactions of the rare isotope beams. Such exotic nuclei often show the neutron halo structure, which is the main focus of this paper. Characteristic features of the Coulomb and nuclear breakup at intermediate to high incident energies are described. Then, recent experimental results on halo nuclei, mainly on ³¹Ne, obtained at the new-generation RI-beam facility, RIBF (RI Beam factory) at RIKEN, are presented. Perspectives for the breakup experiments using the new facility SAMURAI at RIBF ara also discussed.     

Excitation of two-neutron-halo nuclei in a continuum

Reactions induced by collisions of beams of unstable nuclei with nuclear targets are studied. Kinematically full breakup reactions are considered. A microscopic four-body model of the breakup of two-neutron-halo nuclei is formulated with allowance for special features of their structure. The model relies on the distorted-wave method and creates a basis for the spectroscopy of the continuous spectrum via a consistent analysis of various correlation cross sections.     

Influence of experimental conditions on the spectroscopy investigation of~(14)Be by Coulomb breakup reaction

The two-body(core+2n) cluster structure was implemented to describe the two-neutron halo nucleus~(14 )Be, where the core12 Be was assumed inert and at a ground state and the dineutron was assumed at a pure 2S0 state. Based on such a structure the three-body continuum-discretized coupled-channel(CDCC) calculation was successfully used to deal with the~(14) Be breakup reactions of~(14)Be+Pb at 35 Me V/u. Consequently, we modeled the kinematically complete measurement experiment of this reaction with the help of Geant4. With the simulation data the relative energy spectrum was constructed by the invariant mass method and B(E1) spectrum was extracted using the virtual photon model. The influence of the target thickness and detector performance on the energy spectroscopy was investigated.     

Two-body and three-body halo nuclei

We have extracted the nuclear asymptotic normalization coefficients (ANC) for the virtual transitions B→A+N via some transfer reactions and the radioactive nuclear beam experiments. With these coefficients, root-mean-square (rms) radii for the valence particle in some possible halo nuclei have been calculated. The values of rms radii extracted with ANC approach are nearly model-independent, hence are a good quantity for the investigation of nuclear halo. In addition, we have also calculated the rms radii for the two valence neutrons in some three-body systems in terms of the relationship between the radii of valence particle, core nucleus and nuclear matter. With two conditions for nuclear halo formation, we have examined these extracted rms radii. The results show that 11Be(1/2+, g.s), 12B(1-, 2.621 MeV), 13C(1/2+, 3.089 MeV), 14C(0-, 6.903 MeV), 14C(1-, 6.094 MeV), 15C(1/2+, g.s) and 19C(1/2+, g.s) with the valence particle in the 2s ground or excited state are the neutron halo nuclei, whereas 17F(1/2+, 0.495 MeV) and 21Na(1/2+, 2.423 MeV) are the proton halo nuclei in the excited state. For three-body systems, except the well-established two-neutron halo nuclei 6He and 11Li, 14Be and 17B might be the two-neutron halo nuclei as well.     

Studying of the neutron halo structure in quasi-free proton scattering from 6He Halo nucleus

An experimental method based on an analysis of the neutron-neutron correlations in reactions induced by halo nuclei in nuclear photoemulsion is proposed for studying the two-neutron halo structure. Photoemulsion stacks were exposed to a beam of radioactive ⁶He nuclei. Preliminary data on interaction of the ⁶He halo nucleus to hydrogen are compared with the results of the kinematic calculation for the reaction of quasi-free proton scattering from clusters making up the ⁶He halo nucleus. A fraction of quasi-free scattering events with “survival” of the dineutron is evaluated for scattering of protons by the dineutron configuration of the ⁶He nucleus.     

Nuclear structure studies on halo nuclei by direct reactions with radioactive beams

The investigation of direct reactions with exotic beams in inverse kinematics gives access to a wide field of nuclear structure studies in the region far off stability. The basic concept and the methods involved are briefly discussed. The present contribution will focus on the investigation of light neutron-rich halo nuclei. Such nuclei reveal a new type of nuclear structure, namely an extended neutron distribution surrounding a nuclear core. An overview on this phenomenon, and on the various methods which gave first evidence and qualitative confirmation of our present picture of halo nuclei, is given. To obtain more quantitative information on the radial shape of halo nuclei, elastic proton scattering on neutron-rich light nuclei at intermediate energies was recently investigated for the first time. This method is demonstrated to be an effective means for studying the nuclear matter distributions of such nuclei. The results on the nuclear matter radii of ⁶He and ⁸He, the deduced nuclear matter density distributions, and the significance of the data on the halo structure is discussed. The present data allow also a sensitive test of theoretical model calculations on the structure of neutron-rich helium isotopes. A few examples are presented. The investigation of few-nucleon transfer reactions in inverse kinematics may provide new and complementary information on nuclear structure, as well as astrophysical questions. The physics motivation and the experimental concept for such experiments, to be performed due to momentum matching reasons at low incident energies around 5–20 MeV/u at the new generation low energy radioactive beam facilities SPIRAL, PIAFE, etc., is briefly discussed.     

Reaction mechanisms for light halo nuclei

Current nuclear physics focuses on exploring nucleon matter under extreme conditions, such as those that can be created in modern accelerator laboratories. On the neutron-rich side of stability, radioactive beams have already led to the discovery of halos in nuclei with neutron distributions extending to large distances. Halo nuclei are composite systems with prominent features of few-body correlations, which reveal themselves in various reactions involving these systems. We will discuss experiments that probe a halo structure through studying various reactions involving halo nuclei, with special emphasis on how, from the theoretical point of view, such reactions contribute to our knowledge of the structure and dynamics of the nuclear halo.     

Diffractive dissociation of deuterons and exotic nuclei <Superscript>6</Superscript>He and <Superscript>19</Superscript>C

A theory is developed for describing the diffractive dissociation of loosely bound two-cluster nuclei in the nuclear and Coulomb fields of nuclei having a diffuse boundary. The energy spectra of charged products of the breakup of ²H, ⁶He, and ¹⁹C nuclei are calculated on the basis of the proposed approach, and the results are found to be rather sensitive to nuclear structure. For some angles of neutron and proton emission from the reaction ¹²C(d, np)¹²C, the calculated cross sections are in satisfactory agreement with the results of kinematically complete experiments performed recently to study the breakup of intermediate-energy deuterons.     

Coulomb Breakup Reactions of Two-Neutron Halo Nuclei 6He and 11Li Using Complex-Scaled Solutions of the Lippmann–Schwinger Equation

We investigate the three-body Coulomb breakup reactions of two-neutron halo nuclei and discuss the effect of binary subsystem correlations such as of core–n and n–n. We furthermore calculate the invariant mass spectra. It is found that the final-state interactions of core–n and n–n binary subsystems dominantly determine the observed structures of the breakup cross sections, such as the low-lying enhancements.     

The neutron halo structure of 17B studied with the relativistic Hartree-Bogoliubov theory

The properties of neutron-rich boron isotopes are studied in the relativistic continuum Hartree-Bogoliubov theory in coordinate space with NL-SH, PK1 and TM2 effective interactions. Pairing corrections are taken into account by a density dependent force of zero range. The binding energies calculated for these nuclei agree with the experimental data quite well. The neutron-rich nucleus ¹⁷B has been predicted to have a two-neutron halo structure in its ground state. The halo structure of ¹⁷B is reproduced in a self-consistent way, and this halo is shown to be formed by the valence neutron level 2_s1/2.     

Fragmentation processes in nuclear reactions

Fragmentation processes in nuclear collisions are reviewed. The main emphasis is put on light ion breakup at nonrelativistic energies. The post- and prior-form DWBA theories are discussed. The post-form DWBA, appropriate for the “spectator breakup” describes elastic as well as inelastic breakup modes. This theory can also account for the stripping to unbound states. The theoretical models are compared to typical experimental results to illustrate the various possible mechanisms. It is discussed, how breakup reactions can be used to study high-lying single particle strength in the continuum; how they can yield information about momentum distributions of fragments in the nucleus.     

Breakup reaction models for exotic nuclei

Breakup reactions are one of the main tools for the study of exotic nuclei. In particular, Coulomb breakup is expected to provide information on spectroscopic properties of halo nuclei and on astrophysical S factors for radiative-capture reactions. The simplest studies are based on perturbation theory and especially on its first order. However the validity of the first-order approximation may be limited for extended systems such as halo nuclei and its conditions are not always satisfied in existing experiments. More elaborate reaction models are available: resolution of the semi-classical time-dependent Schr?dinger equation, eikonal and dynamical eikonal approximations, method of coupled discretized-continuum channels, adiabatic approximation. These methods are reviewed, summarized and illustrated. Their interest and limitations are discussed.     

Reactions with fast radioactive beams of neutron-rich nuclei

The neutron dripline has presently been reached only for the lightest nuclei up to the element oxygen. In this region of light neutron-rich nuclei, scattering experiments are feasible even for dripline nuclei by utilizing high-energy secondary beams produced by fragmentation. In the present article, reactions of high-energy radioactive beams will be exemplified using recent experimental results mainly derived from measurements of breakup reactions performed at the LAND and FRS facilities at GSI and at the S800 spectrometer at the NSCL. Nuclear and electromagnetically induced reactions allow probing different aspects of nuclear structure at the limits of stability related to the neutron-proton asymmetry and the weak binding close to the dripline. Properties of the valence-neutron wave functions are studied in the one-neutron knockout reaction, revealing the changes of shell structure when going from the beta-stability line to more asymmetric loosely bound neutron-rich systems. The vanishing of the N = 8 shell gap for neutron-rich systems like ¹¹Li and ¹²Be, or the new closed N = 14, 16 shells for the oxygen isotopes are examples. The continuum of weakly bound nuclei and halo states can be studied by inelastic scattering. The dipole response, for instance, is found to change dramatically when going away from the valley of stability. A redistribution of the dipole strength towards lower excitation energies is observed for neutron-rich nuclei, which partly might be due to a new collective excitation mode related to the neutron-proton asymmetry. Halo nuclei, in particular, show strong dipole transitions to the continuum at the threshold, being directly related to the ground-state properties of the projectile. Finally, an outlook on future experimental prospects is given.     

Break-up of neutron-halo nuclei by diffraction dissociation and shakeoff

The interplay of diffraction dissociation and nuclear shakeoff is considered in a schematic but still realistic model for the case of the break-up of halo nuclei on light targets. We demonstrate that the shakeoff effect, arising from the momentum imparted by the core diffraction, is small but still identifiable in the experimental data for the dissociation of the one- and two-neutron halo nuclei ¹¹Be and ¹¹Li. Received: 29 October 1999 / Revised version: 15 January 2000     

Study of the structure of unstable nuclei through the reaction experiments

Along with the development of the radioactive nuclear beam facility, the study of the structure of unstable nuclei has progressed rapidly over the last few decades. Due to the weakly binding property, the structure information of the unstable nuclei comes primarily from the scattering or reaction experiments. Therefore it would be very important to understand clearly the reaction mechanism involved in the experiment. We outlined here the major reaction mechanisms which are adequate to the study of unstable nuclei, with the focus on the new phenomena and methods in comparison with those with traditional stable nucleus beam. Especially emphasized are the breakup and knockout reactions, developed as accurate tools for spectroscopy investigation into the nuclear structure with low intensity secondary beam. Couplings of the breakup channel to the elastic scattering and the fusion and transfer reactions are also reviewed.     

Relating breakup and incomplete fusion of weakly bound nuclei through a classical trajectory model with stochastic breakup

A classical dynamical model that treats breakup stochastically is presented for low energy reactions of weakly bound nuclei. The three-dimensional model allows a consistent calculation of breakup, incomplete, and complete fusion cross sections. The model is assessed by comparing the breakup observables with continuum discretized coupled-channel quantum mechanical predictions, which are found to be in reasonable agreement. Through the model, it is demonstrated that the breakup probability of the projectile as a function of its distance from the target is of primary importance for understanding complete and incomplete fusion at energies near the Coulomb barrier.     

Halo structure of (14)Be

The two-neutron halo nucleus (14)Be has been investigated in a kinematically complete measurement of the fragments ((12)Be and neutrons) produced in dissociation at 35 MeV/nucleon on C and Pb targets. Two-neutron removal cross sections, neutron angular distributions, and invariant mass spectra were measured, and the contributions from electromagnetic dissociation (EMD) were deduced. Comparison with three-body model calculations suggests that the halo wave function contains a large nu(2s(1/2))(2) admixture. The EMD invariant mass spectrum exhibited enhanced strength near threshold consistent with a nonresonant soft-dipole excitation.     

Total Nuclear Reaction Cross Section Induced by Halo Nuclei and Stable Nuclei

We develop a method for calculation of the total reaction cross sections induced by the halo nuclei and stable. nuclei. This approach is based on the Glauber theory, which is valid for nuclear reactions at high energies. It is extended for nuclear reactions at low energies and intermediate energies by including both the quantum correction and Coulomb correction under the assumption of the effective nuclear density distribution. The calculated results of the total reaction cross section induced by stable nuclei agree well with 30 experimental data within 10 percent accuracy. The comparison between the numerical results and 20 experimental data for the total nuclear reaction cross section induced by the neutron halo nuclei and the proton halo nuclei indicates a satisfactory agreement after considering the halo structure of these nuclei, which implies quite different mean fields for the nuclear reactions induced by halo nuclei and stable nuclei. The halo nucleon distributions and the root-mean-square radii of these nuclei can be extracted from the above comparison based on the improved Glauber model, which indicates clearly the halo structures of these nuclei. Especially,it is clear to see that the medium correction of the nucleon-nucleon collision has little effect on the total reaction cross sections induced by the halo nuclei due to the very weak binding and the very extended density distribution.