Core-breakup reactions of the halo nuclei 11Be and 11Li: momentum distributions and shadow effects

The halo nuclei ¹¹Be and ¹¹Li have been studied in core-breakup reactions where the halo neutrons are expected to be released without a major distortion due to the reaction. The widths of the halo-neutron momentum distributions have been extracted in coincidence with He fragments, Γ = 32 ± 4 MeV/c, and Li fragments, Γ = 42 ± 4 MeV/c for ¹¹Be and with He fragments, Γ = 42 ± 6 MeV/c for ¹¹Li. The ¹¹Be breakup gives a very low neutron multiplicity of 0.38±0.09 which is a manifestation of the shadowing of the neutron in the core-breakup reaction. This value can be understood from a simple theoretical calculation, which also accounts for the observed transverse momentum widths at small angles.     

Momentum distributions in halo nuclei

From the analogy between the break-up of weakly bound, neutron-rich nuclei and the phenomenon of optical diffraction, it is possible to formulate a model for the momentum distribution of both the core and the valence neutrons of halo nuclei which displays a simple dependence on nuclear structure parameters. The model is applied to the analysis of reactions where¹¹Be,¹¹Li and¹⁴Be impinge on¹²C, providing an overall account of the experimental findings and predictions for further measurements.     

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.     

Participant-spectator model for fragmentation reactions with halo nuclei

We present the theoretical framework of the participant-spectator model for fragmentation reactions with weakly bound (halo) projectiles. The model allows calculations of differential cross sections for different fragmentation processes. Both nuclear and Coulomb interactions are included and the model can therefore be used for all targets, light and heavy.     

Breakup reactions of two-neutron halo nuclei

Investigation of reactions initiated in collisions of beams of unstable nuclei with nuclear targets has resulted in the discovery of a new type of nuclear structure, the halo, in some light nuclei at the boundary of nucleon stability. A survey of different reactions with two-neutron halo nuclei and their use for gaining information on the structure of exotic nuclei is presented. Kinematically complete breakup reactions, which provide the possibility of obtaining quite reliable information on the structure of the ground state and the continuum of nuclei, are considered in detail. The microscopic four-body model of breakup reactions for two-neutron halo nuclei with account of characteristic specific features of their structure is formulated. The model is based on the distorted wave approximation and is applicable for analysis of low excitations of the continuum near the breakup threshold, the region most sensitive to manifestation of specific features of the halo structure. The described approach enables the calculation of all observables of kinematically complete experiments in nucleus-nucleus collisions at intermediate energies for which one-step processes dominate, and creates the basis for the spectroscopy of continua via successive analysis of various correlation cross sections available in kinematically complete experiments.     

Nucleon momentum distributions in doubly closed shell nuclei

The momentum distributions in nuclei like⁴He,¹⁶O and⁴⁰Ca are explicitly calculated within a phenomenological model which includes dynamical short range and tensor correlation effects. The common behaviour of such distributions in the high momentum region, already established in light nuclei, is extended to the medium weight region. Comparison with existing calculations is discussed and, for completeness, also form factors are evaluated within the same framework.     

Nucleon momentum and density distributions of nuclei

The time dependent Hartee-Fock-BCS code used to study¹¹⁸Pd+¹¹⁸Pd has been extended to study²³⁸U +²³⁸U at 7.5 MeV/A, in three dimensions, in order to look for the fission of the residual nuclei. Two impact parameters corresponding toL _in=150,300 ? are considered. 69 orbits are included in the effective charge quartet model. The energy loss and deflection angle are compatible with the available data and correspond to cases where fission of the residual system is observed experimentally. No fast fission of the final U fragment is predicted, but new details about clutching time, interaction times, dissipation times and other properties of the reaction mechanism such as neck dynamics, are obtained. No surface vibrations are seen.     

Occupation probabilities and momentum distributions in closedS-D shell nuclei

Single-particle occupation probabilities and the depletion of the nuclear Ferrmi sea (caused by the short-range nucleon-nucleon correlations) as well as momentum distributions in closeds-d shell nuclei are calculated within the Jastrow correlation method in its low-order approximation. The theoretical results for the occupation probabilities are discussed in relation to experimental data from (e, e′ p) reactions and to other theoretical estimates.     

Multiplicity distributions in inelastic reactions on nuclei

We compute the multiplicity distribution of the number of knocked-out nucleons and the correlation of the former with the multiplicity of the produced mesons, in inelastic particle-nucleus scattering.     

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.     

Nuclear-matter distributions of halo nuclei from elastic proton scattering in inverse kinematics

Proton-nucleus elastic scattering at intermediate energies, a well-established method for probing nuclear-matter density distributions of stable nuclei, was applied for the first time to exotic nuclei. This method is demonstrated to be an effective means for obtaining accurate and detailed information on the size and radial shape of halo nuclei. Absolute differential cross-sections for small-angle scattering were measured at energies near 700 MeV/u for the neutron-rich helium isotopes ⁶He and ⁸He, and more recently for the lithium isotopes ⁶Li, ⁸Li, ⁹Li and ¹¹Li, using He and Li beams provided by the fragment separator FRS at GSI Darmstadt. Experiments were performed in inverse kinematics using the hydrogen-filled ionization chamber IKAR which served simultaneously as target and recoil-proton detector. For deducing nuclear-matter distributions, differential cross-sections calculated with the aid of the Glauber multiple-scattering theory, using various parametrizations for the nucleon density distributions as input, were fitted to the experimental cross-sections. The results on nuclear-matter radii and matter distributions are presented, and the significance of the data for a halo structure is discussed. Nuclear-matter distributions obtained for ⁶He and ⁸He conform with the concept that both nuclei compose of α-particle like cores and significant neutron halos. The matter distribution in ¹¹Li exhibits, as expected from previous reaction cross-section studies with nuclear targets, the by far most extended halo component of all nuclei being investigated. In addition the present data allow a quantitative comparison of the structure of the He and Li isobares of either the mass number A = 6 or A = 8. The measured differential cross-sections have also been used for probing density distributions as predicted from various microscopic calculations. A few examples are presented. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: p.egelhof@gsi.de     

Structure and reactions of the Li and Be halo nuclei

The phenomenon of s-wave intruder orbits is examined for a range of Li and Be isotopes. Whether these states are mixed or stand alone, they contribute distinctively to the properties of these nuclei. For weakly bound states, they accentuate those features of large sizes, narrow momentum widths and low-lying E1 strengths that are associated with halo nuclei.     

Structure and reactions of halo nuclei: An entangled approach

Halo nuclei are characterised by their weak binding, large spatial extent and hence a quite pronounced, yet highly correlated, few-body structure. This is typically in terms of a well-defined core plus one or more valence nucleons. Over the past decade the properties of halo nuclei have been studied theoretically using a range of reaction models, many of which having served us well for half a century or more in the study of less exotic, “mean-field”, nuclei. However, it is now clear that for many reactions with halo nuclei, it is not appropriate to disentangle (factorise out) the structure information from the reaction information. That is, the few-body nature of these systems requires few-body reaction models in which the nuclear structure and reaction mechanisms are necessarily entangled. This talk will briefly review the physical assumptions made by various reaction models, and point to areas where progress is being made to extend their range of applicability in order to provide further insights into halo structure. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: j.al-khalili@surrey.ac.uk     

A semi-classical description of nuclear phase-space and momentum distributions in hot nuclei

The nuclear phase-space distribution is calculated in a semi-classical approximation using the inverse Laplace transformation of the Bloch density. For a local Woods-Saxon potential, both the phase-space and the momentum distributions are shown as functions of the temperature.     

One dimensional three-body model for low energy reactions of halo nuclei

One dimensional three-body model which simulates the low energy reactions of the nuclei with halo structure, is investigated by solving exactly the three-body Schrödinger equation. The dynamical roles of the halo neutron during the reaction are studied in detail. The decrease of the fusion probability, as well as the large transfer and break-up probabilities, are found for halo nuclei.     

Isospin in halo nuclei: Borromean halo,tango halo,and halo isomers

It is shown that the wave functions for isobaric analog, double isobaric analog, configuration, and double configuration states may simultaneously have components corresponding to nn, np, and pp halos. The difference in the halo structure between the ground and excited states of a nucleus may lead to the formation of halo isomers. A halo structure of both Borromean and tango types can be observed for np configurations. The structure of ground and excited states with various isospins in halo-like nuclei is discussed. The reduced probabilities B(Mλ) and B(Eλ) for gamma transitions in ^6?8Li, ^8?10Be, ^8,10,11B, ^10?14C, ^13?17N, ^15?17,19O, and ¹⁷F nuclei are analyzed. Particular attention is given to the cases where the ground state of a nucleus does not have a halo structure, but where its excited state may have it.