Reaction cross sections for collisions involving exotic light nuclei within the glauber approach

The reaction cross sections for the interaction of exotic nuclei ⁶He and ¹¹Li with ¹²C nuclei are calculated for energies of about 0.8 GeV per nucleon. The cross sections calculated by the exact Glauber formula are compared with their counterparts found by using the formulas of the optical limit, the rigidtarget approximation, and the few-body approximation. The effect of the structure of the nuclei being considered on the calculated cross sections is examined. The root-mean-square radii of the ⁶He and ¹¹Li nuclei are estimated on the basis of experimental data on the cross sections for the interaction of these exotic nuclei with ¹²C nuclei.     

Pairing correlations and soft dipole excitations in nuclei on the neutron-drip line

Paring correlations and soft dipole excitations in weakly bound nuclei on the edge of neutrondrip line are studied by using a three-body model. A density-dependent contact interaction is employed to calculate the ground state of halo nuclei ⁶He and ¹¹Li, as well as a skin nucleus ²⁴O. Dipole excitations in these nuclei are also studied within the same model. We point out that the dineutron-type correlation plays a dominant role in the halo nuclei ⁶He and ¹¹Li having the coupled spin of the two neutrons S = 0, while the correlation similar to the BCS type is important in ²⁴O. Contributions of the spin S = 1 and S = 0 configurations are separately discussed in the low-energy dipole excitations. The calculated results are compared with recent experimental data of ⁶He and ¹¹Li. The text was submitted by the authors in English.     

Sensitivity of cross sections for elastic nucleus-nucleus scattering to halo nucleus density distributions

In order to clear up the sensitivity of the nucleus-nucleus scattering to the nuclear matter distributions in exotic halo nuclei, we have calculated differential cross sections for elastic scattering of the ⁶He and ¹¹Li nuclei on several nuclear targets at the energy of 0.8 GeV/nucleon with different assumed nuclear density distributions in ⁶He and ¹¹Li.     

Rescattering effects in proton scattering on nuclei 6,8He and 8,9Li in the Glauber theory

The differential cross sections of elastic p^6,8He and p^8,9Li scattering are calculated within the Glauber diffraction theory at intermediate energies of 70 to 700 MeV/nucleon. The calculations are based on realistic three-body wave functions α-n-n (for ⁶He), α-2n-2n (for ⁸He), α-t-n (for ⁸Li), α-t-2n (for ⁹Li), obtained using current nuclear models, and the Glauber operator is expanded into a series of multiple scattering corresponding to the three-body nuclei configuration. The approach allows us to calculate the operator matrix elements with allowance for rescattering on all structural components of the investigated nuclei.     

Investigation of neutron and proton distributions of He,Li, and Be isotopes using the new Skyrme-Force parameters

The proton and neutron densities, root-mean-square (rms) radii of proton density and neutron density, and neutron skin thickness of ^4–10He, ^6–11Li, and ^7–12Be isotopes are calculated using Skyrme-Hartree-Fock method with SLy4, SLy5, SLy6, and SLy7 force parameters. The evaluated results are compared with experimental data. Also, the results of halo nuclei (^6,8He, ¹¹Li, and ¹¹Be) are compared with the results of other isotopes for selected nuclei having the same neutron configuration.     

Fusion and transfer reactions in beams of light loosely bound nuclei at energies in the vicinity of the Coulomb barrier

Experiments devoted to studying cross sections for fusion and transfer reactions induced by the interaction of beams of halo-like (⁶He), cluster (⁶Li and ⁷Li), and loosely bound (³He) nuclei with nuclei of light and heavy elements are described. The cross sections obtained experimentally for such reactions are analyzed. Special features in the behavior of the cross sections for the formation of evaporation residues and products of transfer reactions at energies in the vicinity of the Coulomb barrier are revealed. In particular, an increase in the cross sections for fusion and transfer reactions involving halo-like nuclei and proceeding at energies in the subbarrier region is observed. The cross sections for neutron-transfer and light-cluster-transfer reactions reachmaximum values at an energy in the vicinity of the Coulomb barrier for the reaction being considered.     

Angular correlations in peripheral fragmentation of halo nuclei

The angular correlation between momenta of ⁵He and its decay products has been calculated for the peripheral fragmentation of ⁶He using a two-step model in a sudden approximation: (1) One neutron knock-out leading to the unbound nucleus ⁵He. (2) Subsequent decay of ⁵He undisturbed by the target in an α-particle and a neutron. Angular correlations measured in a recent experiment dealing with the peripheral fragmentation of 240 MeV/u ⁶He on a carbon target can be well described by a dominant ⁵He 3/2^? ground state configuration plus a small admixture of ≈ 7% of the first excited 1/2^? state. The influence of an s-state admixture as well as a contribution of the momentum transfer to the correlation function are investigated. The results obtained for ⁶He are then used as a touch stone for a discussion of the methods to investigate peripheral fragmentation of other Borromean halo nuclei like ¹¹Li and ¹⁴Be. It is shown that the evidence on the possible existence of low-lying s-states in ¹⁰Li and ¹³Be can be derived from the corresponding angular correlations.     

Reactions involving loosely bound cluster nuclei: Heavy ions and new technologies

Experimental results on excitation functions for complete-fusion and transfer reactions in the interaction of ⁶He and ^6,8,9Li nuclei with various target nuclei are presented. Data on fusion-reaction cross sections in the case of ⁶He differ strongly from the predictions of the statistical model. A strong enhancement of the cross section at barrier energies is observed for this reaction channel. Also, an increase in the cross sections for neutron-transfer reactions (in the case of ⁶He and ^8,9Li beams) and deuteron-transfer reactions (in the case of ⁶Li) is observed in the deep-subbarrier energy region. The results are discussed from the point of view of the effect of the cluster structure of nuclei on the probability of interaction at barrier energies. The results of employing heavy-ion beams in new technologies are presented.     

Effective nucleon-nucleon forces and interaction of light exotic nuclei with stable nuclei at low energies

The effect of the density dependence of effective nucleon-nucleon forces on the folded potential of the interactions of the light exotic nuclei ⁶He, ¹¹Li, ¹¹Be, and ⁸B with the stable nucleus ¹²C is studied, and the corresponding experimental data on the total reaction cross sections and on elastic scattering are analyzed. A semimicroscopic double-folding model featuring various density-dependent forces based on the M3Y interaction is used together with the nucleon densities as calculated within the density-functional method by using a unified set of parameters for all the above nuclei. It is shown that the angular distributions recently measured for elastic ⁶He scattering on ¹²C at an energy of 41.6 MeV per projectile nucleon and for elastic ¹¹Be scattering on ¹²C at an energy of 49.3 MeV per projectile nucleon can be described satisfactorily if the real part of the optical folded potential is supplemented with a surface term mimicking the contribution of the dynamical polarization potential.     

Special features of nuclear reactions induced by loosely bound <Superscript>6</Superscript>He and <Superscript>6,7</Superscript>Li nuclei in the vicinity of the Coulomb barrier height

Excitation functions are measured for complete-fusion and transfer reactions induced by the interaction of ⁶He and ⁶Li with ²⁰⁶Pb, ²⁰⁹Bi, and Pt. Data obtained for fusion reactions induced by ⁶He ions deviate from the predictions of the statistical model of compound-nucleus decay at projectile energies in the vicinity of the Coulomb barrier height. A strong enhancement of cross sections for fusion reactions induced by the interaction of ⁶He with target nuclei is observed. The cross sections for reactions of cluster transfer, neutron transfer from ⁶He, and deuteron transfer from ⁶Li at deep-subbarrier energies are also found to be enhanced. These results are discussed from the point of view of the effect of the cluster structure of nuclei on the interaction probability at energies in the vicinity of the Coulomb barrier height.     

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.     

Elastic scattering of intermediate-energy weakly bound particles on 12C nuclei

The differential cross-section for elastic scattering of deuterons at 700 MeV, ⁶Li and ⁶He at 2.07 GeV nuclei on ¹²C nucleus is calculated under the assumption of two-cluster (for deuterons and ⁶Li) and three-cluster (for ⁶He) structure of incident particle. For ⁶Li-¹²C and ⁶He-¹²C elastic scattering it is shown that there are quantitative distinctions in the behaviour of the observables calculated in the above approaches. Received: 13 October 1999 / Accepted: 3 January 2001     

Neutron periphery in light nuclei

A spatial configuration of light nuclei that involves two excess neutrons (⁶He, ¹⁰Be, and ¹²B) is studied by analyzing cross sections for various reactions on these nuclei: ⁶He(α, α)⁶He, ⁹Be(d, p)¹⁰Be, and ¹⁰B(t, p)¹²B. Pole dineutron-transfer mechanisms (dineutron configuration of the neutron periphery) and second-order mechanisms involving sequential neutron transfer (cigar-like configuration of the neutron periphery) are taken into account in the calculations. It is shown that the neutron periphery is drastically different in the nuclei in question: in ⁶He, there is a halo receiving a contribution from both configurations; in ¹⁰Be, there is an only slightly noticeable halo featuring a contribution of practically one neutron from the cigar-like configuration; and, in ¹²B, there is a neutron skin.     

Spatial periphery of lithium and beryllium isotopes

The spatial structure of the periphery of lithium and beryllium isotopes is studied by means of charge-exchange reactions and the (t, p) and (d, p) reactions on their nuclei. It is shown that the 0⁺ isobaric-analog state of ⁶Li at 3.56 MeV has a halo structure formed by a proton and a neutron, that there is virtually no manifestation of a neutron halo in the ground state of the ⁹Li nucleus, and that the ¹¹Li nucleus has a Borromean halo structure that two neutrons form with respect to the ⁹Li core and which manifests itself in cigar and dineutron configurations. The ¹⁰Be nucleus has a substantial two-neutron periphery in either configuration both in the ground and in the 2⁺ excited state at 3.37MeV.     

Puzzle of the <Superscript>6</Superscript>Li quadrupole moment: Steps toward solving it

The problem of the origin of the quadrupole deformation in the ⁶Li ground state is investigated with allowance for the three-deuteron component of the ⁶Li wave function. Two long-standing puzzles related to the tensor interaction in the ⁶Li nucleus are known: that of an anomalous smallness of the ⁶Li quadrupole moment (being negative, it is smaller in magnitude than the ⁷Li quadrupole moment by a factor of 5) and that of an anomalous behavior of the tensor analyzing power T_2q in the scattering of polarized ⁶Li nuclei on various targets. It is shown that a large (in magnitude) negative exchange contribution to the ⁶Li quadrupole moment from the three-deuteron configuration cancels almost completely the “direct” positive contribution due to the αd folding potential. As a result, the total quadrupole moment proves to be close to zero and highly sensitive to fine details of the tensor nucleon-nucleon interaction in the ⁴He nucleus and of its wave function.     

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.     

Possibility of Studying Neutron–Neutron Correlations in Halo Nuclei

An experimental investigation of the reaction of core pickup from ⁶He and ¹¹Li two-neutronhalo nuclei is proposed. In such experiments, neutron–neutron correlations in a halo nucleus will be assessed on the basis of the energy of a neutron–neutron quasibound state. A detailed kinematical simulation of the reaction ⁶He + ²H → ⁶Li + (nn) →⁶ Li + n + n is performed. It is shown that the energy of the quasibound state in question can determined from the shape of the energy spectrum of neutrons originating from the breakup of this state. In the proposed exclusive experiment, a beam of ⁶He (¹¹Li) nuclei with an energy of about 5 to 10 MeV per nucleon interacts with a deuterated-polyethylene target. This will permit detecting charged particles (⁶Li and ¹¹Be) and a neutron. On the basis of determining the energy of the neutron–neutron quasibound state, it will become possible to estimate the effective attraction between the valence neutrons in the field of the third particle (core).     

Peculiarities in total cross sections of reactions with weakly bound nuclei <Superscript>6</Superscript>He, <Superscript>9</Superscript>Li

The energy dependence of the total cross sections for the ⁶He + Si and ⁹Li + Si reactions was measured at beam energies between 5 and 20 MeV per nucleon. The results agree with experimental data published for the ⁶He + Si reaction. New data are obtained for the ⁹Li + Si reaction in the vicinity of a local enhancement of the total cross section. A theoretical analysis of the possible reasons behind the appearance of this peculiarity in the case of collisions of ⁶He and ⁹Li nuclei with silicon target nuclei is performed. In particular, the enhancement may owe its origin to the effect of loosely bound projectile nucleons.     

Sensitivity of reaction cross sections to halo nucleus density distributions

In order to clear up the sensitivity of the nucleus-nucleus reaction cross sections σ _R to the nuclear matter distributions in exotic halo nuclei, we have calculated the values of σ _R for scattering of ⁶He, ¹¹Li, and ¹⁹C nuclei on several nuclear targets at the energy of 0.8 GeV/nucleon. The calculations were performed in the “rigid target” approximation to the Glauber theory, different shapes of the nuclear density distributions in ⁶He, ¹¹Li, and ¹⁹C being assumed.