Light Nuclei in the Continuum

The development of light, neutron-rich beams has opened in the last decade new perspectives for the study of many-neutron systems. Breakup experiments at GANIL are described, using beams of ^6,8He, ¹¹Li, ¹⁴Be and ¹⁵B at several tens of MeV/N. Our approach is based on the detection in coincidence of the breakup fragment and the neutrons in order to investigate the different correlations in the final state of these very neutron-rich systems. Several particular cases are discussed: fragment-n correlations in unbound ⁷He, ¹⁰Li and ⁹He; 2n correlations in ⁶He, ¹¹Li and ¹⁴Be; and three-body and 4n correlations in ⁸He and ¹⁴Be.     

Probing Few-Body Correlations in Light, Neutron-Rich Nuclei

 The advent of secondary beams of very neutron-rich nuclei gives access to the investigation of correlations in the few-neutron system. Results of different experiments undertaken at GANIL with ⁶He, ¹¹Li, and ¹⁴Be beams are discussed. These nuclei exhibit a two-neutron halo, in which the correlations between the two neutrons provide the stability of the A-body system. A new technique aiming to explore the possible binding of systems of more than two neutrons will also be presented, together with very preliminary results that suggest the particle stability of ⁴ n. Received October 28, 2001; accepted for publication November 9, 2001     

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.     

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).     

Nuclear structure effects in the isotope shift with halo nuclei

Corrections to atomic energy levels due to nuclear structure effects are discussed. These are the finite nuclear size combined with relativistic and recoil corrections, and the nuclear polarizability. Good understanding of these effects is necessary for interpretation of high-precision measurements of the isotope shifts with neutron-rich nuclei ^6,8He, ¹¹Li and ¹¹Be. The summary of the results of the accurate atomic structure calculations is presented also.     

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.     

Neutron-induced charged-particle reactions in 6Li and 9Be

Angular distributions of tritons from the ⁶Li(n, t)⁴He reaction were measured at E_n = 7.25, 6.77, 6.57, 5.24 and 4.71 MeV. Angular distributions of douterons from respectively, the ⁶Li(n, d)⁵He two-body breakup reaction were measured at E_n = 6.77 and 6.57 MeV, and of protons from the ⁶Li(n, p)⁶He reaction at E_n = 6.77, 5.24 and 4.71 MeV. All these reactions in ⁶Li were analyzed as direct interaction in the formalism of the distorted wave Born approximation. The optical model for the nuclear interaction was found to apply reasonably well to nuclei as light as ⁴He, ⁵He, ⁶He and ⁶Li. In addition, ⁶Li as an alpha-deuteron cluster gives the best bound-state wave function to describe the experimental angular distribution of tritons. The excitation functions at forward angles of the ⁶Li(n, t)⁴He, ⁶Li(n, d)⁵He and ⁶Li(n, p)⁶He reactions were measured for incident neutron energies between 4.4 and 7.3 MeV. It is found that the ⁶Li(n, d)⁵He two-body breakup reaction has a threshold at about E_n = 5.3 MeV. Angular distributions at E_n = 18.3 MeV for tritons and protons from the ⁹Be(n, t)⁷Li and ⁹Be(n, p)⁹Li, respectively, were also measured.     

Nuclear structure near the drip line studied by RNB

The use of radioactive nuclear beams (RNB) has provided an opportunity to study nuclei far from the stability line. Reaction studies using intermediate and high-energy (30–1000 AMeV) radioactive beams have revealed new structures of nuclei that are not seen in nuclei near to the stability line [1]. One such new structure is the neutron halo, a long low-density tail of the neutron distribution [2]. It has been observed in neutron drip-line nuclei, such as⁶He,¹¹Li and¹¹Be. The neutron halo has put light on many new structure problems. Among those, recent studies of a softE1 mode, a low-frequency oscillation of halo neutrons against the core, are discussed in the following section in connection with a recent (p, p′) reaction measurement [3]. Also, the effect of changes in single-particle orbitals on halo formation is discussed [4]. Another new finding is the formation of neutron skins in neutron-rich unstable nuclei [5]. The relation between the equation-of-state (EOS) of asymmetric nuclear matter and the neutron-skin thickness as well as the density distribution of nuclei far from the stability line is discussed in the last section.     

中子滴线附近核异常大半径的解释

基于中子滴线附近核结合能的数据分析,¹¹Li,¹⁴Be和¹⁷B等可看作是核芯-中子-中子组成的三体系统。假定核芯-中子和中子-中子间作用势为弱吸引指数势,不足以形成核芯-中子和中子-中子束缚态。本文的研究表明,核芯-中子-中子三体系统可形成弱束缚态。⁶He,¹¹Li,¹⁴Be和¹⁷Be核的异常大核半径正是由于外层中子的弱束缚所致。 关键词：     

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.     

High-lying excited states in <Superscript>10</Superscript>Be from the <Superscript>9</Superscript>Be(<Superscript>9</Superscript>Be,<Superscript>10</Superscript>Be)<Superscript>8</Superscript>Be reaction

A transfer-reaction experiment of ⁹Be(⁹Be, ¹⁰Be)⁸Be was performed at a beam energy of 45 MeV. Excited states in ¹⁰Be up to 18.80 MeV are produced using missing mass and invariant mass methods. Most of the observed high-lying resonant states, reconstructed from the α + ⁶He and t + ⁷Li decay channels, agree with the previously reported results. In addition, two new resonances at 15.6 and 18.8 MeV are identified from the present measurement. The 18.55 MeV state is found to decay into both the t + ⁷Li_g.s. and t + ⁷Li* (0.478 MeV) channels, with a relative branching ratio of 0.93 ± 0.33. Further theoretical investigations are encouraged to interpret this new information on cluster structure in neutron-rich light nuclei.     

Universal Aspects of Neutron Halos in Light Exotic Nuclei

The theoretical few-body aspects associated with universal properties of weakly-bound neutron-rich light nuclei close to the drip line will be reviewed briefly, considering recent theoretical and experimental works. We will address low-energy properties of the one- and two-neutron halo of light exotic nuclei, which are dominated by s-wave short-range two-body interactions. In view of recent experiments with light neutron-rich nuclei, we will discuss properties of exotic nuclei as ¹¹Li, ¹⁴Be, ²⁰C and ²²C, within a three-bodyneutron–neutron-core model. Particular emphasis will be given to model independent properties associated to halo neutrons, which obey universal scaling laws. We discuss how the scaling laws for the s-wave observables of two-neutron halo will be identified with limit-cycles and Thomas–Efimov effect in a zero-range three-body model.     

Forward-angle yields of 2≤Z≤11 isotopes in the reaction of 18O(35A MeV) with 9Be

A systematic investigation of the forward-angle inclusive yields of 2≤Z≤11 isotopes produced in collisions of ¹⁸O projectile nuclei with a ⁹Be target in the Fermi energy region (35A MeV) is performed. The measurements were based on the use of the COMBAS double achromatic kinematical separator in the spectrometry mode at the Flerov Laboratory of Nuclear Reactions at the Joint Institute for Nuclear Research, FLNR (JINR, Dubna). The velocity, isotopic, and element distributions are presented. There is no unique mechanism that would explain the total set of results obtained in this experiment. A dominant role of low-energy reaction mechanisms is observed. The intensity of secondary beams of halolike nuclei ¹¹Li, ¹²Be, and ¹⁴Be is determined.     

Trinucleon cluster structure at high-excitation energies in A=6 nuclei

Trinucleon molecular structures in ⁶He and ⁶Be were investigated by using the ⁶Li(⁷Li, ⁷Be)⁶He reaction at 455 MeV and ⁶Li(³He, t)⁶Be reaction at 450 MeV, respectively. Binary decays into t + t from a broad state at E _x =18.0±1.0 MeV in ⁶He and into ³He + ³He from one at E _x =18.0±1.2 MeV in ⁶Be, respectively, were observed by measuring trinucleon cluster decays in coincidence with reaction particles. The branching ratios for binary decay were estimated to be about 0.7 for ⁶He and ⁶Be. These large branching ratios show that a trinucleon cluster state exists as an isobaric partner around E _x =18 MeV in ⁶He and ⁶Be.     

Multichannel neutron scattering on <Superscript>11</Superscript>Be nucleus

The effect of the Pauli exclusion principle on the relative motion of colliding light neutron-rich nuclei is investigated within a microscopic method for the examples of the ¹¹Be + n and ¹⁰Be + ² n reactions. The effective interaction of nuclei that is due to the change in the kinetic energy of their relative motion under the effect of the antisymmetrization operator is analyzed on the basis of a discrete representation of harmonic-oscillator states allowed by the Pauli exclusion principle. It is concluded that the bound state of the ¹²Be nucleus owes its origin to the impact of exchange effects on the operator of the kinetic energy of the relative motion of the neutron and the ¹¹Be nucleus. The structure of the ¹²Be ground state is discussed in the approximation of two coupled cluster configurations. The cross section for the inelastic-scattering reaction ¹¹Be(n, ² n)¹⁰Be is estimated.     

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.     

The3He(α,γ)7Be reaction and the solar neutrino problem

The capture reaction³He(α,γ)⁷Be has been investigated in the energy range ofE _c.m. =107 to 1,266 keV. The⁴He or³He beams of up to 300 μA particle current were incident on³He or⁴He gas targets, respectively. The gas target systems were all of the windowless and recirculating type. Excitation functions have been obtained with the use of an extended-static gas target, while the measurements ofγ-ray angular distributions involved a quasi-point supersonic jet system. The determination of absolute cross sections has been carried out with both types of gas target systems. Theγ-ray yields in the³He(α,γ)⁷Be reaction were detected using 80 cm³ Ge(Li) detectors. The data lead to a zero-energy intercept of the astrophysicalS(E) factor ofS(0)=0.30±0.03 keV-b. This result reduces the calculated solar neutrino rate by a factor of 1.76.     

Die Breite des 4+(11,4 MeV)-Zustandes von8Be aus7Li(d,n) 2α

With the reaction⁷Li+“d→n+⁸Be→n+2α the location and width of the⁸Be(4,+) level is redetermined. While the location at 11.4±0.05 MeV is found in agreement with known values, the width is found to be onlyΓ=2.8±0.2 MeV thereby disagreeing with data fromα-α-scattering but being close to a recent determination from the reaction¹⁰B(d,α)⁸Be (Γ=2.6 MeV). — No indication for participation of an excited state of⁵He in the simultaneously possible reaction via⁵He is found.     

One-nucleon spectroscopy of light nuclei

The capabilities and limitations of the conventional many-particle shell model and modern potential cluster models are discussed. New revaluated and more accurate calculations of one-nucleon spectroscopic characteristics of the light nuclei of 1p shell are presented. In many-particle shell model for nuclei with A = 7, 9, 11, 13, and 15 nucleon partial widths of highly excited states with the isotopic spin T = 3/2 were calculated both for “allowed” and “forbidden” transitions. One-nucleon spectroscopic factors were calculated in threebody multicluster models of ⁶Li{αnp}, ⁸Li{αtn}, and ⁹Be{ααn} nuclei. For isobar-analogue nuclei ⁷Li and ⁷Be, the spectroscopic proton S _p and neutron S _n factors for transitions to the ground and excited states of corresponding residue nuclei of the triplet ⁶Li-⁶He-⁶Be were calculated in the framework of binary potential αtand ατ models. Integral, differential and polarization characteristics of photonuclear processes ⁷Li(γ, n ₀)⁶Li, ⁶He(p, γ_{0 + 1})⁷Li, ⁷Li(γ, p ₀)⁶He, and ⁹Be(γ, p _{0 + 1})⁸Li were calculated in this approach.