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     

Experimental studies of the nuclear spatial structure of neutron-rich He and Li isotopes

Results of several experiments aimed at exploring the nuclear spatial structure of neutron-rich He and Li isotopes are presented and briefly discussed. The study of the density distributions in these nuclei by small-angle proton elastic scattering at intermediate energy is considered in more detail. The performed investigations allow one to obtain information on the total matter distributions, radii of the matter, neutron and proton distributions, effective and internal core sizes, halo sizes, and spatial correlations of the halo nucleons in the studied nuclei. The text was submitted by the authors in English.     

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.     

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.     

Nuclear exoticism

Extreme states of nuclearmatter (such that feature high spins, large deformations, high density and temperature, or a large excess of neutrons and protons) play an important role in studying fundamental properties of nuclei and are helpful in solving the problem of constructing the equation of state for nuclear matter. The synthesis of neutron-rich nuclei near the nucleon drip lines and investigation of their properties permit drawing conclusions about the positions of these boundaries and deducing information about unusual states of such nuclei and about their decays. At the present time, experimental investigations along these lines can only be performed via the cooperation of leading research centers that possess powerful heavy-ion accelerators, such as the Large Hadron Collider (LHC) at CERN and the heavy-ion cyclotrons at the Joint Institute for Nuclear Research (JINR, Dubna), where respective experiments are being conducted by physicists from about 20 JINR member countries. The present article gives a survey of the most recent results in the realms of super neutron-rich nuclei. Implications of the change in the structure of such nuclei near the nucleon drip lines are discussed. Information about the results obtained by measuring the masses (binding energies) of exotic nuclei, the nucleon-distribution radii (neutron halo) and momentum distributions in them, and their deformations and quantum properties is presented. It is shown that the properties of nuclei lying near the stability boundaries differ strongly from the properties of other nuclei. The problem of the stability of nuclei that is associated with the magic numbers of 20 and 28 is discussed along with the effect of new magic numbers.     

Quasifree proton scattering on halo nuclei as a tool for studying the neutron-halo structure

An experimental method is proposed for investigating the structure of the two-neutron halo in quasifree proton scattering on clusters of halo nuclei. This scattering process is studied in inverse kinematics by using a ⁶He beam incident to a stack of track emulsions. Preliminary data on the reaction ⁶He + p → ⁴He + p + X are compared with the results of simple kinematical calculations for quasifree proton scattering on the clusters forming the halo of the ⁶He nucleus.     

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.     

Helium halo nuclei from low-momentum interactions

We present ground-state energies of helium halo nuclei based on chiral low-momentum interactions, using the hyperspherical-harmonics method for ⁶He and coupled-cluster theory for ⁸He , with correct asymptotics for the extended halo structure.     

Structure of nuclei far from stability

The structure of neutron-rich unstable nuclei is discussed by focusing on three different subjects; (i) a superdeformed halo nucleus ¹¹Be studied by a deformed Woods-Saxon potential, (ii) retarded β decay due to neutron halo in ¹¹Li, and (iii) giant neutron excitations in nuclei with neutron skin.     

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.     

Implication of proton-nucleus scattering for density distributions of unstable nuclei

The use of elastic proton scattering at intermediate and high energies to obtain information about the density distributions of unstable nuclei is investigated. A comparison between the relativistic impulse approximation (RIA) and Glauber model for proton scattering from ¹⁶O, ⁴⁰Ca, ⁴⁴Ca and ⁴⁸Ca at medium energies is performed. We used density distributions derived from the relativistic mean-field theory, employing the recent relativistic force NL-RA1, as well as experimental and phenomenological densities. It is found that the eikonal approximation can describe the cross-section only at small scattering angles and is weakly sensitive to the density distributions, while the RIA nicely produced the experimental cross-sections, even at medium and larger angles, and was very sensitive to the nuclear densities. Furthermore, the RIA better describes the isospin dependence of the cross-section. We used the RIA to investigate the density distribution of ⁵⁸Ca for proton scattering at different energies. It is found that the cross-section strongly depends on the parameters of the density distribution even at a small scattering angle. These results are important in extracting information about the structure of unstable nuclei. We also investigated the RIA and its sensitivity in describing halo nuclei such as ⁶He. We used for ⁶He a no-halo Gaussian density and a realistic-halo density that derived in the cluster orbital shell model approximation and contains the extended distribution of the valence nucleons. Comparison with the recent experimental data at GSI at 717 MeV/nucleon shows that the RIA successfully described the data at all considered range of the momentum transfer and on the other hand favor the halo structure of ⁶He. Received: 1 December 2001 / Accepted: 31 July 2002 / Published online: 11 February 2003 RID="a" ID="a"e-mail: mrashdan@hotmail.com Communicated by P. Schuck     

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.     

Pionic Fusion Study of the halo analogue state6Li

The isobaric analogue state of the ground state of the halo nucleus⁶He,⁶Li* has been studied in a pionic fusion experiment at the CELSIUS storage ring facility in Uppsala, Sweden. This was the first of two proposed experiments with the aim to study the high momentum part of the wave functions of the halo nuclei⁶He and⁶Li (0⁺, T=1). The Li nuclei were produced in inverse kinematics reactions with alpha particles incident on a deuterium cluster jet target. The⁶Li ions were detected in a zero-degree spectrometer situated in the fourth quadrant of the CELSIUS ring. The measurement was done for three different beam energies corresponding to 5.4, 2.2 and 1.5 MeV above threshold in the c.m. The cross-sections slowly increase with beam energy from 95 nb at the lowest energy to about 250 nb at 5.4 MeV above threshold.     

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.     

TITAN: An ion trap facility for on-line mass measurement experiments

Precision determinations of ground state or even isomeric state masses reveal fingerprints of nuclear structure. In particular, at the limits of existence for very neutron-rich or -deficient isotopes, one can extract detailed information about nuclear structure from separation energies or binding energies. Mass measurements are important to uncover new phenomena, to test new theoretical predictions, or to refine model approaches. For example, the N?=?28 shell has proven more stable than previously expected; however, the predicted new “magic” number at N?=?34 in the K and Ca isotopes has yet to be confirmed experimentally. For these neutron-rich nuclei, the inclusion of three-body forces leads to significantly better predictions of the ground-state mass. Similarly, halo nuclei present an excellent application for ab-initio theory, where ground state properties, like masses and radii, test our understanding of nuclear structure. Precision mass determinations at TRIUMF are carried out with the TITAN (TRIUMF’s Ion Traps for Atomic and Nuclear science) facility. It is an ion-trap setup coupled to the on-line facility ISAC. TITAN has measured masses of isotopes as short-lived as 9 ms (almost an order of magnitude shorter-lived than any other Penning trap system), and it is the only one with charge breeding capabilities, which allow us to boost the precision by almost 2 orders of magnitude. We recently made use of this feature by measuring short-lived, proton-rich Rb-isotopes, up to ⁷⁴Rb while reaching the 12?+ charge state, which together with other improvements led to an increase in precision by a factor 36.     

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     

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.     

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.     

Rearrangements in neutron shell closures far from stability

A survey of experimental results obtained at GANIL (Caen, Prance) on the study of the properties of very neutron-rich nuclei (Z = 6–20, A = 20–60) near the neutron drip line and resulting in an appearance of further evidence for the new magic number N = 16 is presented. Very recent data on mass measurements of neutron-rich nuclei at GANIL and some characteristics of binding energies in this region are discussed. Nuclear binding energies are very sensitive to the existence of nuclear shells and together with the measurements of instability of doubly magic nuclei ¹⁰He and ²⁸0 they provide information on changes in neutron shell closures of very neutron-rich isotopes. The behaviour of the two-neutron separation energies S_2n derived from mass measurements gives a very clear evidence for the existence of the new shell closure N = 16 for Z = 9 and 10 appearing between 2s_1/2 and ld_3/2 orbitals. This fact, strongly supported by the instability of C, N and O isotopes with N > 16, confirms the magic character of N = 16 for the region from carbon up to neon while the shell closure at N = 20 tends to disappear for Z ≤ 13. Decay studies of these hardly accessible short-lived neutron-rich nuclei from oxygen to silicon using the in-beam γ-ray spectroscopy are also reported.     

Nuclear-matter incompressibility from fits of generalized Skyrme force to breathing-mode energies

In an attempt to extend the range of values of K_v, the incompressibility of symmetric nuclear matter, for which fits to the measured breathing-mode energies are possible, we investigate generalized Skyrme-type forces with a term that is both density- and momentum-dependent. Acceptable fits are found to be possible only for values of K_v in the range 215±15 MeV. For higher values fits are impossible, while for lower values fits are achieved only by introducing an unphysical collapse of nuclear matter. Thus our generalization of the Skyrme force does not permit a significantly wider range of values of K_v than that already given by force SkM¹. However, with a view to having a more reliable estimate of the compressional properties of the highly neutron-rich nuclear matter that comprises the core of collapsed stars, we present a new version of this latter force giving a much better fit to the masses of neutron-rich nuclei. Comparison with force SkM¹ also shows that the value of K_v extracted from the breathing-mode energies is essentially independent of the choice of effective mass. By providing a counter-example, we show that K_v cannot be extracted from masses and charge distributions alone. As for the third-order coefficient K′, we cannot be more precise than to say that it lies in the interval 700 ± 500 MeV.