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.     

Neutron halos in hypernuclei

Properties of single- Λ and double- Λ hypernuclei for even-N Ca isotopes ranging from the proton dripline to the neutron dripline are studied using the relativistic continuum Hartree-Bogoliubov theory with a zero-range pairing interaction. Compared with ordinary nuclei, the addition of one or two Λ-hyperons lowers the Fermi level. The predicted neutron dripline nuclei are, respectively, ⁷⁵ _ΛCa and ⁷⁶ _2ΛCa, as the additional attractive force provided by the Λ-N interaction shifts nuclei from outside to inside the dripline. Therefore, the last bound hypernuclei have two more neutrons than the corresponding ordinary nuclei. Based on the analysis of two-neutron separation energies, neutron single-particle energy levels, the contribution of continuum and nucleon density distribution, giant halo phenomena due to the pairing correlation, and the contribution from the continuum are suggested to exist in Ca hypernuclei similar to those that appear in ordinary Ca isotopes. Received: 21 October 2002 / Accepted: 11 January 2003 / Published online: 8 April 2003     

The surface diffuseness and the spin-orbital splitting in relativistic continuum Hartree-Bogoliubov theory

The relativistic continuum Hartree-Bogoliubov (RCHB) theory, which is the extension of the relativistic mean field and the Bogoliubov transformation in the coordinate representation, has been used to study tin isotopes. The pairing correlation is taken into account by a density-dependent force of zero range. The RCHB theory is used to describe the even-even tin isotopes all the way from the proton drip line to the neutron drip line. The contribution of the continuum which is important for nuclei near the drip-line has been taken into account. The theoretical S_2n as well as the neutron, proton, and matter rms radii are presented and compared with the experimental values where they exist. The change of the potential surface with the neutron number has been investigated. The diffuseness of the potentials in tin isotopes is analyzed through the spin-orbital splitting in order to provide new way to understand the halo phenomena in exotic nuclei. The systematic of the isospin and energy dependence of these results are extracted and analyzed.     

Halo structure of 11Li in proton scattering: A folding model description with isospin,density and momentum dependent effective interaction

Recent ¹¹Li+p elastic scattering data at 62, 68.4, and 75 MeV and inelastic scattering data at 68.4 MeV, taken at RIKEN, are analysed with an isospin, density and momentum dependent finite range effective interaction (SBM) and M3Y interaction in a single folding model. The M3Y folded ¹¹Li+p potentials are found to be almost similar to the folded ⁹Li+p potentials. But the SBM folded ¹¹Li+p potentials are distinctly different, causing small but significant change in the angular distribution. Folded potentials need appreciable reduction factors indicating possible effects of strong breakup channel coupling. No significant change in results is found if ⁹Li core + Gaussian two-neutron halo density is used instead of the COSM density of ¹¹Li although the radial extent of the latter is much larger. The angular distribution of the recently discovered excited state at 1.3 MeV, well reproduced by the SBM folded potential, is found to be predominantly dipole in nature.     

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.     

Nuclear field theory predictions for 11Li and 12Be: Shedding light on the origin of pairing in nuclei

Recent data resulting from studies of two-nucleon transfer reaction on ¹¹Li, analyzed through a unified nuclear-structure-direct-reaction theory have provided strong direct as well as indirect confirmation, through the population of the first excited state of ⁹Li and of the observation of a strongly quenched ground state transition, of the prediction that phonon-mediated pairing interaction is the main mechanism binding the neutron halo of the 8.5-ms-lived ¹¹Li nucleus. In other words, the ground state of ¹¹Li can be viewed as a neutron Cooper pair bound to the ⁹Li core, mainly through the exchange of collective vibration of the core and of the pigmy resonance arizing from the sloshing back and forth of the neutron halo against the protons of the core, the mean field leading to unbound two-particle states, a situation essentially not altered by the bare nucleon-nucleon interaction acting between the halo neutrons. Two-neutron pick-up data, together with (t, p) data on ⁷Li, suggest the existence of a pairing vibrational band based on ⁹Li, whose members can be excited with the help of inverse kinematic experiments as was done in the case of ¹¹Li(p, t)⁹Li reaction. The deviation from harmonicity can provide insight into the workings of medium polarization effects on Cooper-pair nuclear pairing, let alone specific information concering the “rigidity” of the N = 6 shell closure. Further information concerning these questions is provided by the predicted absolute differential cross sections σ _abs associated with the reactions ¹²Be(p, t)¹⁰Be(g.s.) and ¹²Be(p, t)¹⁰Be(pv) (≈¹⁰Be(p, t)⁸Be(g.s.)). In particular, concerning this last reaction, predictions of σ _abs can change by an order of magnitude depending on whether the halo properties associated with the d _5/2 orbital are treated selfconsistently in calculating the ground state correlations of the (pair removal) mode, or not.     

The quadrupole moment of the neutron-halo nucleus11Li

The quadrupole moment ratio of⁹Li and¹¹Li was measured by a combination of in-beam laser induced nuclear polarization and Β-NMR in LiNbO₃. The result ¦Q(¹¹Li)/Q(⁹Li)¦=1.14(16) is consistent with cluster models describing¹¹Li as composed of a⁹Li core and a far extended halo of two loosely bound neutrons.     

Proton magic even-even isotopes and giant halos of Ca isotopes with relativistic continuum Hartree-Bogoliubov theory

We study the proton magic O, Ca, Ni, Zr, Sn, and Pb isotope chains from the proton drip line to the neutron drip line with the relativistic continuum Hartree-Bogoliubov (RCHB) theory. Particulary, we study in detail the properties of even-even Ca isotopes due to the appearance of giant halos in neutron rich Ca nuclei near the neutron drip line. The RCHB theory is able to reproduce the experimental binding energiesE _b and two neutron separation energiesS _2n very well. The predicted neutron drip line nuclei are²⁸O,⁷²Ca,⁹⁸Ni,¹³⁶Zr,¹⁷⁶Sn, and²⁶⁶Pb. Halo and giant halo properties predicted in Ca isotopes withA>60 are investigated in detail through analysis of two neutron separation energies, nucleon density distributions, single particle energy levels, and the occupation probabilities of energy levels including continuum states. The spin-orbit splitting and the diffuseness of nuclear potential in these Ca isotopes, as well as the neighboring lighter isotopes in the drip line Ca region and find certain possibilities of giant halo nuclei in the Ne−Na−Mg drip line nuclei are also studied.     

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     

Relativistic mean-field study on proton skins and proton halos in exotic nuclei

We investigate the ground state properties of proton-rich nuclei in the framework of the relativistic mean-field model. Calculations show that the experimental proton halo in the nuclei ^26,27,28P can be reproduced by the model. The proton halos can appear in proton-rich nuclei because the total nuclear potential is attractive up to the radial distance r ≈ 5.5 fm. But the size of proton halos is finite due to the limitation of the Coulomb potential barrier. The mean-square radius of a halo proton is not very sensitive to the separation energy of the last proton in some very proton-rich nuclei due to the effect of the Coulomb barrier. This behavior is different from the case of a neutron halo where the mean-square radius of a halo neutron is inversely proportional to the separation energy of the last halo neutron. We have also analysed the differences of the relativistic mean-field potentials of ²⁵Al and ²⁶P and found that the isovector potential from the p meson has an important effect on the differences.     

Neutron-neutron correlation approach for 11Li halo structure investigation

The preemission of neutrons from ¹¹Li halo nuclei is considered. The present problems of investigation of ¹¹Li halo nucleus structure by means of the C _nn correlation function are briefly presented. The influence of the target screening on the halo neutron preemission is described. It is shown that, owing to the diminishing of the screening effect, the yield of preemission neutron pairs is expected to be much larger in the case of ¹²C than in the case of Si target. It is shown that a new experiment on a ¹²C target will allow one to solve the standing problems of C _nn and to test experimentally a recent new theory of C _nn. The text was submitted by the authors in English.     

Study of the Isospin Mixing in 6Li with α + p + n Three-Body Model

We calculate the isospin mixing probabilities for both T = 0 and T = 1 states of ⁶Li systematically, and compare them to clarify the relation between the structure of ⁶Li and the isospin mixing probabilities. As a result, the effect of halo structure on the isospin mixing cannot be seen clearly. The effect of the coupling to the continuum states such as of ⁵He + p and ⁵Li + n is suggested.     

Three-body continuum structure and response functions of halo nuclei (I): 6He

Three-body scattering states of the Borromean two-neutron halo nuclei are explored in a core + n + n model using the method of hyperspherical harmonics. We analyse the continuum structure (the properties of the continuum wave functions) separately from the continuum response (the magnitudes of one-step transitions from the ground state to the continuum). Predictions are made for the positions and strengths of the isoscalar monopole, electric dipole and quadrupole excitations, as well as for nuclear inelastic and charge-exchange response functions, for the ⁶He nucleus. The known 2⁺ resonance in ⁶He is reproduced. We find 1⁻ strength concentrations at lower energies in the proximity of the three-body threshold, and predict new 2⁺, 1⁺ (and possibly 0⁺) resonances at slightly higher energies in ⁶He.     

Structure of the neutron periphery of isotopes 9,11Li

The spatial periphery structure of lithium isotopes with A = 9 and 11 is investigated using the (t, p) reaction for ^7,9Li nuclei. It is shown that the neutron halo is almost absent in the ⁹Li nucleus, while the ¹¹Li nucleus has the Borromean halo structure formed by two neutrons relative to the ⁹Li core, which manifests itself in both the cigar and the dineutron configurations.     

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.     

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.     

Spatial periphery of lithium isotopes

The spatial structure of lithium isotopes is studied with the aid of the charge-exchange and (t, p) reactions on lithium nuclei. It is shown that an excited isobaric-analog state of ⁶Li (0⁺, 3.56MeV) has a halo structure formed by a proton and a neutron, that, in the ⁹Li nucleus, there is virtually no neutron halo, and that ¹¹Li is a Borromean nucleus formed by a ⁹Li core and a two-neutron halo manifesting itself in cigar-like and dineutron configurations.     

Inclusion of the Δ resonance in the optical potential between two nuclei and its application to medium energy12C-12C scattering

An energy dependent complex optical potential between two nuclei is calculated from the potential energy density for two colliding nuclear matters generated by solving the Bethe-Goldstone equation in whichNΔ and ΔΔ channels are explicitly coupled to theNN channel. By adding the contributions from the third and fourth order ring diagrams and the relativistic correction to the calculated potential energy density, the saturation property of a nuclear matter is reasonably well reproduced. This is used together with the kinetic energy density to calculate the optical potential for the¹²C+¹²C system in the energy density formalism with the local density approximation. The surface correction term and the symmetry energy term in the energy density functional are determined to reproduce the observed binding energy and the rms radius of¹²C. Using this potential, the differential cross sections for elastic¹²C-¹²C scattering atE _lab=1440 and 2400 MeV are calculated and compared with recent experimental data.     

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.