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).     

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：     

Experimental investigation of highly excited states of the 5,6He and 5,6Li nuclei in the (6Li, 7Be) and (6Li, 7Li) one-nucleon pickup reactions

The (⁶Li, ⁷Be) and (⁶Li, ⁷Li) reactions on ⁶Li and ⁷Li nuclei were investigated in the angular interval 0°–20° in the laboratory system at a ⁶Li energy of 93 MeV. In addition to low-lying states of the ^5,6He and ^5,6Li nuclei, broad structures were observed near the t(³He)+d and t(³He)+t thresholds at the excitation energies of 16.75 (3/2⁺) and ～20 MeV (for ⁵He), 16.66 (3/2⁺) and ～20 MeV (⁵Li), 14.0 and 25 MeV (⁶He), and ～20 MeV (⁶Li). The angular distributions measured in the ⁷Li(⁶Li, ⁷Be)⁶He reaction for transitions to the ground state (0⁺) and excited states at E _x=1.8 MeV (2⁺) and 14.0 MeV of the ⁶He nucleus were analyzed by the finite-range distorted-wave method assuming the 1p-and 1s-proton pickup mechanism. The (⁶Li, ⁷Be) and (⁶Li, ⁷Li) reactions were shown to proceed predominantly through the one-step pickup mechanism, and the broad structures observed at high excitation energies are considered as quasimolecular states of the t(³He)+d and t(³He)+t types.     

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     

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.     

Photodisintegration of Light Nuclei

The first microscopic calculation of inelastic reactions on nuclei with mass number A = 6 is presented. In particular, we consider the total photoabsorption cross section of ⁶He and ⁶Li. It is shown that the halo nucleus ⁶He exhibits two types of dipole resonances, the normal giant dipole resonance and a low-energy soft dipole resonance associated with the excitation of the outer neutrons. Comparing our results with available experimental data we note the role of P-wave interaction. Calculations are performed using the Lorentz integral transform (LIT) method and the effective interaction in the hyperspherical harmonics formalism (EIHH).     

Microscopic analysis of the energy dependence of the 6He, 6Li + 28Si total reaction cross sections in the energy range E = 5−50 A MeV

The experimental data on the total cross sections of the ^{4, 6}He, ^{6, 7}Li + ²⁸Si reactions at energies E=5−50 A MeV are reported. The data for the ⁶Li, ⁶He + ²⁸Si reactions have been analyzed within the microscopic model of double-folding optical potential, in which the real and imaginary parts are calculated at different densities of the projectile nucleus. The cross sections calculated with the microscopic double-folding Coulomb potential and the standard Coulomb potential for uniform charge distribution are compared with each other. Semimicroscopic potentials providing agreement with experimental data have been constructed on the basis of renormalized microscopic potentials and their derivatives, added to take into account collective effects. Original Russian Text ￠ K.V. Lukyanov, E.V. Zemlyanaya, V.K. Lukyanov, I.N. Kukhtina, Yu.E. Penionzhkevich, Yu.G. Sobolev, 2008, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2008, Vol. 72, No. 3, pp. 382–386.     

Effect of cluster polarization on the spectrum of the <Superscript>7</Superscript>Li nucleus and on the reaction <Superscript>6</Superscript>Li(<Emphasis Type="Italic">n</Emphasis>, <Superscript>3</Superscript>H)<Superscript>4</Superscript>He

The effect of polarization of the ⁶Li and ³H clusters on the parameters of states of the ⁷Li nucleus and on the cross section for the reaction ⁶Li(n,³H)⁴He was studied. The ⁴He + d + n three-cluster configuration was invoked for this purpose, and cluster dynamics was determined within a microscopic model where the relative motion of the clusters was described in terms of Faddeev amplitudes. The ⁴He + d + n three-cluster configuration made it possible to consider the ⁴He + ³H and ⁶Li + n binary channels, which are dominant in ⁷Li, and to take simultaneously into account the cluster polarization of ⁶Li as a two-cluster subsystemin the ⁴He + d representation and the cluster polarization of ³Has a two-cluster subsystem in the d + n representation.     

First measurement of the 2H(6He,7Li)n angular distribution and proton spectroscopic factor in 7Li

The angular distribution of the ²H ( ⁶He,⁷Li n reaction was measured with a secondary ⁶He beam of 36.4MeV for the first time. The proton spectroscopic factor of ⁷Li ground state was extracted to be 0.42±0.06 by normalizing the calculational differential cross-sections with the distorted-wave Born approximation to the experimental data. It was discussed that the uncertainty of extracted spectroscopic factors from the one-nucleon transfer reactions induced by deuteron might be reduced by determining the volume integrals of imaginary optical potentials precisely.     

An experimental study of He elastic,inelastic and charge-exchange scattering from Li

A target of ⁶Li was bombarded with the ³He beam from the University of Illinois cyclotron. Differential cross sections for the elastic scattering, the inelastic scattering to the first two excited states of ⁶Li, and the (³He, t) charge-exchange reaction to the ground state of ⁶Be were determined over angular ranges of approximately 20° to 115° (c.m.) at ³He energies of 24.6 MeV and 27.0 MeV. (The weak inelastic transition to the 3.56 MeV state of ⁶Li, ordinarily obscured by a background of three-body break-up, was observed by requiring a coincidence at most angles between the scattered ³He and the ⁶Li recoil.) The ratio of the integrated charge-exchange cross section between 55° and 115° to the integrated inelastic cross section for this transition (both with ΔT = 1) is somewhat less than expected from isospin considerations (i.e., about 1.6 instead of 2.0).     

Elastic scattering of 86 MeV9Li and 55 MeV6He on208Pb

The cross sections of elastically scattered⁹Li and⁶He on²⁰⁸Pb were measured. The scattered particles were detected by an annular CR-39 solid state nuclear track detector and the monitoring was done with a triple telescope of silicon detectors. The classical and optical model analyses of the measured elastic cross sections have been carried out. It was shown that the peripheral⁹Li interaction region has a rather high transparency. Strong dynamical polarization of⁹Li ions in the process of scattering is suggested.     

Microscopic form factor calculations for the quasielastic (6Li, 6He) reactions

We present a simple procedure for calculating microscopic form factors for quasielastic reactions which does not make us of a multipole expansion of the interaction potential. The form factor of the (⁶Li, ⁶He) reactions is studied to reveal its general properties.     

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.     

Consideration on direct reaction mechanisms in the unified microscopic nuclear theory

In the framework of a unified microscopic nuclear theory the starting equations for the discussion of the different phenomenological direct reaction theories are derived. Subsequently in continuation of a previous investigation the⁶Li(p,³He)⁴He reaction as a realistic example is discussed to obtain a better physical insight into the different kinds of reaction mechanisms.     

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.     

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.     

Three-cluster model of radiative capture reactions in seven-nucleon systems. Effects of cluster polarization

We apply the microscopic three-cluster model, developed by the authors recently, to study the effects of cluster polarization on the capture reactions ³He(??, ??)⁷Be, ³H(??, ??)⁷Li, ⁶Li(p, ??)⁷Be, and ⁶Li(n, ??)⁷Li. These reactions are of great importance for astrophysical applications. Thus, the main attention is paid to the cross sections (or the astrophysical S factor) of the reactions in the low-energy region. Correlations between the astrophysical S factor of the reactions at zero energy and different quantities associated with the ground state of a compound nucleus are studied in detail.     

Potential cluster approach to the description of the 7Li + γ ai p6He reactions

Angular distributions for the ⁶He(p, γ_{0 + 1})⁷Li process at the energy E _γ = 40 MeV are calculated within the potential cluster approach. It is shown that the observed cross section is well reproduced when E1 and E2 transitions are taken into account; in this case, unlike the case in the RGM calculations, the dominating mechanism is direct capture to the ground state of the ⁷Li nucleus. Total cross sections for direct photodisintegration ⁷Li (γ, p₀)⁶He in the energy interval E _γ = 22–30 MeV are calculated.     

Electromagnetic properties of 7Li and 7Be in a cluster model

The electromagnetic properties of ⁷Li (⁷Be) are studied by using a microscopic α-t (³He) cluster model. Among the several properties are the Coulomb and magnetic form factors for the ground spin-doublet states of ⁷Li (⁷Be), density distribution radii, static moments and radiative transition probabilities. Provided that the stability conditions for the binding energies are satisfied for both the constituent nuclei α and t (³He), the calculated results are in good agreement with many available data. Several interesting differences are predicted between ⁷Li and ⁷Be.