Halo structure of (14)Be

The two-neutron halo nucleus (14)Be has been investigated in a kinematically complete measurement of the fragments ((12)Be and neutrons) produced in dissociation at 35 MeV/nucleon on C and Pb targets. Two-neutron removal cross sections, neutron angular distributions, and invariant mass spectra were measured, and the contributions from electromagnetic dissociation (EMD) were deduced. Comparison with three-body model calculations suggests that the halo wave function contains a large nu(2s(1/2))(2) admixture. The EMD invariant mass spectrum exhibited enhanced strength near threshold consistent with a nonresonant soft-dipole excitation.     

Properties of proton-rich nuclei in a three-body model

Using a three-body model and realistic two-body potentials, we investigate the properties of the nuclei ¹⁸Ne and ²⁸S near the proton dripline. We figure out the two-proton separation energies, occupation of the valence protons, root-mean-square radii of matter and the valence protons. Besides, the spatial correlation densities are displayed to reflect the correlation between the two valence protons. The first excited 0⁺ state of ¹⁸Ne is most likely to be a halo state according to our calculation. Turning off the Coulomb interactions among the three-body systems, we get the two-neutron separation energies and configuration of the valence neutrons of their corresponding mirror nuclei. The results indicate that the three-body model is proper to describe some proton-rich nuclei and can be used to deduce reliable information.     

Influence of experimental conditions on the spectroscopy investigation of~(14)Be by Coulomb breakup reaction

The two-body(core+2n) cluster structure was implemented to describe the two-neutron halo nucleus~(14 )Be, where the core12 Be was assumed inert and at a ground state and the dineutron was assumed at a pure 2S0 state. Based on such a structure the three-body continuum-discretized coupled-channel(CDCC) calculation was successfully used to deal with the~(14) Be breakup reactions of~(14)Be+Pb at 35 Me V/u. Consequently, we modeled the kinematically complete measurement experiment of this reaction with the help of Geant4. With the simulation data the relative energy spectrum was constructed by the invariant mass method and B(E1) spectrum was extracted using the virtual photon model. The influence of the target thickness and detector performance on the energy spectroscopy was investigated.     

Observation of strong low-lying E1 strength in the two-neutron halo nucleus 11Li

An exclusive measurement has been made of the Coulomb dissociation of the two-neutron halo nucleus 11Li at 70 MeV/nucleon at RIKEN. Strong low-energy (soft) E1 excitation is observed, peaked at about Ex = 0.6 MeV with B(E1) = 1.42(18) e2fm2 for Erel < or = 3 MeV, which was largely missed in previous measurements. This excitation represents the strongest E1 transition ever observed at such low excitation energies. The spectrum is reproduced well by a three-body model with a strong two-neutron correlation, which is further supported by the E1 non-energy-weighted cluster sum rule.     

Universal properties and structure of halo nuclei

The universal properties and structure of halo nuclei composed of two neutrons (2n) and a core are investigated within an effective quantum mechanics framework. We construct an effective interaction potential that exploits the separation of scales in halo nuclei and treat the nucleus as an effective three-body system. The uncertainty from higher orders in the expansion is quantified through theoretical error bands. First, we investigate the possibility to observe excited Efimov states in 2n halo nuclei. Based on the experimental data, ²⁰C is the only halo nucleus candidate to possibly have an Efimov excited state, with an energy less than 7 keV below the scattering threshold. Second, we study the structure of ²⁰C and other 2n halo nuclei. In particular, we calculate their matter form factors, radii, and two-neutron opening angles.     

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.     

Study of the structure of neutron halo using neutron transfer reaction

To estimate the probability of two-neutron configurations in halo nuclei, we propose an experimental method of studying neutron-neutron correlations at periphery of such nuclei by measuring two-neutron transfer reaction. The experimental study of ⁶He + A ↦ ⁴He + B for various targets is performed using ⁶He beam of Flerov Laboratory of Nuclear Reactions (JINR, Dubna) at energy of about 15 MeV/u and technique of nuclear photoemulsions. Searching for events of two-nucleon transfer reaction and their processing is performed using the PAVICOM-setup at P.N. Lebedev Physical Institute.     

Effective Field Theory and the Gamow Shell Model

We combine halo/cluster effective field theory (H/CEFT) and the Gamow shell model (GSM) to describe the 0⁺ ground state of ⁶He as a three-body halo system. We use two-body interactions for the neutron-alpha particle and two-neutron pairs obtained from H/CEFT at leading order, with parameters determined from scattering in the p_3/2 and s₀ channels, respectively. The three-body dynamics of the system is solved using the GSM formalism, where the continuum states are incorporated in the shell model valence space. We find that in the absence of three-body forces the system collapses, since the binding energy of the ground state diverges as cutoffs are increased. We show that addition at leading order of a three-body force with a single parameter is sufficient for proper renormalization and to fix the binding energy to its experimental value.     

晕核的标度定律

利用重叠函数的渐近归一化常数(ANC)计算了一系列核的价核子处于核外的几率及价核子密度分布的均方根半径〈r2〉1/2. 由于实验上抽取的核ANC近似与模型参数无关,因此由核ANC计算的核外几率和均方根半径是考察晕核的可靠且有效的观察量. 依价核子处于核外的几率大于50%为条件， 证实了一些核为晕核， 且给出了比较宽松的晕核出现的条件. 此外， 还用〈r2〉/R2≥1.5及〈r2〉1/2/rc≥2.0为判据考察了一系列晕核候选者. 最后， 利用r2算符在有限方势阱中的预期值给出了晕核的标度定律. We have extracted the probability for a valence particle being out the binding potential, as well as the root mean square radius of the probability distribution from the measured nuclear asymptotic normalization coefficients. According to the criterion of nuclear halo, i.e., the valence particle has larger than 50% probability being out of the nuclear binding potential, a number of halo nuclei have been confirmed. Based on these results, we have obtained a very relaxed condition for nuclear halo formation. In addition, a number of nuclear halo candidates have been analyzed with the criteria of 〈r2〉/R2≥1.5 and 〈r2〉1/2/rc≥2.0. Furthermore, we present the scaling laws for the dimensionless quantity 〈r2〉/R2 of the nuclear halo in terms of an analytical expressions of the expectation value for the operator r2 in a finite square well potential.     

Momentum distribution of 15B fragments from the breakup of 17B

The two-neutron removal cross section (sigma(-2n)) and the longitudinal momentum distribution of 15B fragments from the breakup of 17B on 9Be were measured at 70A MeV. The distribution in the projectile rest frame is characterized by a FWHM of 80+/-10 MeV/c for 15B. The sigma(-2n) is found to be 0.22+/-0.05 b. A Glauber-type analysis of the data provides clear evidence of a two-neutron halo structure in 17B.     

New method for solution of coupled radial Schrödinger equations: application to the Borromean two-neutron halo nucleus 22C

A generalized Prüfer transformation within the framework of the modified variable phase method has been used for numerical solution of coupled radial Schrödinger equations at negative energies. The method has been applied to calculations of the Borromean two-neutron halo nucleus ²²C, for which an unusually large value of the matter radius has recently been extracted from measured reaction cross sections. The giant size can only be explained by an extremely loose binding that is, however, not yet known experimentally. Within the three-body cluster model we have explored the sensitivity of the ²²C matter and charge radii and soft dipole mode excitations to the two-neutron separation energy.     

推广的Glauber理论及其在晕核散射中的应用

介绍了推广到晕核散射的Glauber理论,并用其研究晕核¹⁴Be的散射问题.弹核的密度分布分别采用谐振子密度分布和相对论平均场理论计算得到具有两个晕中子结构的密度分布,对晕核模型的多重积分采用蒙特卡洛数值积分方法.计算了不同能量下¹⁴Be,¹²Be与靶核¹²C散射的反应截面,并与实验结果进行比较,¹⁴Be的两个中子采用具有晕中子密度分布的理论计算与实验符合较好,而采用不具有晕中子密度分布的结果与实验值相差较大.     

晕核反应总截面和密度分布

利用考虑了量子修正、库仑修正、核子–核子碰撞同位旋效应和假定有效原子核密度分布后得到的改进的Glauber理论,计算了晕核与稳定核反应总截面,研究了晕核结构对反应总截面的影响.结果发现对于¹¹Be,¹⁴Be和¹¹Li等入射核,必须考虑它们的晕核结构和利用自由的核子–核子碰撞截面才能得到与实验符合的反应截面,并可依据反应总截面来确定晕核的密度分布和均方半径等信息.     

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.     

Break-up of neutron-halo nuclei by diffraction dissociation and shakeoff

The interplay of diffraction dissociation and nuclear shakeoff is considered in a schematic but still realistic model for the case of the break-up of halo nuclei on light targets. We demonstrate that the shakeoff effect, arising from the momentum imparted by the core diffraction, is small but still identifiable in the experimental data for the dissociation of the one- and two-neutron halo nuclei ¹¹Be and ¹¹Li. Received: 29 October 1999 / Revised version: 15 January 2000     

恒星能量下核子俘获反应率的晕核效应

恒星能量下俘获截面很难直接测量。¹⁰Be（n，γ）¹¹Be俘获反应涉及到非均匀宇宙大爆炸核合成，无直接测量实验截面数据。利用转移反应¹⁰Be（d，p）¹¹Be的渐近归一化系数（ANC）方法，计算了¹⁰Be（n，γ）¹¹Be俘获反应截面和反应率。¹¹Be是中子晕核。研究表明，在恒星能量下俘获到晕态的截面和反应率显著增大。     

利用直接核反应研究轻丰中子核的奇特结构

直接核反应(包括弹性散射、非弹性散射、转移反应等)是研究丰中子核奇特结构的常用实验手段之一。以6,8He、11Li、11,12Be、14,15B、15,16C等N=8附近核的结构研究为例，综述了如何利用这几种反应从实验上研究丰中子核的奇特结构。利用6,8He，11Be等晕核在质子和氘靶上的弹性散射数据，拟合得到了这些反应体系的有效相互作用(光学势)。利用16C在质子和氘靶上的非弹性散射数据，抽取了16C 的形变参数，结果表明16C的形变不可忽略。利用单核子转移反应，定量研究了8He, 11,12Be等丰中子核基态及低占据态中的p-，s-，以及d-波成分的强度。结果表明:8He基态中的4个价中子，除了可以构成正常的 (0p_3/2)4 组态外，还有一定的几率构成($ 0 p_{3/2} $)2(0p_1/2)2组态；12Be的基态以d波闯入为主，而其临近的11Be的基态以s波闯入为主。     

Observation of abnormally large radii of nuclei in excited states in the vicinity of neutron thresholds

Differential cross sections for inelastic scattering leading to the excitation of some nuclear states situated near neutron-emission thresholds were analyzed. With the aid of a modified diffraction model, abnormally large radii were found for the 1/2₁⁺ state of the ¹³C nucleus at 3.09 MeV, for the first levels of positive-parity rotational bands in the ⁹Be (1/2⁺ level at 1.68 MeV and 5/2⁺ level at 3.05 MeV) and ¹¹Be (5/2⁺ level at 1.78 MeV and 3/2⁺ level at 3.41 MeV) nuclei, and for the 2₁⁺ state of the ¹⁴Be nucleus at 1.54 MeV and 1₁⁻ state of the ¹²Be nucleus at 2.7 MeV. All of these states possess signatures typical of neutron halos.     

Nuclear charge radius of 8He

The root-mean-square (rms) nuclear charge radius of 8He, the most neutron-rich of all particle-stable nuclei, has been determined for the first time to be 1.93(3) fm. In addition, the rms charge radius of 6He was measured to be 2.068(11) fm, in excellent agreement with a previous result. The significant reduction in charge radius from 6He to 8He is an indication of the change in the correlations of the excess neutrons and is consistent with the 8He neutron halo structure. The experiment was based on laser spectroscopy of individual helium atoms cooled and confined in a magneto-optical trap. Charge radii were extracted from the measured isotope shifts with the help of precision atomic theory calculations.     

Properties of A = 7-9 Drip-Line Nuclei in RMF Theory

The relativistic mean-field （RMF） theory is used to calculate the properties of A =7-9 drip-line nuclei ^7Li, ^7;9Be, ^8;9B, and ^9C. Systematic deviations between experimental and theoretical binding energies are found. Possible reasons of these systematic deviations are discussed in terms of pairing energy. The root-mean-square （rms） radii of matter distributions for these nuclei agree with the experimental data quite well. The one-proton halo structure in ^8B is reproduced well, and the two-proton halo in ^9C is predicted. The calculations show that the RMF theory is valid in studying the properties of light drip-line nuclei.