Two-body and three-body halo nuclei

We have extracted the nuclear asymptotic normalization coefficients (ANC) for the virtual transitions B→A+N via some transfer reactions and the radioactive nuclear beam experiments. With these coefficients, root-mean-square (rms) radii for the valence particle in some possible halo nuclei have been calculated. The values of rms radii extracted with ANC approach are nearly model-independent, hence are a good quantity for the investigation of nuclear halo. In addition, we have also calculated the rms radii for the two valence neutrons in some three-body systems in terms of the relationship between the radii of valence particle, core nucleus and nuclear matter. With two conditions for nuclear halo formation, we have examined these extracted rms radii. The results show that 11Be(1/2+, g.s), 12B(1-, 2.621 MeV), 13C(1/2+, 3.089 MeV), 14C(0-, 6.903 MeV), 14C(1-, 6.094 MeV), 15C(1/2+, g.s) and 19C(1/2+, g.s) with the valence particle in the 2s ground or excited state are the neutron halo nuclei, whereas 17F(1/2+, 0.495 MeV) and 21Na(1/2+, 2.423 MeV) are the proton halo nuclei in the excited state. For three-body systems, except the well-established two-neutron halo nuclei 6He and 11Li, 14Be and 17B might be the two-neutron halo nuclei as well.     

同位旋效应对F同位素s-d能级间隙的影响

在单粒子势模型的框架下, 计算了O同位素和F同位素的基态和某些低激发态的能级值、均方根半径值及密度分布。通过在伍兹 萨克逊势中引入同位旋依赖项, 研究了同位旋效应对F同位素s-d能级间隙的影响。理论计算得到的均方根半径值和自旋宇称值与实验结果一致。尤其是, 理论计算能够实现16F, 15F和14F中2s_1/2与1d_5/2质子能级间的反转, 且F同位素中s-d质子能级间隙及其整体变化趋势与已知实验结果符合较好。此外, 理论结果表明17F的(1/2)+第一激发态为单质子晕态。 The level structures of O and F isotopes are investigated in the framework of the single particle potential model. The isospin effect on the s d level spacing in F isotopes is studied by introducing an isospin dependent term in the depth of the Woods Saxon potential. The theoretical results of RMS radii and spin parity values are in agreement with the experimental data. In particular, the level inversion between proton levels of 2s_1/2 and 1d_5/2 in 16F, 15F and 14F is reproduced. The global tendency of the s-d level spacing agrees with the observed fact. In addition, the study confirms the one proton halo structure in 17F(2s_1/2).     

晕核~（11）Li，~（14）Be和~（17）B的进一步研究

在三体模型的基础上，采用汤川作用势，进行变分计算，进一步研究了晕核１１Ｌｉ，１４Ｂｅ和１７Ｂ的基态性质，给出了晕中子密度分布的一个解析表达式．理论计算结果与最新的实验数据一致．     

Study of the structure of borromean nucleus 17Ne

The 17Ne nucleus is a possible candidate with a two-proton borromean halo structure. Since the theoretical model is difficult to handle the three-body system, it is difficult to determine the two-proton halo structure in 17Ne. In the present research, we try to study the breakup reaction of 17Ne. For the Borromean nuclei, one-proton knockout results in an unstable nucleus which is decaying further by proton emission. This process will result in an angular correlation between the direction of the aligned recoiling unstable nucleus and its decay products. The angular correlations can give us information about the configuration of the valence proton in the 17Ne. Furthermore, theoretical calculations indicate that the momentum distributions of 16F c.m are sensitive to the structure of the halo in 17Ne. Thus the measurement of momentum distributions of 16F c.m may also give us conclusive information on the structure of 17Ne. The present experiment has been done at IMP in Lanzhou using the radioactive beam 17Ne at 30.8 MeV/u on a 43mg/cm2 12C target. The data analysis is under procedure and the primary results are provided.     

The properties of halo structure for 17B

The total reaction cross section (1724 ± 93 mb) of ¹⁷B at the energy of 43.7 A MeV on C target has been measured by using the transmission method at the Radioactive Ion Beam Line in Lanzhou (RIBLL). Assuming ¹⁷B consists of a core ¹⁵B plus two halo neutrons, the total cross section of ¹⁷B on C target was calculated with the zero-range Glauber model, where double Gaussian density distributions and Gaussian plus HO density distributions were used. It can fit the experimental data very well. The characteristic of halo structure for ¹⁷B was found with a large diffusion of the neutrons density distribution. Supported by the National Natural Science Foundation of China (Grant Nos. 10475098, 10605033 and 10221003), the Chinese Academy of Sciences (Grant Nos. CXTD-J2005-1 and KJCX2-SW-N18), and Hundred Talent Project of CAS (Grant No. 0501080BR0)     

用电子散射研究丰质子核的质子晕结构

理论和实验结果都表明¹⁷F的第一激发态有质子晕存在.用相对论平均场理论和Eikonal近似研究了质子晕核¹⁷F的第一激发态的电子弹性散射过程. 计算了¹⁷F的第一激发态的电荷形状因子,并与¹⁶O和¹⁹F的结果进行了对比和讨论.结果显示质子晕的存在会使中等转移动量的电荷形状因子产生明显的变化,并且使低转移动量的电荷形状因子趋于降低.这说明电子散射对质子晕的存在是非常敏感的,表明可以用电子散射对奇特核的质子晕结构进行更精细的研究.     

Uncertainty evaluation of the isotope shift factors for 2s2p~(3,1)P_1~o–2s~2 ~1S_0 transitions in B Ⅱ

Accurate isotope shift factors of the 2s2p~(3,1)P_1~o–2s~2 ~1S_0 transitions in B II, obtained with the multi-configuration Dirac–Hartree–Fock and the relativistic configuration interaction methods, are reported. We found a linear correlation relation between the mass shift factors and the energies for the transitions concerned, considering all-order electron correlations. This relation is important for estimating the uncertainty in the calculation of isotope shift factors. These atomic data can be used to extract the nuclear mean-square charge radii of the boron isotopes with halo structures or to resolve the high precise spectroscopy of B II in astronomical observation.     

Nuclear structure studies on halo nuclei by direct reactions with radioactive beams

The investigation of direct reactions with exotic beams in inverse kinematics gives access to a wide field of nuclear structure studies in the region far off stability. The basic concept and the methods involved are briefly discussed. The present contribution will focus on the investigation of light neutron-rich halo nuclei. Such nuclei reveal a new type of nuclear structure, namely an extended neutron distribution surrounding a nuclear core. An overview on this phenomenon, and on the various methods which gave first evidence and qualitative confirmation of our present picture of halo nuclei, is given. To obtain more quantitative information on the radial shape of halo nuclei, elastic proton scattering on neutron-rich light nuclei at intermediate energies was recently investigated for the first time. This method is demonstrated to be an effective means for studying the nuclear matter distributions of such nuclei. The results on the nuclear matter radii of ⁶He and ⁸He, the deduced nuclear matter density distributions, and the significance of the data on the halo structure is discussed. The present data allow also a sensitive test of theoretical model calculations on the structure of neutron-rich helium isotopes. A few examples are presented. The investigation of few-nucleon transfer reactions in inverse kinematics may provide new and complementary information on nuclear structure, as well as astrophysical questions. The physics motivation and the experimental concept for such experiments, to be performed due to momentum matching reasons at low incident energies around 5–20 MeV/u at the new generation low energy radioactive beam facilities SPIRAL, PIAFE, etc., is briefly discussed.     

Neutron halos in the excited states for N=127 isotones

Properties of the ground states and the excited states of N=127 isotones are investigated by using the nonlinear relativistic mean field theory with the interactions PK1. By analyzing the rms of proton and neutron, the single particle energies of valence nucleon and the density distributions of neutron, proton and the last neutron, it can be found that there exists a neutron halo in the excited states of 3d5/2, 4s1/2 and 3d3/2 in 209Pb. It is also predicted that there exists a neutron halo in the excited states of 3d5/2, 4s1/2 and 3d3/2 in 207Hg, 208Tl, 210Bi and 211Po.     

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。     

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.     

基于不稳定核基本性质测量的原子核结构研究

精密激光谱学是通过测量核素原子光谱的超精细结构和同位素移位来研究原子核的基本性质,为原子核自旋、磁矩、电四极矩及电荷均方根半径的确定提供了一种模型独立的测量方式。这些原子核基本性质的测量,能够比较精确地描述原子核微观结构的演化。近年来,随着放射性束流装置的发展,产生远离β-稳定线的丰中子/丰质子核素成为可能,也进一步促进了高分辨和高灵敏度的激光谱技术更加广泛的应用。简单介绍了基于放射性核素超精细结构的激光谱学测量原理,并通过几个经典实例来回顾近年来激光谱学在原子核奇特结构研究领域的独特贡献。主要通过分析几个重要核区原子核的基本性质,结合大尺度壳模型、ab initio理论、密度泛函理论等,来探索丰中子核中展现出来的一些新的奇特现象,如晕结构、幻数演化、形状共存等。High-precision laser spectroscopy technique is used to determine the ground state properties of exotic nuclei by probing its electronic hyperfine structure and isotope shift. It provides a model-independent measurement of nuclear spin, magnetic moment, electric quadrupole moment and charge radii. These nuclear parameters can be used to investigate the nuclear structure evolution and the nuclear shapes. With the development of accelerators and isotope separators, exotic isotopes far from β stability became accessible experimentally, which enhanced the capability of the laser spectroscopy technique being applied in the field of nuclear physics. A brief introduction to experimental principle is given, followed by a review of several typical examples for the experimental investigations in the different regions of nuclear chart. This aims to demonstrate the contributions of ground state properties measurement by using laser spectroscopy technique to the nuclear structure study of exotic isotopes. This discussion involves several different nuclear theory models in order to interpret the exotic phenomena observed in the neutron-rich isotopes, such as halo structure, shell evolution, shape coexistence and so on.     

Neutron halos in the excited states for N=127 isotones

Properties of the ground states and the excited states of N=127 isotones are investigated by using the nonlinear relativistic mean field theory with the interactions PK1. By analyzing the rms of proton and neutron, the single particle energies of valence nucleon and the density distributions of neutron, proton and the last neutron, it can be found that there exists a neutron halo in the excited states of 3d5/2, 4s1/2 and 3d3/2 in ²⁰⁹Pb. It is also predicted that there exists a neutron halo in the excited states of 3d5/2, 4s1/2 and 3d3/2 in ²⁰⁷Hg, ²⁰⁸Tl, ²¹⁰Bi and ²¹¹Po.     

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.     

Momentum Distribution of a Fragment and Nucleon Removal Cross Section in the Reaction of Halo Nuclei

Recently the research on the halo structure of drip-line nuclei has shown some interesting properties of the existence of one or more halo nucleons. In the framework of few-body Glauber model, the momentum distribution of a fragment and nucleon removal cross section in the reaction of halo nuclei is presented and extended to nuclei having more than one halo nucleons. The reaction mechanism is treated with and without taking account of the final-state interaction. The wave function of removal halo nucleons in the continuum state is modified by imposing an orthogonal condition to the bound state. An analytical expression of the longitudinal momentum distribution of the fragment is derived when the bound state wave function of halo nucleons is taken as a Gaussian-type function. This is useful in the further investigation on the structure of halo nuclei.     

Skyrme-Hartree-Fock approach to the change of level occupancy of low mass halo nuclei

With a new parameterization of potential parameters which reproduces the ground state properties of shell closed nuclei fairly accurately, the role of occupancy of 2s _1/2 level in determining the halo structures of ¹⁷O, ¹⁶N, ¹⁵C, ¹⁴B, ¹³Be have been investigated. The results show interesting cross over of level occupancies which may explain the increase in interaction radii.     

Momentum Distribution of a Fragment and Nucleon Removal Cross Section in the Reaction of Halo Nuclei

Recently the research on the halo structure of drip-line nuclei has shown some interesting properties of the existence of one or more halo nucleons. In the framework of few-body Glauber model, the momentum distribution of a fragment and nucleon removal cross section in the reaction of halo nuclei is presented and extended to nuclei having more than one halo nucleons. The reaction mechanism is treated with and without taking account of the final-state interaction. The wave function of removal halo nucleons in the continuum state is modified by imposing an orthogonal condition to the bound state. An analytical expression of the longitudinal momentum distribution of the fragment is derived when the bound state wave function of halo nucleons is taken as a Gaussian-type function. This is useful in the further investigation on the structure of halo nuclei.     

镜像核13N-13C 和15N-15O中的激发态晕或皮(英文)

用非线性相对论平均场对两对镜像核13N-13C 和15N-15O进行了研究. 发现无论在基态还是激发态， 用两套参数所得的结合能都跟实验值很接近. 计算结果显示13N的第一激发态（2s1/2）和第三激发态（1d5/2）各存在一个非束缚的质子晕， 而13C的第三激发态（1d5/2）存在一个弱束缚的中子皮. 另外研究表明, 在另一对镜像核15N-15O的第二激发态（2s1/2）和第一激发态（2s1/2）分别存在一个中子晕和质子皮. Properties of two pairs of mirror nuclei 13N-13C and15N-15O are investigated by using the nonlinear relativistic mean field theory. It is found that all the calculated binding energies with two different parameter sets are very close to the experimental ones for both the ground states and the excited states. The calculations show that the first excited state (2s1/2) and the third excited state (1d5/2) in 13N are both unbound resonances with proton halo structure, whereas the third excited state (1d5/2) in 13C is weakly bound with a neutron skin. It is also predicted that there has a proton halo in the second excited state (2s1/2) of 15N as well as a neutron skin in the first excited state (2s1/2) of 15O.     

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.     

Big deformation in ~(17)C

Reaction and interaction cross sections of ¹⁷C on a carbon target have been re-analyzed using the modified Glauber model. The analysis with a deformed Woods-Saxon density/potential suggests a big deformation structure for ¹⁷C. The existence of a tail in the density distribution supports the possibility of it being a one-neutron halo structure. Under a deformed core plus a single-particle assumption, analysis shows a dominant d-wave of the valence neutron in ¹⁷C.