An analysis of nuclear charge radii based on the empirical formula

Several nuclear charge radii had been calculated based on the law of A^1/3 and isospin dependence Z^1/3 formula which had been used to describe the charge radii data. It is achieved that the isospin dependence Z^1/3 formula is superior to the generally accepted A^1/3 law through mean root square deviation analysis, that is, the Z^1/3 formula is more effective to describe the charge radii data.     

Rotational bands in 169Re

Based on the systematic investigation of the data available for nuclei with A≥ 40, a Z ^1/3-dependence for the nuclear charge radii is shown to be superior to the generally accepted A ^1/3 law. A delicate scattering of data around R _c/Z ^1/3 is inferred as owing to the isospin effect and a linear dependence of R _c/Z ^1/3 on N/Z (or (N - Z)/2) is found. This inference is well supported by the microscopic Relativistic Continuum Hartree-Bogoliubov (RCHB) calculation conducted for the proton magic Ca, Ni, Zr, Sn and Pb isotopes including the exotic nuclei close to the neutron drip line. With the linear isospin dependence provided by the data and RCHB theory, a new isospin-dependent Z ^1/3 formula for the nuclear charge radii is proposed. Received: 23 September 2001 / Accepted: 21 January 2002     

关于原子核电荷半径的研究

结合原子核电荷半径实验数据, 对885个中子数N≥8和质子数Z≥8的核电荷半径做了系统的研究. 对于单参数核电荷半径公式, Z^1/3律公式计算的结果优于A^1/3律的结果, 而对于两参数和三参数公式, Z^1/3律和A^1/3律的结果基本相当. 考虑到壳效应及奇偶摆动现象, 在原有的三参数公式基础上提出了加入Casten因子项和δ项的核电荷半径新公式. 利用该公式计算得到的核电荷半径理论值和实验值符合得非常好, 均方根偏差仅为σ=0.0266 fm, 此值比常用的三参数公式的结果下降了近50%, 理论计算值能更好地反映出壳效应及核电荷半径奇偶摆动的变化趋势.     

Exploring nuclear symmetry energy with isospin dependence in neutron skin thickness of nuclei

We propose an alternative way to constrain the density dependence of the symmetry energy from the neutron skin thickness of nuclei which shows a linear relation to both the isospin asymmetry and the nuclear charge with a form of Z^2/3. The relation of the neutron skin thickness to the nuclear charge and isospin asymmetry is systematically studied with the data from antiprotonic atom measurement, and with the extended Thomas-Fermi approach incorporating the Skyrme energy density functional. An obviously linear relationship between the slope parameter L of the nuclear symmetry energy and the isospin asymmetry dependent parameter of the neutron skin thickness can be found, by adopting 70 Skyrme interactions in the calculations. Combining the available experimental data, the constraint of -20 MeV L 82 MeV on the slope parameter of the symmetry energy is obtained. The Skyrme interactions satisfying the constraint are selected.     

中能重离子碰撞中的同位旋分馏过程

利用同位旋相关的量子分子动力学模型研究了中能重离子碰撞中同位旋分馏过程.研究结果表明自由粒子中质比与碎片中质比的比值即同位旋分馏强度灵敏地依赖于对称势,而对同位旋相关核子–核子碰撞截面的依赖很弱.同位旋分馏对对称势的灵敏主要来自于气相部分,而液相部分对对称势不够灵敏.气相部分灵敏地依赖于对称势是直接造成同位旋分馏强度对对称势灵敏的主要原因.同时还讨论了各种液相部分的取法,其结果表明不同取法对以上结论的影响不大.因此理论结果与实验数据可以直接比较从而提取对称势的知识.并对引发同位旋分馏的动力学的起因进行了分析和讨论.     

Symmetry dependence of rms Charge Radii

The nucleon number dependence of rms charge radii is often approximated by some simple formula containing the mass number only, R(A)=r(A)A^1/3, where r(A) is a slowly varying function of A. However, for nuclei off the stability line, the mass number A=N + Z is not enough to characterise the dependence of the R(Z, N) radius surface on the nucleon numbers Z and N. In the present work, an additional term has been included, depending on the symmetry parameter I=(N ? Z)/A. Several parametrisations were tried, using weighted least-squares procedures for the fit to a present-day data base. The best fit (with χ²/ń=17) was found for R(A, I)=r(A)A^1/3 + b_I/(I ? I_stab), where I_stab=(N_stab ? Z_stab)/A is the value of the symmetry parameter of the stable isobar with mass number A, and b_I=?0.83 fm. The formula R(A, I)=[r(A) + a_I(I ? I_stab)]A^1/3 is only slightly inferior to the previous one, moreover, it is supported by simple model calculations; here a_I=?0.20 fm (χ²/ń=20). The difficulty in determining the right parametrisation is caused by the fact that the surface R_exp(A, I) is not smooth: there are strong shell and deformation effects. To avoid the distorting effect of these deviations on the parameter values, more than half of the original data had to be omitted.     

DIFFUSENESS AND DEFORMATION EFFECT IN NUCLEAR CHARGE RADIUS

On the basis of Yukawa folded density distribution, a new formula of nuclear charge radius is proposed to include the effect of both spheroidal and tetroidal deformation. With the values of only two constants, the resulting root-mean-square error in calculated nuclear radii of 148 nuclides is 0.034 fm, which is near to that of Droplet model. It can be used to explain the nuclear radii of some isotopic sequences where the Z^1/3 law has difficulties. Taking the fluctuation of diffuseness width into account, the peculiar behaviors of some isotopic sequences can be well explained. The dependence of all the fluctuation on the neutron shell structure is also discussed.     

Isospin dependence of proton and neutron radii within relativistic mean field theory

The proton and neutron radii of even-even β-stable nuclei with A ⩾ 40 and a few chains of isotopes with Z = 50, 56, 82, 94 protons and isotones with N = 50, 82, 126 neutrons are analyzed. The average isospin dependence of the radii evaluated within the relativistic mean field theory is studied. A simple, phenomenological formula for neutron radii is proposed.     

Improved Z^1/3 Law of Nuclear Charge Radius

An improved Z^1/3 law of nuclear charge radius is presented. The comparison between the calculated and experimental nuclear charge radii now available shows that this new formula is better than the other conventional formulae.     

中能重离子碰撞中同位旋分馏的同位旋效应

基于改进的同位旋相关量子分子动力学模型,研究了中能重离子碰撞中同位旋分馏强度(N/Z)_气(N/Z)_液随着碰撞系统中子–质子比和碰撞参数的变化所呈现出的同位旋效应,得到了一些有兴趣的结果.如在碰撞系统质量、入射能量和碰撞参数固定的条件下,(N/Z)_气(N/Z)_液随碰撞系统中子–质子比的增加而增加.对于丰中子系统而言,(N/Z)_气(N/Z)_液灵敏地依赖于对称势而较弱地依赖于核子–核子碰撞截面;而缺中子系统,(N/Z)_气(N/Z)_液对于对称势和介质中核子–核子碰撞截面都不灵敏.对于造成这种现象的物理机制进行了分析和讨论.一般核反应中,碰撞参数是各种物理观测量的灵敏函数,但计算结果表明同位旋分馏强度对于碰撞参数并不灵敏,故对于丰中子系统而言,同位旋分馏强度是提取对称势知识的灵敏物理观测量.     

Universal charge-radius relation for subatomic and astrophysical compact objects

Electron-positron pair creation in supercritical electric fields limits the net charge of any static, spherical object, such as superheavy nuclei, strangelets, and Q balls, or compact stars like neutron stars, quark stars, and black holes. For radii between 4 x 10(2) and 10(4) fm the upper bound on the net charge is given by the universal relation Z=0.71R(fm), and for larger radii (measured in femtometers or kilometers) Z=7 x 10(-5)R_(2)(fm)=7 x 10(31)R_(2)(km). For objects with nuclear density the relation corresponds to Z approximately 0.7A(1/3)( (10(8)10(12)), where A is the baryon number. For some systems this universal upper bound improves existing charge limits in the literature.     

原子核基态性质的系统研究

在Skyrme-Hartree-Fock-Bogoliubov（SHFB）理论框架下,利用SkOP1,SkOP2,SKC和SKD 4套新的Skyrme相互作用参数系统地研究了Ca,Ni,Sn和Pb同位素链上原子核的结合能、电荷半径等基态性质,并重点讨论了丰中子Ca核的新中子幻数以及Pb的同位素位移现象。通过与实验数据和SLy5相互作用参数的结果对比,发现这4套相互作用参数都能很好地再现结合能的实验数据,其预言精度比SLy5要高。对于丰中子Ca核,只有SKC和SKD相互作用参数能够再现N=28处的壳效应,而对于实验上发现的新幻数N=32和34,所有的相互作用参数均不能再现这一结果。对于电荷半径,发现所有的相互作用参数均不能很好地预言Ca同位素链电荷半径的演化规律以及Pb的同位素位移现象。另外,还将这些相互作用参数推广至远离β稳定线原子核的单粒子能级结构研究,发现其不适用于描述其随同位旋的演化行为。因此,为了更好地描述远离β稳定线原子核的宏观性质及单粒子能级,建议在拟合Skyrme相互作用参数时,除自旋-轨道耦合项包括合理的同位旋依赖外,还要考虑张量力成分。The nuclear ground state properties of Ca, Ni, Sn and Pb isotopes, such as the binding energies, the charge radii, are studied systematically by 4 sets of new Skyrme parametrizations SKC, SKD, SkOP1 and SkOP2 in the framework of the Skyrme-Hartree-Fock-Bogoliubov (SHFB) method. The new magic numbers of neutronrich Ca isotopes and the isotopic shift of Pb isotopes are discussed emphatically. By the comparisons between the calculations and the experimental data and results from the SLy5 interaction parametrization, it is found that the experimental binding energies can be reproduced accurately by all parametrizations. The calculated accuracies of SKC, SKD SkOP1 and SkOP2 parametrizations are higher than the ones of SLy5 parametrization. For the neutron-rich Ca nuclei, the shell effect of N=28 can be reproduced by the SKC and SKD parametrizations, but the magic numbers at N=32 and 34 are not found by the calculations of all the parametrizations. For the charge radii, the experimental evolution tendency of Ca isotopes and isotopic shift of Pb isotopes can not be reproduced by all the parametrizations. In addition, all Skyrme parametrizations are extended to study the structure of the nuclei far from the β stability line, it is shown that the single-particle energy evolutions with the isospin are not suitable for being studied by these parametrizations. Thus the tensor force component should be considered besides the isospin dependence in spin-orbit coupling term when the Skyrme interaction parametrizations are fitted.     

Isospin Effects in the Isospin Fractionation Process in Intermediate Energy HeavyIon Collisions

Based on the isospin dependent quantum molecular dynamics model we investigated the isospin effects of isospin fractionation (N/Z)_gas/(N/Z)_liq from the neutron-proton ratio of colliding system and impact parameter. Here (N/Z)_gasand (N/Z)_liq is the neutron-proton ratio of nucleon emission for gas phase and that of fragment emission for liquid phase, respectively. Our results show that the (N/Z)_gas/(N/Z)_liq increases with the neutron-proton ratio of colliding systems when the system mass, incident energy and impact parameters are fixed. For the neutron-rich systems, the (N/Z)_gas/(N/Z)_liq depends sensitively to the form of symmetry potential and weakly on the isospin effect of the in-medium nucleon-nucleon cross section; For the neutron-poor colliding system, however, the (N/Z)_gas/(N/Z)_liq is not sensitive to both the form of symmetry potential and the isospin effect of the in-medium nucleon-nucleon cross section. We also found that the dependence of (N/Z)_gas/(N/Z)_liq on the impact parameter is not obvious. Detailed discussion and explanation for leading to these results are presented in the paper. According to these results, we propose that (N/Z)_gas/(N/Z)_liq can be directly compared with the experimental data to get the information about symmetry potential.     

Measurement of interaction cross sections using isotope beams of Be and B and isospin dependence of the nuclear radii

Interaction radii for ^11,12,14Be and ^{8,12,13,14,15}B have been determined by the measurement of interaction cross sections at 790 MeV/nucleon. Effective root-mean-square (RMS) radii of nucleon distribution of these nuclei have been deduced using a Glauber-model calculation. Isospin dependence of nuclear radii are presented for isobars of mass numbers from 6 to 12, and compared with theoretical predictions by the droplet model and by a Hartree-Fock (HF) model. The HF model with the Skyrme-III potential, which includes a strong density-dependent force, reproduce the observed isospin dependence.     

Three-Body Force Effects on EOS of Asymmetric Nuclear Matter and Proton Fraction in Neutron Star Matter

The three-body force effects on the equation of state and its iso-spin dependence of asymmetric nuclearmatter and on the proton fraction in neutron star matter have been investigated within Brueckner-Hartree-Fock approachby using a microscopic three-body force. It is shown that, even in the presence of the three-body force, the empiricalparabolic law of the energy per nucleon vs. isospin asymmetry β＝ ( N - Z) /A is fulfilled in the whole asymmetry range0≤β≤1 and also up to high density. The three-body force provides a strong enhancement of symmetry energy at highdensity in agreement with relativistic approaches. It also shows that the three-body force leads to a much more rapidincreasing of symmetry energy with density in relatively high density region and to a much lower threshold density forthe direct URCA process to occur in a neutron star as compared to the predictions adopting only pure two-body force.     

轻粒子产额及其关联的同位旋效应

用晶格气体模型系统地研究了热发射体的粒子发射特性,阐述了发射体系的同位旋对轻系统的中子、带电粒子和轻粒子产额,以及对轻粒子产额比和双产额同位素比的影响.发现轻粒子产额和产额比是复合系统同位旋的敏感观测量,而双产额同位素比几乎不依赖于体系的同位旋.     

中能重离子碰撞中的同位旋效应

利用改进的量子分子动力学模型,研究了中心和擦边重离子反应中的同位旋效应.研究结果表明,在丰中子体系的中心和擦边反应中出射核子的N/Z都对对称势敏感,但对称势的密度依赖对中心和擦边反应的影响显示不同的特征.     

中能重离子碰撞中的气–液相变和同位旋分馏

利用核物质理论研究气–液相变结果表明,气–液相变中临界温度T_c随系统质量的增加而增加,但随碰撞系统同位旋的增加而减小.利用改进的同位旋相关的量子分子动力学模型,研究了中能重离子碰撞过程中同位旋分馏强度随碰撞系统的同位旋和系统质量的变化,结果表明,同位旋分馏强度与气–液相变临界温度T_c有对应的关系,特别是气–液相变和同位旋分馏都发生在正常核密度以下低密度的spinodal不稳定区.这表明气–液相变和同位旋分馏具有相类似的动力学行为和内在联系,也预示着可以通过对同位旋分馏强度的研究和测量来揭示中能重离子碰撞过程中气–液相变的动力学特征     

Heavy Hadron Spectra to the Order 1/M in Heavy Quark Effective Theory

The heavy meson and baryon spectra are studied to the order of 1/M_Q in heavy quark effective theory. A phenomenological formula for the dependence of the spectra on the isospin and strangeness of the light quark system contained in heavy hadrons is proposed and its predictions are in agreement with the present experimental data. The predictions of beauty hadron masses including the 1/M_Q corrections are given. The parameters of the order of 1/M_Q are estimated from phenomenological analyses.