Isotopic dependence of the nuclear charge radii and binding energies in the relativistic Hartree-Fock formalism

Relativistic nonlinear models based on the Hartree and Hartree-Fock approximations, including the σ, ω, π, and ρ mesons, are worked out to explore the behavior of the nuclear charge radii and the binding energies of several isotopic chains. We find a correlation between the magnitude of the anomalous kink effect (KE) in the Pb isotopic family and the compressibility modulus (K) of nuclear matter. The KE appears to be sensitive, in particular, to the mechanisms which control the K value. The influence of the symmetry energy on the Ca isotopic chain is also studied. The behavior of the charge radii of single-particle states for some special cases and its repercussion on the nuclear charge radius is analyzed. The effect of pairing correlations on the models improves considerably the quality of the results in both binding energy and KE.     

Skyrme-Hartree-Fock Description of the Nuclear Structure in Ca Isotopes (Ⅰ)Binding Energy and Shell Effects,Radii and Density Distributions

The ground state properties of Ca isotopes far from stability line were systematically studied using the Skyrme Hartree Fock model.The shell effects on the binding energy and two neutron separation energy are discussed.The isospin dependency of the unclear radii and nucleon density distributions and the shell effects on these properties are also studied.It is shown that the neutron magic number affests the width of nuclear surface and the nucleon density distributions beyond the nuclear surface.The change of proton rms radii R_rms with neutron number excess I=(N-Z)/A follows R_rms=3/5(1+αI+βI²)r_pZ^1/3.The effect of the centrifugal potential on the nuclear density in the outer trach of nuclear surface is clearly shown.     

Topics in atomic hyperfine structure and isotope shift

Recent developments in atomic hyperfine structure and isotope shift are discussed under the following aspects: (i) Precise evaluation of nuclear moments and isotopic change of nuclear charge radii by quantitative computation of atomic structure or by calibration of the atomic constants through results from electronic and mesic X-ray spectroscopy. (ii) How to apply spectroscopic methods to nuclei far off stability. (iii) What can be learned from a systematic investigation of long isotopic chains.     

Precision mass measurements of neutron halo nuclei using the TITAN Penning trap

Precise atomic mass determinations play a key role in various fields of physics, including nuclear physics, testing of fundamental symmetries and constants and atomic physics. Recently, the TITAN Penning trap measured the masses of several neutron halos. These exotic systems have an extended, diluted, matter distribution that can be modelled by considering a nuclear core surrounded by a halo formed by one or more of loosely bound neutrons. Combined with laser spectroscopy measurements of isotopic shifts precise masses can be used to obtain reliable charge radii and two-neutron-seperation energies for these halo nuclei. It is shown that these results can be used as stringent tests of nuclear models and potentials providing an important metric for our understanding of the interactions in all nuclei.     

The Relation of Isotopic Distribution of Heavy Ion Peripheral Reaction Products to Neutron-Skin and Excitation Energy in Intermediate Energy Range

The relation of isotopic distribution of the heavy ion peripheral reaction products in intermediate energy range to neutron-skin and excitation energy has been studied.The thickness of neutron-skin predicated by the droplet model and emperical one-body disspation in the intermediate energy range has been considered.The experimental isotopic distribution produced by ⁴⁰Ar and ⁸⁶Kr as projectiles in the intermediate energy can be reproduced by calculation.     

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.     

Collinear laser spectroscopy on unstable isotopes—A tool of nuclear physics

Atomic hyperfine structures and isotope shifts yield basic information about nuclear ground-state spins, moments and mean square charge radii. Recently, the collinear-beam laser experiments at ISOLDE have considerably enlarged the range of elements for which these studies can be extended into regions far from β-stability. The essential features of these experiments are outlined, and examples of the results on the rare-earth and radium isotopic chains are given. Finally, further improvements in sensitivity using non-optical detection are discussed.     

Isospin Effect on Level Spacing of N=9 Isotones

The ground-state properties of N=8 and N=9 isotones are investigated in the framework of the single-particle shell model. The isospin effect on the average nuclear potential is taken into account 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. Especially, the level inversion between neutron levels 2s_1/2 and 1d_5/2 in N=9 isotones is reproduced. A detailed discussion on numerical results is given and one-neutron halos in the ground states of ¹⁴B and ¹⁵C are presented.     

Lasers at accelerators—past,present and future

The application of lasers at accelerators is reviewed with emphasis on laser spectroscopy of short-lived isotopes and the determination of nuclear spins, moments, and changes of charge radii in long isotopic chains leading far-off stability. Experimental techniques as well as future directions are discussed.     

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.     

Improved Q2-Rescaling Model and the Nuclear Effect of Parton Distribution Functions

Considering that the original Q²-rescaling model has some shortcomings in explaining the experimental data,we propose animproved Q²-rescaling model in which,in order to compensate for the loss of nuclear momentum,we employ different Q²-rescaling parameters for momentum distributions of valence quark,sea quark and glouns.By using improved Q²-rescaling model,We can well explain the experimental data of the EMC effect in the whole x region,the nuclear Drell-Yan Process and J/ψ photoproduction process.     

Simple formula for nuclear charge radius

A new formula for the nuclear charge radius is proposed, dependent on the mass numberA and neutron excessN-Z in the nucleus. It is simple and it reproduces all the experimentally available mean square radii and their isotopic shifts of even-even nuclei much better than other frequently used relations.This work is partly supported by the Polish Committee of Scientific Research under contract No. 203119101     

Charge radii and structural evolution in Sr,Zr, and Mo isotopes

The evolution of the ground-state nuclear shapes in neutron-rich Sr, Zr, and Mo isotopes, including both even-even and odd-A nuclei, is studied within a self-consistent mean-field approximation based on the D1S–Gogny interaction. Neutron separation energies and charge radii are calculated and compared with available data. A correlation between a shape transition and a discontinuity in those observables is found microscopically. While in Sr and Zr isotopes the steep behavior observed in the isotopic dependence of the charge radii is a consequence of a sharp prolate–oblate transition, the smooth behavior found in Mo isotopes has its origin in an emergent region of triaxiality.     

Measurement of nuclear moments and radii by collinear laser spectroscopy and by β-NMR spectroscopy

Experiments using laser spectroscopy and nuclear magnetic resonance techniques have been performed at ISOLDE on the unstable isotopes of several light elements. The results include nuclear ground state spins, magnetic dipole and electric quadrupole moments, and the behaviour of mean square nuclear charge radii within isotopic strings. These give important information about the nuclear structure at shell closures and close to the drip lines. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the charge distribution of calcium nuclei

The mean square charge radii and the quadrupole moments of Ca nuclei are discussed in the light of theoretical predictions. The very peculiar dependence of the charge radii on the mass number between double magic⁴⁰Ca and double magic⁴⁸Ca can be ascribed to changes of the nuclear deformation, whereas the volume of the nuclear charge remains constant for all the Ca isotopes. Furthermore, correlations between nuclear charge radii and binding energies are discussed.     

SHELL (DEFORMATION) EFFECT IN NUCLEAR CHARGE RADIUS

It is shown that without exception the observed rms charge radius constants of strongly deformed nuclei, rp's, are a little larger than those of the neighbouring spherical nuclei. The local variations among the charge radii of the sequence of isotopes, the in complete neutron shells [1p_3/2(N~3—6), 1d_5/2(N~9—14), 1f_7/2(N~20—28), 1g_9/2(N~40—50), 1h_11/2(N~70—82)], display some peculiar behaviors (eg. rms cnarge radii decrease with increasing A) which are sharply conflicting with the traditional A^1/3 law. Taking the deformation effect into account, these strange variations can be accounted for with the Z^1/3-law.     

Constraints on the symmetry energy using the mass-radius relation of neutron stars

The nuclear symmetry energy is intimately connected with nuclear astrophysics. This contribution focuses on the estimation of the symmetry energy from experiment and how it is related to the structure of neutron stars. The most important connection is between the radii of neutron stars and the pressure of neutron star matter in the vicinity of the nuclear saturation density n_s. This pressure is essentially controlled by the nuclear symmetry energy parameters S_v and L , the first two coefficients of a Taylor expansion of the symmetry energy around n_s. We discuss constraints on these parameters that can be found from nuclear experiments. We demonstrate that these constraints are largely model-independent by deriving them qualitatively from a simple nuclear model. We also summarize how recent theoretical studies of pure neutron matter can reinforce these constraints. To date, several different astrophysical measurements of neutron star radii have been attempted. Attention is focused on photospheric radius expansion bursts and on thermal emissions from quiescent low-mass X-ray binaries. While none of these observations can, at the present time, determine individual neutron star radii to better than 20% accuracy, the body of observations can be used with Bayesian techniques to effectively constrain them to higher precision. These techniques invert the structure equations and obtain estimates of the pressure-density relation of neutron star matter, not only near n_s, but up to the highest densities found in neutron star interiors. The estimates we derive for neutron star radii are in concordance with predictions from nuclear experiment and theory.     

Study of Exotic Nuclei

A high-sensitive fluorescence cell has been developed with an aim to perform laser spectroscopy of exotic nuclei. This fluorescence cell has been tested off-line for stable isotope ¹³³Cs. Also, an investigation of the nuclear root mean square (r.m.s.) charge and neutron radii, and of the binding energies of the cesium long isotopic chain has been carried out in the relativistic mean field (RMF) and relativistic Hartree–Bogoliubov (RHB) formalisms. The RMF/RHB calculations are compared with the experimental data and are found to be in good agreement.     

ON THE TRANSFER MECHANISM OF 16O+24Mg AND 20Ne+24Mg ELASTIC SCATTERING

The mechanism of transfering a cluster of nucleons between two colliding nuclei is considered to explain the backward angle oscillatory rise in the differential cross section of the elastic scattering between certain nuclei, such as ¹⁶O+²⁴Mg or ²⁰Ne+²⁴Mg. The nuclear molecular orbit approximation theory is applied. For one-step transfer, if the parameter involved is assumed to be adjustable, the numerical calculations can be made to fit the experimental results naturally.     

Nuclear radii of Na and Mg isotopes

The effective root-mean-square (rms) matter radii of ^ANa (A = 20–23, 25–32) and ^AMg (A = 20, 22, 23, 27, 29–32) have been deduced from the measured interaction cross sections using a Glauber-type calculation. It was found that the increase of rms matter radii in Na isotopes is primarily a consequence of the increase of rms neutron radii. A correlation between the radii, corrected for quadrupole deformation, and the Fermi-energy difference was observed for both Na and Mg isotopes. This correlation can be explained by a model that assumes the valence nucleons are responsible for the changes in nuclear radii. The presence of a neutron skin is suggested for neutron-rich Na and Mg isotopes. An application to the nuclear equation of state (EOS) is discussed.