Study of the nuclear periphery with Antiprotons

In the experiments of the PS209 collaboration at the Low Energy Antiproton Ring LEAR at CERN two methods were applied to study the nuclear periphery: first the yields of residual nuclei with mass number A — 1 were determined with radiochemical methods, and secondly the widths and shifts of the last observable transitions in antiprotonic atoms were measured with Ge detectors. The ratio of yields after annihilation for nuclei with one neutron missing to those with one proton missing from the target nucleus was found to depend strongly on the binding energy of the most loosely bound neutron of the target nucleus. The values were in astonishingly good agreement with a rather simple model for the proton and neutron density distribution devised by Gambhir et al. Furthermore the normalized yield ratio stays constant up to a relative neutron excess of about 0.15 and afterwards rises steeply. Widths for in total 62 x-ray Unes from antiprotonic atoms were compared with the results of calculations of Batty et al. The agreement is reasonable on a semiquantitative basis, but improvements are desirable. For a number of nuclei the differences between the diffuseness values for the proton and neutron distributions were determined directly from the x-ray-line intensity and width data. The root-mean-square radii for the neutron and proton distributions may be derived from these results. The experimental data for four tin isotopes are in reasonable agreement with the experiments of Krasznahorkay et al., but lower than theory predicts.     

Semi-empirical mass formula and nuclear radii

The semi-empirical mass formula is extended to include different radii for the proton and neutron distributions. By minimising the energy, the radii are determined. Our model predicts that the proton radius equals the neutron radius for all stable nuclei and that this radius has an accurate A^1/2 dependence.     

Cluster decay half-lives using asymmetry dependent densities

By adopting different neutron and proton density distributions, cluster decay half-lives were investigated using double-folding potentials with constant and nuclear asymmetry dependent sets of nuclear density parameters. Two adopted asymmetry dependent sets of parameters were fitted based on microscopic calculations, and they were calculated based on the neutron skin/halo-type nuclei assumption and by employing experimental rms charge radii. A bulk agreement between theory and experiment was obtained for all sets of parameters using a calculated cluster preformation probability. Few differences were observed between the skin and halo-type assumptions. However, the notable role of the asymmetry parameter was observed in the relatively large differences between the skin and skin-type with zero thickness.     

Experimental studies of the nuclear spatial structure of neutron-rich He and Li isotopes

Results of several experiments aimed at exploring the nuclear spatial structure of neutron-rich He and Li isotopes are presented and briefly discussed. The study of the density distributions in these nuclei by small-angle proton elastic scattering at intermediate energy is considered in more detail. The performed investigations allow one to obtain information on the total matter distributions, radii of the matter, neutron and proton distributions, effective and internal core sizes, halo sizes, and spatial correlations of the halo nucleons in the studied nuclei. The text was submitted by the authors in English.     

应用原子核的宏观－微观模型研究远离稳定线核的性质

应用原子核的宏观－微观模型研究远离稳定线核的性质，得到了一些结果，例如质子和中子滴线，质子和中子密度分布及其均方根半径和中子皮厚度随同位素位移的变化．对一些奇异核性质的计算结果同相对论平均场方法计算的结果作了比较，对质子滴线附近核的质子放射性也作了简要讨论．     

Nuclear properties far from the stability line in the relativistic mean field theory

We study the nuclear properties far from the stability line in the relativistic mean field theory. We find that the parameter set NL 1 provides very good results on binding energies of unstable nuclei, while NL2 results are not good, although both parameter sets give equally good results on nuclear properties for stable nuclei. We discuss the neutron number dependence of the proton and the neutron root mean square radii of proton magic nuclei.     

Microscopic structure of nuclei from scattering through isobaric analogue resonances

Microscopic nuclear structure information that can be reached by proton scattering through isobaric analogue resonances (IAR) is discussed, mainly within the framework of weak-coupling. The concept of isospin for unbound states is examined. A critical evaluation of the methods for extracting nuclear structure information from the experimental results (such as excitation functions, angular distributions, etc.) is given. The mass regions that are studied in detail are the Pb-region and the N = 82 neutron single-closed shell nuclei. Attention is given to the comparison between weak-coupling calculations and experimental results supporting this concept in many nuclei. Level schemes as well as proton partial decay widths and angular distributions have been calculated and compared with the existing data concerning the proton decay of IAR. The concept of generalized neutron particle-hole (GNPH) state is introduced and its occurence extensively discussed within the Pb-region and N = 82 nuclei.     

Neutron radii and skins in the Hartree-Fock-Bogoliubov calculations

We examine the systematic predictions for proton and neutron radii in even-even nuclei made by the self-consistent Skyrme-Hartree-Fock-Bogoliubov theory. Such an approach allows us to describe nuclei far from stability, where the spatial extensions of a nuclear system crucially depend on the continuum effects. We concentrate on the influence of spherical shell structure on global behavior of radii. The (N, Z)-localization of neutron and proton skins is discussed.     

Properties of lead isotopes in the vicinity of the neutron drip line

On the basis of the Hartree-Fock method with Skyrme forces of the Ska, SkM*, and Sly4 type, the position of the neutron drip line and the properties of neutron-rich lead isotopes are studied with allowance for deformations. It is shown that, in extremely neutron-rich nuclei, the neutron and proton density distributions are characterized by an anomalously large deformation parameter of β ～ 0.6. Also, nuclei of superdeformed lead isotopes have anomalously large root-mean-square radii. The existence of the isotopes ^266–288Pb, which are stable to the emission of one neutron, is predicted.     

一个奇异中子分布结构存在的判据

通过小液滴模型的中子皮厚度计算出的中子、质子均方根半径之差与实验的比较发现,实验提取的正常核的均方根半径之差与小液滴模型计算基本一致;有奇异中子分布结构(皮或晕)核的均方根半径之差的实验结果比小液滴模型的计算结果有异常增大.提出了一个与分离能相关的有效中子皮厚度,它能很好地反映有奇异中子分布结构核的中子皮厚度的反常增加,建议把它作为奇异中子分布结构存在的判据.     

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.     

The neutron halo in heavy nuclei calculated with the Gogny force

The proton and neutron density distributions, one- and two-neutron separation energies and radii of nuclei for which neutron halos are experimentally observed, are calculated using the self-consistent Hartree-Fock-Bogoliubov method with the effective interaction of Gogny. Halo factors are evaluated assuming hydrogen-like antiproton wave functions. The factors agree well with experimental data. They are close to those obtained with Skyrme forces and with the relativistic mean-field approach.     

Thick skin in neutron/proton-rich sodium isotopes

Nucleon (both neutron and proton) density distributions of the chain of sodium isotopes are calculated using a semi-phenomenological model of nuclear density which incorporates correctly the asymptotic behaviour and the behaviour near the centre. The experimental charge root-mean-square radii and the single neutron and proton separation energies, required as input, are used. The calculated interaction cross-sections using these densities in the Glauber model agree well with the experiment. The calculated neutron rms radii r _n and the nuclear skin thickness ( r _n - r _p) closely agree with the corresponding experimental values and also are consistent with the Relativistic Hartree-Bogoliubov (RHB) calculations. Received: 24 April 2001 / Accepted: 28 June 2001     

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.     

Binding energies of nuclei and their density distributions in a nonlocal extended Thomas-Fermi approximation

Basic properties of the ground states of spherical nuclei are investigated in a nonlocal extended Thomas-Fermi approximation under the assumption of Skyrme forces. It is shown that, for nuclei occurring near the β-stability line, the binding energies, the root-mean-square radii, and the density distributions found on this basis agree well with experimental data. Binding energies, root-mean-square radii, and density distributions are also calculated for the ground states of nuclei lying far off the β-stability line and for superheavy elements. For the proton, the neutron, and the total particle density, the thickness of the diffuse layer is investigated as a function of the number of neutrons in tin isotopes.     

Total Nuclear Reaction Cross Section Induced by Halo Nuclei and Stable Nuclei

We develop a method for calculation of the total reaction cross sections induced by the halo nuclei and stable. nuclei. This approach is based on the Glauber theory, which is valid for nuclear reactions at high energies. It is extended for nuclear reactions at low energies and intermediate energies by including both the quantum correction and Coulomb correction under the assumption of the effective nuclear density distribution. The calculated results of the total reaction cross section induced by stable nuclei agree well with 30 experimental data within 10 percent accuracy. The comparison between the numerical results and 20 experimental data for the total nuclear reaction cross section induced by the neutron halo nuclei and the proton halo nuclei indicates a satisfactory agreement after considering the halo structure of these nuclei, which implies quite different mean fields for the nuclear reactions induced by halo nuclei and stable nuclei. The halo nucleon distributions and the root-mean-square radii of these nuclei can be extracted from the above comparison based on the improved Glauber model, which indicates clearly the halo structures of these nuclei. Especially,it is clear to see that the medium correction of the nucleon-nucleon collision has little effect on the total reaction cross sections induced by the halo nuclei due to the very weak binding and the very extended density distribution.     

Total Nuclear Reaction Cross Section Induced by Halo Nuclei and Stable Nuclei

We develop a method for calculation of the total reaction cross sections induced by the halo nuclei and stable nuclei. This approach is based on the Glauber theory, which is valid for nuclear reactions at high energies. It is extended for nuclear reactions at low energies and intermediate energies by including both the quantum correction and Coulomb correction under the assumption of the effective nuclear density distribution. The calculated results of the total reaction cross section induced by stable nuclei agree well with 30 experimental data within 10 percent accuracy.The comparison between the numerical results and 20 experimental data for the total nuclear reaction cross section induced by the neutron halo nuclei and the proton halo nuclei indicates a satisfactory agreement after considering the halo structure of these nuclei, which implies quite digerent mean fields for the nuclear reactions induced by halo nuclei and stable nuclei. The halo nucleon distributions and the root-mean-square radii of these nuclei can be extracted from the above comparison based on the improved Glauber model, which indicates clearly the halo structures of these nuclei. Especially,it is clear to see that the medium correction of the nucleon-nucleon collision has little effect on the total reaction cross sections, induced by the halo nuclei due to the very weak binding and the very extended density distribution.     

Isomorphic shell model for closed-shell nuclei

The classical part of the isomorphic model for closed-shell nuclei is presented based on two physical assumptions, namely (a) the nucleons of a closed shell nucleus, considered at their most probable positions, are in an instantaneous dynamic equilibrium on spherical shells, and (b) the dimensions of the shells are determined by their close packing given that a neutron and a proton are represented by hard spheres of definite sizes. The first assumption leads to the instantaneous angular structure, and the second to the instantaneous radial structure of closed-shell nuclei. Applications of the model coming from this classical part alone and presented here are structural justification of all magic numbers, neutron (proton) and charge rms radii, nuclear densities of closed-shell nuclei, and Coulomb, kinetic, and binding energies. All the predictions are in good agreement with experimental data. A characteristic novelty of the isomphic model is that assumption (a) is related to the independent particle model, and assumption (b) to the liquid-drop model. The isomorphic model may provide a link between these two basic nuclear physics models since it incorporates features of both.     

Oscillator parameters in nuclei

The dependence on nucleon numbers of the harmonic oscillator length parameter b or energy spacing ℏω in nuclei is determined, using an extensive tabulation of nuclear charge radii and an empirical expression for the difference between proton and neutron radii. Various possible constraints on the parameters or radii are discussed. Alternative parametrizations are compared and a preferred “universal” parametrization is proposed. It is argued that the established Blomqvist–Molinari formula is perfectly adequate for determining the oscillator parameter for specific applications.     

The anomalies of the droplet model

The droplet model predictions for nuclear density distributions are systematically compared with the results of a self-consistent model with Strutinsky smoothing. The discrepancies between the two predictions for stable nuclei are as large as the discrepancies between the old liquid drop model and the self-consistent one: although the droplet model reproduces quite well the trends of the variations of nuclear radii and neutron skins, it is not able to predict correctly their values. A preliminary discussion is given as to which hypothesis of the droplet model should be modified to generalise it, and two possible variants are suggested.