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.     

Neutron density distributions deduced from antiprotonic atoms

The differences between neutron and proton density distributions at large nuclear radii in stable nuclei were determined. Two experimental methods were applied: nuclear spectroscopy analysis of the antiproton annihilation residues one mass unit lighter than the target mass and the measurements of strong-interaction effects on antiprotonic x rays. Assuming the validity of two-parameter Fermi neutron and proton distributions at these large radii, the conclusions are that the two experiments are consistent with each other and that for neutron rich nuclei it is mostly the neutron diffuseness which increases and not the half-density radius. The obtained neutron and proton rms radii differences are in agreement with previous results.     

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.     

A study of the dependence of coulomb-energy shifts on the symmetry energy of density-dependent effective interactions

Using Hartree-Fock theory and standard density-dependent effective interactions, we show that by appropriately modifying their symmetry energy properties sizeable changes in the Coulomb energy shifts can be produced. These changes are the result of different degrees of isovector core polarization, while the variations coming from the neutron excess are small. Forces are presented that give satisfactory agreement with experiment for both charge radii and Coulomb displacement energies in mirror and heavy nuclei, and thus no systematic Nolen-Schiffer anomaly is found. No significant changes appear in the values of other bulk properties like total binding energies, proton densities and single-particle spectra. Properties directly related to the symmetry energy, like isotopic mass differences and electric dipole polarizabilities, are also satisfactorily reproduced.     

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.     

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.     

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．     

Nucleon charge radius from QCD sum rules

The proton and neutron electric radii are calculated within QCD using the sum rules method for processes with small momentum transfers. The agreement with experimental values is good for the proton radius and somewhat poorer for the neutron one due to the numerical smallness.     

The neutron distribution in nuclei from bremsstrahlung-weighted cross-sections

Bremsstrahlung-weighted cross-section (bwcs) measurements may be a decisive step to obtain information about the difference between neutron and proton radii. A model-independent relation is discussed between the total bwcs, the relative intensity of the bwcs of the upper (T_>) fragment of the dipole excitation and the neutron and proton radii.     

Reaction cross sections and radii of A=17 and A=20 isobars

Reaction cross sections and root-mean-square (rms) radii of A=17 and A=20 isobars are calculated by using a simplified Glauber model and spherical and deformed Hartree-Fock (HF) wave functions. The small separation energy effect is discussed on the reaction cross sections of A=17 isobars and possible proton halo in ¹⁷Ne by using modified spherical HF wave functions. The calculated rms mass radii of A=20 isobars are increased appreciably by the deformation effect and show a similar irregular pattern as a function of the isospin to that of the observed radii.     

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.     

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.     

Proton radius,Darwin-Foldy term and radiative corrections

We discuss the role of the so-called Darwin-Foldy term in the evaluation of the proton and deuteron charge radii from atomic hydrogen spectroscopy and nuclear scattering data. The question of whether this term should be included or excluded from the nuclear radius has been controversially discussed in the literature. We attempt to clarify which literature values correspond to which conventions. A detailed discussion of the conventions appears useful because a recent experiment [R. Pohl et al., Nature 466, 213 (2010)] has indicated that there is a discrepancy between the proton charge radii inferred from ordinary (“electronic”) atomic hydrogen and muonic hydrogen. We also investigate the role of quantum electrodynamic radiative corrections in the determination of nuclear radii from scattering data, and propose a definition of the nuclear self energy which is compatible with the subtraction of the radiative corrections in scattering experiments.     

Estimating proton radius and proportion of other non-perturbative components in the proton by the maximum entropy method

In this paper,we apply the Maximum Entropy Method to estimate the proton radius and determine the valence quark distributions in the proton at extremely low resolution scale Q_0~2.Using the simplest functional form of the valence quark distribution and standard deviations of quark distribution functions in the estimation of the proton radius,we obtain a quadratic polynomial for the relationship between the proton radius and the momentum fraction of other non-perturbative components in the proton.The proton radii are approximately equal to the muonic hydrogen experimental result r_p = 0.841 fm and the CODATA analysis r_p = 0.877fm when the other non-perturbative components account for 17.5% and 22.3% respectively.We propose "ghost matter" to explain the difference in other non-perturbative components(4.8%) that the electron can detect.     

Hydration and translocation of an excess proton in water clusters: Anab initio molecular dynamics study

The hydration structure and translocation of an excess proton in hydrogen bonded water clusters of two different sizes are investigated by means of finite temperature quantum simulations. The simulations are performed by employing the method of Car-Parrinello molecular dynamics where the forces on the nuclei are obtained directly from ‘on the fly’ quantum electronic structure calculations. Since no predefined interaction potentials are used in this scheme, it is ideally suited to study proton translocation processes which proceed through breaking and formation of chemical bonds. The coordination number of the hydrated proton and the index of oxygen to which the excess proton is attached are calculated along the simulation trajectories for both the clusters.     

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     

Elastic and inelastic scattering of neutrons from Fe and Cu : (II). Scattering and nuclear structure effects from coupled channels calculations

The differential cross sections for neutron scattering from ^{54, 56}Fe and ^{63, 65}Cu at energies between 8 and 14 MeV, which were reported in a companion paper, have been analyzed in the framework of the coupled channels formalism. Neutron potential deformations were extracted and compared with corresponding deformations deduced from the reanalysis of proton scattering measurements and Coulomb excitation results. The size of the Coulomb correction term in the absorptive proton potential is discussed. Matter root-mean-square radii are estimated from our potential and compared with results from -particle folding model calculations.     

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.     

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.     

Charge Radii of Argon Isotopes in the f7/2 Shell and Radii Systematics in the Ca-Region

Changes in mean square (ms) nuclear charge radii of Ar isotopes across the 1f_7/2 shell are studied by fast-beam collinear laser spectroscopy using an ultra-sensitive detection method based on optical pumping and state-selective collisional ionization. The new data set on Ar, in combination with the known charge radii of K, Ca and Ti in the ν1f_7/2 shell, offers an opportunity to obtain a more complete overview of nuclear radii trends around the proton shell closure Z = 20 and between the neutron shell closures N = 20 and N = 28.