Study on Charge Form Factors of the Exotic Nuclei 6,8He

Charge radius and charge form factors of different charge density distributions for ^6,8He are calculated with the relativistic Eikonal approximation. Detailed comparisons and discussions are presented. It is found that the charge form factors curves of ^6,8He are much lower than the experimental ones of ⁴He. This is, in principle, consistent with the experimental fact. Whereas detailed comparison among the charge form factors which correspond to different charge distributions show significant deviations. This indicates that the effects of the correlations between the halo neutrons and the α-core in ^6,8He with different charge density distributions are quite different. This result would provide a useful reference for the possible experiments on the next-generation electron-nucleus collider and for the tests of different theoretical models for the exotic nuclei ^6,8He.     

Theoretical study of the central depression of nuclear charge density distribution by electron scattering

The charge form factors of elastic electron scattering for isotones with N=20 and N=28 are calculated using the phase-shift analysis method, with corresponding charge density distributions from relativistic mean-field theory. The results show that there are sharp variations at the inner parts of charge distributions with the proton number decreasing. The corresponding charge form factors are divided into two groups because of the unique properties of the s-states wave functions, though the proton numbers change uniformly in two isotonic chains. Meanwhile, the shift regularities of the minima are also discussed, and we give a clear relation between the minima of the charge form factors and the corresponding charge radii. This relation is caused by the diffraction effect of the electron. Under this conclusion, we calculate the charge density distributions and the charge form factors of the A=44 nuclei chain. The results are also useful for studying the central depression in light exotic nuclei.     

Empirical transverse charge densities in the deuteron

Using the recent empirical information on the deuteron electromagnetic form factors we map out the transverse charge density in the deuteron as viewed from a light front moving towards the deuteron. The charge densities for a transversely polarized deuteron are characterized by monopole, dipole and quadrupole patterns.     

Empirical transverse charge densities in the nucleon and the nucleon-to-delta transition

Using only the current empirical information on the nucleon electromagnetic form factors we map out the transverse charge density in proton and neutron as viewed from a light front moving towards a transversely polarized nucleon. These charge densities are characterized by a dipole pattern, in addition to the monopole field corresponding with the unpolarized density. Furthermore, we use the latest empirical information on the N-->Delta transition form factors to map out the transition charge density which induces the N-->Delta excitation. This transition charge density in a transversely polarized N and Delta contains both monopole, dipole and quadrupole patterns, the latter corresponding with a deformation of the N and Delta charge distribution.     

Analysis on experimental valence charge density in germanium at RT and 200 K

The electronic structure and hence the valence charge distribution of germanium at 296 and 200 K has been elucidated from structure factors measured by X-ray diffraction experiment using maximum entropy method (MEM) and multipole model. The methods adopted here are used to extract the fine details of the charge density distribution in the valence region. The charge density evaluated using both the models along the bond path and at the mid bond positions are compared and found to confirm the covalent bond existing in the solid. Topology of the charge density in the crystal is analysed and the critical points determined reveal unique spatial arrangement of valence charge in the direction normal to the bonding direction. The Laplacian of the charge density is also analysed for the understanding of the spatial distribution and the partitioning of the valence charge. The local charge concentration and the mapping of the electron pairs of the Lewis and valence shell electron pair repulsion (VSEPR) models have been done using electron localization function (ELF) and localized orbital locator (LOL).     

奇特原子核6,8He的电荷形状因子研究

应用相对论Eikonal近似计算了用不同模型给出的^6,8He的电荷半径和电荷分布的形状因子, 并将结果与⁶He和⁴He的实验结果进行了比较. 结果显示不同模型给出的电荷半径和电荷形状因子差别很大, 表明不同模型给出的晕中子与α核芯的关联有很大的差异. 计算和讨论结果为在下一代电子-原子核对撞机上可能进行的实验提供了理论参考, 同时, 也为现有讨论奇特原子核的理论模型提供了检验.     

Electronic structure and lattice properties of zinc-blende InN under high pressure

Dependencies of electronic structure and lattice properties of InN with zinc-blende structure on hydrostatic pressure are presented based on band structures computed using the empirical pseudopotential method. The pressure behavior of the pseudopotential form factors have been analyzed. The effect of pressure on the density of states has been examined. Trends in bonding and ionicity under pressure are also discussed. Our results show as well that the absolute value of the Fourier transform of the valence charge density might be useful in the prediction of the phase transition in zinc-blende materials. Received 25 May 2001 and Received in final form 16 January 2002     

Two-pion exchange charge density and its related problems

The two-pion exchange charge density operators are derived in the static approximation. Their contributions to the charge form factors of ³He and ³H are investigated with the use of simple wave functions and are found to be appreciable at high momentum transfer (3 to 5 fm^?1). It is also shown that the exchange charge density modifies the enhancement factor of the electric dipole sum rule by around 10%. The distinguishing feature between the isoscalar and isovector exchange charge densities is pointed out.     

Nuclear longitudinal form factors for axially deformed charge distributions expanded by nonorthogonal basis functions

In this paper,the nuclear longitudinal form factors are systematically studied from the intrinsic charge multipoles.For axially deformed nuclei,two different types of density profiles are used to describe their charge distributions.For the same charge distributions expanded with different basis functions,the corresponding longitudinal form factors are derived and compared with each other.Results show the multipoles C_λ of longitudinal form factors are independent of the basis functions of charge distributions.Further numerical calculations of longitudinal form factors of~(12)C indicates that the C_0 multipole reflects the contributions of spherical components of all nonorthogonal basis functions.For deformed nuclei,their charge RMS radii can also be determined accurately by the C_0 measurement.The studies in this paper examine the model-independent properties of electron scattering,which are useful for interpreting electron scattering experiments on exotic deformed nuclei.     

Charge form factor and cluster structure of the 6Li nucleus

The charge form factor of the 6Li nucleus is considered on the basis of its cluster structure. The charge density of ⁶Li is presented as a superposition of two terms. One of them is a folded density and the second one is a sum of the ⁴He and deuteron densities. Using the available experimental data for ⁴He and deuteron charge form factors, a satisfactory agreement of the calculations within the suggested scheme is obtained with the experimental data for the charge form factor of ⁶Li, including those in the region of large transferred momenta.      

Electronic charge density in simple metals

The valence electron density is calculated for aluminum, magnesium, and sodium using an OPW-based pseudopotential method. The Fourier transform of the charge density is used to calculate atomic form factors which compare very well with experimental X-ray scattering form factors. The non-local and energy-dependent nature of the pseudopotential and corrections from the orthogonalization hole are shown to be important.     

Elastic charge density representation of the interaction via the nematic director field

The interaction between particle-like sources of the nematic director distortions (e.g., colloids, point defects, macromolecules in nematic emulsions) allows for a useful analogy with the electrostatic multipole interaction between charged bodies. In this paper we develop this analogy to the level corresponding to the charge density and consider the general status of the pairwise approach to the nematic emulsions with finite-size colloids. It is shown that the elastic analog of the surface electric charge density is represented by the two transverse director components on the surface imposing the director distortions. The elastic multipoles of a particle are expressed as integrals over the charge density distribution on this surface. Because of the difference between the scalar electrostatics and vector nematostatics, the number of elastic multipoles of each order is doubled compared to that in the electrostatics: there are two elastic charges, two vectors of dipole moments, two quadrupolar tensors, and so on. The two-component elastic charge is expressed via the vector of external mechanical torque applied on the particle. As a result, the elastic Coulomb-like coupling between two particles is found to be proportional to the scalar product of the two external torques and does not directly depend on the particles' form and anchoring. The real-space Green function method is used to develop the pairwise approach to nematic emulsions and determine its form and restrictions. The pairwise potentials are obtained in the familiar form, but, in contrast to the electrostatics, they describe the interaction between pairs (dyads) of the elastic multipole moments. The multipole moments are shown to be uniquely determined by the single-particle director field, unperturbed by other particles. The pairwise approximation is applicable only in the leading order in the small ratio particle size-to-interparticle distance as the next order contains irreducible three-body terms.     

Proton electromagnetic-form-factor ratios at low Q2

We study the ratio R identical with muG_{E}(Q2)/G_{M}(Q2) of the proton at very small values of Q2. Radii commonly associated with these form factors are not moments of charge or magnetization densities. We show that the form factor F2 is correctly interpretable as the two-dimensional Fourier transformation of a magnetization density. A relationship between the measurable ratio and moments of true charge and magnetization densities is derived and used to show that the magnetization density extends further than the charge density, in contrast with expectations based on the measured reduction of R as Q2 increases.     

Probing proton halo of the exotic nucleus ~(28)S by elastic electron scattering

~~Probing proton halo of the exotic nucleus ~(28)S by elastic electron scattering~~     

Effective electron-electron interactions and magnetic phase transition in a two-dimensional electron liquid

We investigate the spin-dependent effective electron-electron interactions in a uniform system of two-dimensional electrons to understand the spontaneous magnetization expected to occur at very low density. For this purpose, we adopt the Kukkonen-Overhauser form for the effective interactions which are built by accurately determined local-field factors describing the charge and spin fluctuations. The critical behavior of the effective interaction for parallel spin electrons allows us to quantitatively locate the transition to the ferromagnetic state at r_s≈27. When the finite width effects are approximately taken into account the transition occurs at r_s≈30 in agreement with recent quantum Monte Carlo calculations.     

The determination of the nuclear ground state and transition charge density from measured electron scattering data

The evaluation of elastic and inelastic electron scattering cross sections is discussed in terms of the Fourier-Bessel expansion of the nuclear ground state and transition charge density, respectively. The method allows one to deduce the charge distributions and the moments as well as the corresponding errors, which originate on the one hand from the uncertainties in the measured data and on the other hand from the lack of knowledge about the large-q behaviour of the form factors; these two contributions are determined separately. The method is described and proved with an evaluation of pseudodata and then applied to ²⁰⁸Pb cross sections. For this nucleus, detailed results concerning the possible structure of the charge density are presented.     

A Discussion of Deuteron Transverse Charge Densities

The deuteron transverse charge density ρ_C(b) is the two-dimensional Fourier transform of its charge form factor in the impact space. We show that different parameterizations of the charge form factors provide different ρ_C(b), in particular at the central value of impact parameter (b=0), although all the parameterizations can well reproduce the form factors in the region of small Q². In addition, we also check the explicit contributions from the different coordinate intervals of the deuteron wave function to its root-mean-square radius.     

Nuclear mass form factors from coherent photoproduction of πmesons

Data for coherent photoproduction of π⁰ mesons from nuclei ( ¹²C, ⁴⁰Ca, ⁹³Nb, ^natPb), recently measured with the TAPS detector at the Mainz MAMI accelerator, have been analyzed in view of the mass form factors of the nuclei. The form factors have been extracted in plane-wave approximation of the A(γ,π⁰)A reaction and corrected for final-state interaction effects with the help of distorted-wave impulse approximations. Nuclear mass rms radii have been calculated from the slope of the form factors for q² → 0. Furthermore, the Helm model (hard-sphere form factor folded with Gaussian) was used to extract diffraction radii from the zeroes of the form factor and skin thicknesses from the position and height of its first maximum. The diffraction radii from the Helm model agree with the corresponding charge radii obtained from electron scattering experiments within their uncertainties of a few per cent. The rms radii from the slope of the form factors are systematically lower by up to 5% for PWIA and up to 10% for DWIA. Also the skin thicknesses extracted from the Helm model are systematically smaller than their charge counterparts.     

A class of exactly solvable potentials II. The three-dimensional Schrödinger equation

The three-dimensional Schrödinger equation with an effective mass is solved for a new class of angular momentum dependent potentials with varying depths and shapes. The energy eigen, values and resonances are given in algebraic form as a function of the effective mass and depth and shape of the potential. The eigenfunctions, scattering function, and Green's function are given in closed form in terms of known special functions. The charge density of ²⁰⁸Pb is calculated using eigenfunctions of a particular potential and this charge density is compared to the measured charge density.