Studies of the electron density at the nucleus and radial expectation values of the ground state for lithium-like systems from Z=11 to 18

The electron density at the nucleus ρ(0) and radial expectation values 〈rⁿ〉 (n=-2–10) of the ground state for lithium-like systems from Z=11 to 18 are calculated with the full core plus correlation wave functions. By using these obtained expectation values, accurate inequalities of radial expectation values derived by Gálvez and Porras [Phys. Rev. A 44, 144 (1991)] are examined and verified. The final results show that the full core plus correlation wave functions for lithium-like systems with higher nuclear charge are also accurate in the full configuration space and can give satisfactory electron density at the nucleus and radial expectation values.     

Specifications of dust-ion-acoustic shock waves affected by dust charge variation in four-component dissipative quantum plasma

ABSTRACT

Nonlinear propagation of dust-ion-acoustic shock waves in an unmagnetized, collisionless four-component quantum plasma containing electrons, positrons, ions and negatively charged dust grains affected by dust charge variations and viscosity of ions is studied using quantum hydrodynamic model. Considering dust charge variation give rise to calculating of charging currents of the plasma particles. These currents have been calculated with orbit limited motion theory and using Fermi-distribution functions or Boltzmann–Maxwell distribution depending on quantum or classical particles, respectively. The basic characteristics of quantum dust-ion-acoustic shock waves are investigated by deriving Korteweg–de Vries–Burgers equation under the reductive perturbation method. Depending on the relative values of the dispersive and dissipative coefficients, oscillatory and monotonic shock waves can propagate in the plasma model. The effect of chemical potential and density of dust particles on the shock wave’s height and thickness is investigated. In addition, the critical value of H (H_c) is calculated and it is shown that for R?>?0 compressive shock waves and for R?<?0 rarefactive ones can exist. The present study is applicable to researchers on quantum nonlinear structures in dense astrophysical objects and ultra-small micro- and nano-electronic devices.     

Higher order bulk characteristic parameters of asymmetric nuclear matter

The bulk parameters characterizing the energy of symmetric nuclear matter and the symmetry energy defined at normal nuclear density ρ ₀ provide important information on the equation of state (EOS) of isospin asymmetric nuclear matter. While significant progress has been made in determining some lower order bulk characteristic parameters, such as the energy E ₀(ρ ₀) and incompressibility K ₀ of symmetric nuclear matter as well as the symmetry energy E _sym(ρ ₀) and its slope parameter L, yet the higher order bulk characteristic parameters are still poorly known. Here, we analyze the correlations between the lower and higher order bulk characteristic parameters within the framework of Skyrme Hartree-Fock energy density functional and then estimate the values of some higher order bulk characteristic parameters. In particular, we obtain J ₀ = (−355±95) MeV and I ₀ = (1473±680) MeV for the thirdorder and fourth-order derivative parameters of symmetric nuclear matter at ρ ₀ and K _sym = (−100 ± 165) MeV, J _sym = (224 ± 385) MeV, I _sym = (−1309 ± 2025) MeV for the curvature parameter, third-order and fourth-order derivative parameters of the symmetry energy at ρ ₀, using the empirical constraints on E ₀(ρ ₀), K ₀, E _sym(ρ ₀), L, and the isoscalar and isovector nucleon effective masses. Furthermore, our results indicate that the three parameters E ₀(ρ ₀), K ₀, and J ₀ can reasonably characterize the EOS of symmetric nuclear matter up to 2ρ ₀ while the symmetry energy up to 2ρ ₀ can be well described by E _sym(ρ ₀), L, and K _sym.

     

氦原子和类氦离子基态能量的变分计算及相对论修正

采用一个包含坐标伸缩系数的简单有效的变分波函数,同时考虑到核的运动,利用Mathematic a语言开发了一个用变分法计算三体问题的程序,对氦原子和类氦离子(H^-,He,Li ⁺,Be⁺⁺,B³⁺,C⁴⁺,N⁵⁺,O ⁶⁺)的非相对论基态能量和解析波 函数进行了变分计算.在此基础上,对非相对论哈密顿量进行相对论和辐射修正,并考虑到有 限核电荷半径的影响,得到了氦原子和类氦离子高精度的基态能量值. 关键词： 氦原子 类氦离子 变分法 基态能量 相对论修正     

Relativistic effects in bound two-particle systems

The predictions of relativistic Schrödinger theory (RST) for the relativistic effects in helium-like ions with high nuclear charge ( -80) are elaborated in the electrostatic approximation (i.e. neglection of the magnetic interactions). The corresponding RST results are found to meet with the experimental data and with the predictions of other theoretical approaches, provided an estimate of the (neglected) magnetic effects is taken into account. This suggests to carry through high-precision calculations (including the magnetic forces) in order to further test the physical significance of RST.Received: 28 August 2003, Published online: 20 April 2004PACS: 03.65.Pm Relativistic wave equations - 03.65.Ge Solutions of wave equations: bound states - 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bells inequalities, GHZ states, etc.)     

Microscopic Analysis of 5d States Splitting and Charge Transfer Energies Dependence on Interionic Distance in Alkaline Earth Fluorides Doped with Light Trivalent Lanthanides

A first principles fully relativistic analysis (K. Ogasawara et al., Phys. Rev. B 2001, 64, 115413) of the dependence of 5d orbitals splitting (10Dq) and charge transfer (CT) energies on interionic distance has been performed for light lanthanides (Ce³⁺, Pr³⁺, Nd³⁺) in CaF₂, SrF₂, BaF₂ crystals. The salient feature of the method is that four‐component molecular orbitals (MO) composed of atomic wave functions are used as the basis set. Without any fitting parameter, the power dependencies for 10Dq and linear dependencies for the CT energies on the distance between rare‐earth (RE) ions and ligands were obtained. A comparison with experimental values is discussed.     

Variational theory for correlated lattice fermions in high dimensions

A diagrammatic approach to the evaluation of correlated variational wave functions for strongly interacting fermions is presented. Diagrammatic rules for the calculation of the one-particle density matrix and the Hubbard interaction are derived which are valid for arbitraryd-dimensional lattices. An exact evaluation of expectation values is performed in the limitd=. The wellknown Gutzwiller approximation is seen to become the exact result for the expectation value of the Hubbard Hamiltonian in terms of the Gutzwiller wave function ind=. An efficient procedure to correct the Gutzwiller approximation in finite dimensions is developed. A detailed discussion of expectation values ind= in terms of explicit antiferromagnetic wave functions is given. Thereby an approximate result for the ground state energy of the Hubbard model, obtained recently within a slave-boson approach, is recovered.     

Dynamical coupling in the differential equations approach to atom-diatom exchange reactions

The atomic exchange reaction A + BC → AB + C is investigated quantum mechanically employing a coupled differential equations approach. The relative motion in reactant and product channels is described in the common coordinate R ₃ (the AC nuclear separation) and is developed in three-dimensional space. The total wave functions of the system are expressed as a superposition of valence bond electronic states of the initial (A, BC) and final (AB, C) configurations, with the coefficients describing the relative and internal (vibrational, rotational) nuclear motions. Choosing convenient trial functions with the appropriate boundary conditions and using the Kohn variational principle, a set of differential (rather than the usual integro-differential) equations is obtained for the relative motion wave functions in R ₃. The potential matrix elements turn out to be dynamical in that they depend on the initial k ₁ and final k ₂ wave vectors. Two-state coupled channel calculations of the differential and integral cross sections for the isotopic species D + H₂, H + H₂ and D + D₂ are presented for collision energies up to 0·8 eV.     

Double ionization and excitation ionization in the Compton scattering of high-energy photons for metastable states of heliumlike ions

Double ionization and excitation ionization in Compton scattering for heliumlike ions in metastable states are investigated. The electron energy distribution for double ionization and the total cross sections for both processes are calculated. The calculations are carried out in the zeroth order of perturbation theory with respect to electron-electron interaction, using Coulomb wave functions as the first approximation. The resulting equations are valid only in the high-energy nonrelativistic range. It is assumed that Z≫1, but αZ≪1 (Z is the charge of the nucleus, and α is the fine-structure constant). Zh. éksp. Teor. Fiz. 116, 1889–1902 (December 1999)     

The generalized Bethe logarithm for tightly bound electrons

We derive a closed relativistic expression that makes it possible to calculate the self-energy of multiply charged ions in an external Coulomb field without resorting to a series expansion in powers of αZ. The expression contains the generalized Bethe logarithm for tightly bound electrons. We do numerical calculations of the self-energy for the 1s _1/2-electrons of multiply charged hydrogenlike ions. The proposed method allows for self-energy calculations for any values of the nuclear charge Z. Zh. éksp. Teor. Fiz. 112, 1197–1208 (October 1997)     

Resonances and Gamow States in Non-Local Potentials

For a large class of non-local, non separable potentials with non-compact support, the solution of the radial integrodifferential equation may be reduced to the solution of a homogeneous linear integral equation of Fredholm type with a quadratically integrable kernel. In this way we derive expansions of the wave functions and the Green's function of the Schrödinger equation with a non-local potential in terms of bound states, resonant states and a continuum of scattering functions with complex wave number. The rules of normalization, orthogonality and completeness satisfied by the eigenstates of the Schrödinger equation belonging to complex eigenvalues with Im E_n < 0, (Gamow or resonant states) are also derived. Finally, by means of a realistic example, it is shown how to use these expansions to exhibit the resonant behaviour of the differential cross section. Explicit expressions for the transition amplitudes and the partial widths in terms of expectation values of operators computed with Gamow functions are given.     

Computer simulation of the non-local dielectric function of polar liquids: boundary conditions revisited

For the calculation of ε(k) via the correlation function of the bound charge density fluctuations or the ratio of the bound charge density to an external charge density, a generalized form of the fluctuation dissipation theorem is derived which accounts for different types of boundary conditions through a modified Green's function. It is demonstrated for the case of an interaction site model of water that it is possible to obtain consistent results for the non-local dielectric function with different types of boundary conditions. This is shown by calculating ε(k) both from the correlation function 〈ρ_b(k)ρ_b(-k)〉 and from the dielectric response to an external electric field.     

Relativistic configuration interaction calculations for the K α X-ray transitions of Co XV to Co XXVI ions

Relativistic configuration interaction calculations with the inclusion of the Breit interaction, quantum electrodynamics (QED) and finite nuclear mass corrections have been carried out in the extended optimal level scheme using multiconfiguration Dirac-Fock wave functions on the wavelengths, electric dipole rates, oscillator strengths and line strengths of cobalt ions with a single vacancy in the K shell. The calculated values are compared with the other available data on He-like to Be-like cobalt and are found to be in very good agreement with them. This confirms the present calculations. We predict new data for several levels where no other theoretical and/or experimental results are available. These data provide reference values for level lifetimes, charge state distribution and the average charge of cobalt plasmas.     

Three-Parameter Wave Functions for ns2-Orbitals in Alkali—Metal Negative Ions

A three-parameter variational wave function is used to describe the binding energy of alkali—metal negative ions using a two-electron system in the ns²-state. Each electron is described by a modified screened hydrogenic wave function involving two free screening parameters denoted by c and a in addition to the core-screened nuclear charge, . The model is applied to lithium, sodium, potassium, rubidium, and cesium anions, where the optimum values of the variational parameters are deduced through fitting the optimized energy to the available experimental values. It is also applied to group-II isoelectronic neutral atoms of Be, Mg, Ca, Sr, and Ba. The results of our calculation are compared with other two-electron methods.     

Effect of Polarization Temperature on the Chain Segment Motion and Space Charge Detrapping in Polyamide 610 Film Electrets

The effect of polarization temperature on the chain segment motion and charge trapping and detrapping in polyamide 610 films has been investigated by means of thermally stimulated depolarization current (TSDC) and wide-angle X-ray diffraction (WAXD). A small part of the amorphous phase of quenched polyamide 610 changes into the crystalline state with increasing polarization temperature. There are three current peaks (named α, ρ₁, and ρ₂ peak, respectively) in the TSDC spectra. The α peak corresponds to the glass transition, the ρ ₁ peak is attributed to space charge trapped in the amorphous phase, and interphase between crystalline and amorphous phases, and the ρ ₂ peak originates from space charge trapped in the crystalline phase. By analyzing the characteristic parameters of these peaks, it was found that the increase of polarization temperature induced a decrease of the chain segment mobility and promoted the creation of structural traps in polyamide 610. The decrease of the chain segment mobility in the amorphous phase made the intensity of the α peak weak and the activation energy increased. The higher the polarization temperature, the higher the degree of crystallinity and the more charge carriers trapped in the crystalline phase. So, the increase of polarization temperature made the intensity of the ρ ₂ peak strong and increased the stability of trapped charge in the crystalline phase. The increase of polarization temperature also made the intensity of the ρ ₁ peak strong and decreased the stability of trapped charge in the amorphous phase and interphase.     

原子核体积效应对类锂离子体系基态能量的修正

用全实加关联的方法得到类锂离子15~22s(Z=21～30)波函数,给出了原子核体积效应公式,计算了原子核的体积效应及质量效应对类锂离子能级的修正.结果显示。在中等大小的核电核情形,原子核体积效应对类锂离子能级的修正要比质量效应对类锂离子能级的修正要显著;随着核电核数的增加,原子核体积效应越来越重要.     

原子核体积效应对类锂离子体系基态能量的修正

用全实加关联的方法得到类锂离子1s22s（Z=21~30）波函数, 给出了原子核体积效应公式, 计算了原子核的体积效应及质量效应对类锂离子能级的修正. 结果显示, 在中等大小的核电核情形, 原子核体积效应对类锂离子能级的修正要比质量效应对类锂离子能级的修正要显著; 随着核电核数的增加, 原子核体积效应越来越重要.     

Tests of quantum electrodynamics using ion traps

Experiments in ion traps on the g factors for the free and the bound electron in low-Z, hydrogen-like ions have provided the most accurate tests of quantum-electrodynamics calculations. Moreover they have been used to determine new and precise values for fundamental constants. Extensions to more stringent tests using ions of higher values of the nuclear charge Z are on the way. Also other QED tests such as Lamb shifts or hyperfine structures in H-like ions using traps will be feasible in the near future. The tests in bound systems, however, will be limited by nuclear structure effects which are difficult to calculate. Assuming the QED calculations as correct, the experimental results may be used to determine nuclear contributions and thus support nuclear models. Contribution presented at the TCP06, Vancouver Island, 2006.     

类锂体系(Z=21—30)基态1s22s电离能和相对论项能的理论计算

使用全实加关联方法和里兹(Ritz)变分方法计算了类锂体系(Z=21—30)基态1s²2s的非相对论能量和波函数；包括动能修正、电子-电子接触项、轨道-轨道相互作用项以及Darwin项的相对论修正和质量极化项由全实加关联波函数的一阶微扰给出，量子电动力学修正QED(quantum electronic dynamic)由有效核电荷方法和类氢公式计算；给出了中等核电荷的高电离类锂体系基态的电离能、相对论效应的项能(term energy)，并将计算结果与实验数据进行了比较，表明FCPC 关键词： 类锂体系 全实加关联 电离能 项能