A relativistic canonical symplectic particlein-cell method for energetic plasma analysis

A relativistic canonical symplectic particle-in-cell(RCSPIC)method for simulating energetic plasma processes is established.By use of the Hamiltonian for the relativistic Vlasov-Maxwell system,we obtain a discrete relativistic canonical Hamiltonian dynamical system,based on which the RCSPIC method is constructed by applying the symplectic temporal discrete method.Through a 106-step numerical test,the RCSPIC method is proven to possess long-term energy stability.The ability to calculate energetic plasma processes is shown by simulations of the reflection processes of a high-energy laser(1?×?1020 W cm-2)on the plasma edge.

Application of Homotopy Analysis Method to Solve Relativistic Toda Lattice System

In this letter, the homotopy analysis method is successfully applied to solve the Relativistic Toda lattice system. Comparisons are made between the results of the proposed method and exact solutions. Analysis results show that homotopy analysis method is a powerful and easy-to-use analytic tool to solve systems of differential-difference equations.

Relativistic Schrodinger Wave Equation for Hydrogen Atom Using Factorization Method

In this investigation a simple method developed by introducing spin to Schrodinger equation to study the relativistic hydrogen atom. By separating Schrodinger equation to radial and angular parts, we modify these parts to the associated Laguerre and Jacobi differential equations, respectively. Bound state Energy levels and wave functions of relativistic Schrodinger equation for Hydrogen atom have been obtained. Calculated results well matched to the results of Dirac’s relativistic theory. Finally the factorization method and supersymmetry approaches in quantum mechanics, give us some first order raising and lowering operators, which help us to obtain all quantum states and energy levels for different values of the quantum numbers n and m.

Relativistic Calculations for Be-like Iron

Relativistic configuration interaction calculations for the states of 1s^22s^2, 1s^22s3l （l = s,p,d） and 1s^22p31 （l=s,p,d） configurations of iron are carried out using relativistic configuration interaction （RCI） and multi-configuration Dirac-Fock （MCDF） method in the active interaction approach. In the present calculation, a large-scale configuration expansion was used in describing the target states. These results are extensively compared with other available calculative and experimental and observed values, the corresponding present results are in good agreement with experimental and observed values, and some differences are found with other available calculative values. Because more relativistic effects are considered than before, the present results should be more accurate and reliable.

Relativistic Configuration Interaction Calculations on Kα X-Ray Satellites of Manganese

With contributions from Breit interaction, quantum electrodynarnics （QED） corrections and nuclear mass corrections to the initial and final levels are taken into account. The transition energies, transition probabilities, and absorption oscillator strengths of Kα x-ray from Mn XVII to Mn XXIV have been calculated by using relativistic configuration interaction （RCI） and multi-configuration Dirac Fock （MCDF） method in the active interaction approach. Compared with the only available experimental transition data on He-like and Li-like manganese, the present results are in good agreement with them, and the rest of transition data of the present results are new ones. These wide range data can provide useful parameters for the study of the manganese plasma.

Effect of High-Frequency Electric Field on Propagation of Electrostatic Wave in a Non-Uniform Relativistic Plasma Waveguide

The effect of a high frequency （HF） electric field on the propagation of electrostatic wave in a 2D non-uniform relativistic plasma waveguide is investigated. A variable separation method is applied to the two-fluid plasma model. An analytical study of the reflection of electrostatic wave propagation along a magnetized non-uniform relativistic plasma slab subjected to an intense HF electric field is presented and compared with the case of a non relativistic plasma. It is found that, when the frequency of the incident wave is close to the relativistic electron plasma frequency, the plasma is less reflective due to the presence of both an HF field and the effect of relativistic electrons. On the other hand, for a low-frequency incident wave the reflection coefficient is directly proportional to the amplitude of the HF field. Also, it is shown that the relativistic electron plasma leads to a decrease in the value of reflection coefficient in comparison with the case of the non relativistic plasma.

Nonlinear ion-acoustic solitary waves in an electron-positron-ion plasma with relativistic positron beam

The propagation characteristics of nonlinear ion–acoustic（IA） solitary waves（SWs） are studied in thermal electron–positron–ion plasma considering the effect of relativistic positron beam. Starting from a set of fluid equations and using the reductive perturbation technique, we derive a Korteweg–de Vries（KdV） equation which governs the evolution of weakly nonlinear IA SWs in relativistic beam driven plasmas. The properties of the IA soliton are studied, and it is shown that the presence of relativistic positron beam significantly modifies the characteristics of IA solitons.

Relativistic R-matrix calculations for L-shell photoionization cross sections of CⅡ

The photoionization cross section of the ground state 2s22p 2Po1/2 and the first excited state 2s22p2po1/2 of C II ions are systematically calculated using the fully relativistic R-matrix code DARC. The detailed resonances are presented and identified for the photon energy ranging from threshold （24.38 eV） up to 41.5 eV where the L-shell （2p, 2s） photoionization process is dominant. In the calculations, the relativistic effect and electronic correlation effect are well considered. It is found that the relativistic effect is very important for the light atomic system CII, which accounts for experimentally observed fine structure resonance peaks. A careful comparison is made between the present results and the experimental values, and also other theoretical data available in the literature, showing that good agreement is obtained for the resonance peaks.

K-P-Burgers equation in negative ion-rich relativistic dusty plasma including the effect of kinematic viscosity

The stationary solution is obtained for the K–P–Burgers equation that describes the nonlinear propagations of dust ion acoustic waves in a multi-component, collisionless, un-magnetized relativistic dusty plasma consisting of electrons, positive and negative ions in the presence of charged massive dust grains. Here, the Kadomtsev–Petviashvili(K–P) equation, threedimensional(3D) Burgers equation, and K–P–Burgers equations are derived by using the reductive perturbation method including the effects of viscosity of plasma fluid, thermal energy, ion density, and ion temperature on the structure of a dust ion acoustic shock wave(DIASW). The K–P equation predictes the existences of stationary small amplitude solitary wave,whereas the K–P–Burgers equation in the weakly relativistic regime describes the evolution of shock-like structures in such a multi-ion dusty plasma.

Relativistic atomic data for W XLVⅡ

Energy levels, radiative rates, and lifetimes are calculated for all levels of 3s23p, 3s23d, 3s3p2, 3s3d2, 3s3p3d, 3p23d, 3s3d2, 3p3d2, 3p3, and 3d3 configurations of Al-like tungsten ion （W XLVII）. Multiconfigurational Dirac-Fock （MCDF） method is adopted for calculating energy levels and radiative rates. Oscillator strengths, radiative rates, and line strengths are reported for some E1 transitions from the ground level. Comparisons are made with the available data in the literature and good agreement has been found which confirms the reliability of our results.

Propagation of Electrostatic Waves in an Ultra-Relativistic Dense Dusty Electron-Positron-Ion Plasma

The nonlinear propagation of waves (specially solitary waves) in an ultra-relativistic degenerate dense plasma (containing ultra-relativistic degenerate electrons and positrons, cold, mobile, inertial ions, and negatively charged static dust) have been investigated by the reductive perturbation method. The linear dispersion relation and Korteweg de-Vries equation have been derived whose numerical solutions have been analyzed to identify the basic features of electrostatic solitary structures that may form in such a degenerate dense plasma. The existence of solitary structures has been also verified by employing the pseudo-potential method. The implications of our results in astrophysical compact objects have been briefly discussed.

Relativistic Study of Spinless Particles for Generalized Hylleraas Potential with Position Dependent Mass

The relativistic study of spinless particles under a special case of equal scalar and vector generalized Hylleraas potential with position dependent mass has been studied. The energy eigenvalues and the corresponding wave functions expressed in terms ofa Jacobi polynomial are obtained using the parametric generalization of NU （Nikiforo-Uvarov） method. In obtaining the solutions for this system, we have used an approximation scheme to evaluate the centrifugal term （potential barrier）. To test the accuracy of the result, we compared the approximation scheme with the centrifugal term and the result shows a good agreement with the centrifugal term for a short-range potential. The results obtained in this work would have many applications in semiconductor quantum well structures, quantum dots, quantum liquids. Under limiting cases, the results could be used to study the binding energy and interaction of some diatomic molecules which is of great applications in nuclear physics, atomic and molecular physics and other related areas. We have also discussed few special cases of generalized Hylleraas potential such as Rosen-Morse, Woods-Saxon and Hulthen potentials.

Quasi-Radial Modes of Pulsating Neutron Stars: Numerical Results for General-Relativistic Rigidly Rotating Polytropic Models

In this paper we compute general-relativistic polytropic models simulating rigidly rotating, pulsating neutron stars. These relativistic compact objects, with a radius of ~10 km and mass between ~1.4 and 3.2 solar masses, are closely related to pulsars. We emphasize on computing the change in the pulsation eigenfrequencies owing to a rigid rotation, which, in turn, is a decisive issue for studying stability of such objects. In our computations, we keep rotational perturbation terms of up to second order in the angular velocity.

基于实稳定方法的原子核单粒子共振相对论Hartree-Fock模型

利用坐标空间的实稳定方法,在相对论Hartree-Fock(RHF)理论框架下发展了原子核单粒子共振态结构模型.具体以^(120)Sn的低激发中子共振态为例,探讨了交换项在影响共振能量、宽度以及自旋-轨道劈裂等性质中的作用.相较于一般的相对论平均场(RMF)理论,RHF中交换项的引入改变了核介质中有效核力的动力学平衡机制,进而影响共振态单粒子势的描述.对于一般的宽共振态,这可能导致相对更低的共振能量和更小的共振宽度.此外,对^(120)Sn共振态中νi_(13/2)与νi_(11/2)自旋伙伴态,还分析了交换项对其自旋-轨道劈裂的相关效应.与束缚态情形相比,共振态中自旋伙伴态的波函数可能存在显著区别,单粒子有效势与能量也相应发生改变.结果表明,不仅自旋-轨道相互作用,单粒子有效势中其他成分也是影响共振态自旋-轨道劈裂的重要因素.

Adomian Decomposition Method and Padé Approximants for Nonlinear Differential-Difference Equations

Combining Adomian decomposition method （ADM） with Pade approximants, we solve two differentiaidifference equations （DDEs）： the relativistic Toda lattice equation and the modified Volterra lattice equation. With the help of symbolic computation Maple, the results obtained by ADM-Pade technique are compared with those obtained by using ADM alone. The numerical results demonstrate that ADM-Pade technique give the approximate solution with faster convergence rate and higher accuracy and relative in larger domain of convergence than using ADM.

Influence of the Earth's rotation on measurement of gravitational constant G with the time-of-swing method

In the measurement of the Newtonian gravitational constant G with the time-of-swing method,the influence of the Earth's rotation has been roughly estimated before,which is far beyond the current experimental precision.Here,we present a more complete theoretical modeling and assessment process.To figure out this effect,we use the relativistic Lagrangian expression to derive the motion equations of the torsion pendulum.With the correlation method and typical parameters,we estimate that the influence of the Earth's rotation on G measurement is far less than 1 ppm,which may need to be considered in the future high-accuracy experiments of determining the gravitational constant G.

Computing Differentially Rotating Neutron Stars Obeying Realistic Equations of State by Using Hartle’s Perturbation Method

In this paper, we use the well-known Hartle’s perturbation method in order to compute models of differentially rotating neutron stars obeying realistic equations of state. In our numerical treatment, we keep terms up to third order in the angular velocity. We present indicative numerical results for models satisfying a particular differential rotation law. We emphasize on computing the change in mass owing to this differential rotation law.

AnAdaptive Moving Mesh Method for Two-Dimensional Relativistic Hydrodynamics

This paper extends the adaptive moving mesh method developed by Tang and Tang[36]to two-dimensional(2D)relativistic hydrodynamic(RHD)equations.The algorithm consists of two“independent”parts:the time evolution of the RHD equations and the(static)mesh iteration redistribution.In the first part,the RHD equations are discretized by using a high resolution finite volume scheme on the fixed but nonuniform meshes without the full characteristic decomposition of the governing equations.The second part is an iterative procedure.In each iteration,the mesh points are first redistributed,and then the cell averages of the conservative variables are remapped onto the new mesh in a conservative way.Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed method.

Electron-impact ionization of W^(9+)and W^(10+)

Electron-impact single-ionization(EISI)cross sections for W^(q+)(q=9,10)ions have been calculated by using the level-to-level distorted-wave(LLDW)method with emphasis on the contribution of metastable states to the total ionization cross sections.Contributions from direct-ionization(DI)and excitation-autoionization(EA)processes are taken into account.The calculated cross sections include the contributions from both the ground configuration and the long-lived metastable states with lifetimes exceeding 10^(-6)s.Calculated cross sections are in good agreement with experimental measurements when the influence of metastable states on the total ionization cross section are well considered.

Magic wavelengths for 6s_(1/2)→5d_(3/2,5/2)transitions of Yb~+ions

The wave functions,energy levels and matrix elements of Yb+ions are calculated using the relativistic configuration interaction plus core polarization(RCICP)method.The static and dynamic electric dipole polarizabilities of the ground state and low-lying excited states are determined.Then,the magic wavelengths of the magnetic sublevel 6s_(1/2,m=1/2)→5d_(3/2,m=±3/2,±1/2)and 6s_(1/2,m=1/2)→5_(d5/2,m=±5/2,±3/2,±1/2)transitions in the linearly,right-handed,and left-handed polarized light are further determined.The dependence of the magic wavelengths upon the angle between the direction of magnetic field and the direction of laser polarization is analyzed.