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1.
A new analytical, independent-particle model potential with four shell-independent parameters is proposed, which is suitable for high, medium, and low Z atoms. The four parameters are determined for 101 atoms from Li to Lr by fitting the results of the X a method found in the literature. The average fitting error 0.675% of the new potential for the 101 atoms is far better than 3.92% of the widely used Green’s potential. The radial Schrödinger equation with the new potential is solved by using Numerov’s numerical method for 7 typical atoms: Ne, Ca, Zn, Zr, Sn, Yb, and Th. The energy eigenvalues, radial wave functions, and atomic ground-state energy are in good agreement with the results of the X a method. The new potential here shows greater flexibility and better accuracy compared with the Green’s potential. 相似文献
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V. V. Hoang 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2011,61(3):627-635
Glass formation in simple monatomic nanoparticles has been studied by
molecular dynamics simulations in spherical model with a free surface.
Models have been obtained by cooling from the melt toward glassy state.
Atomic mechanism of glass formation was monitored via spatio-temporal
arrangement of solid-like and liquid-like atoms in nanoparticles. We use
Lindemann freezing-like criterion for identification of solid-like atoms
which occur randomly in supercooled region. Their number grows intensively
with decreasing temperature and they form clusters. Subsequently, single
percolation solid-like cluster occurs at temperature above the glass
transition. Glass transition occurs when atoms aggregated into this single
percolation cluster are in majority in the system to form relatively rigid
glassy state. Solid-like domain is forming in the center of nanoparticles
and grows outward to the surface. We found temperature dependence of
potential energy, mean-squared displacement (MSD) of atoms, diffusion
constant, incoherent intermediate scattering function, radial distribution
function (RDF), local bond-pair orders detected by Honeycutt-Andersen
analysis, radial density profile and radial atomic displacement
distributions in nanoparticles. We found that liquid-like atoms in models
obtained below glass transition have a tendency to concentrate in the
surface layer of nanoparticles. However, they do not form a purely
liquid-like surface layer coated nanoparticles. 相似文献
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A closed form expression is given for the correlation function of a hard sphere dimer fluid. A set of integral equations is obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with Percus-Yevick approximation. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of the individual correlation functions are obtained. By the inverse Laplace transformation, the radial distribution function (RDF) is obtained in closed form out to 3D (D is the segment diameter). The analytical expression for the RDF of the hard dimer should be useful in developing the perturbation theory of dimer fluids. 相似文献
5.
应用简单的方法———Laplace变换法来求最弱受约束电子势模型(WBEPM势)的径向Schrdinger方程.通过这种方法使得两阶微分方程变为一阶微分方程,这样可以直接运用积分得到WBEPM势束缚态能量方程和归一化的波函数,所得结果与文献一致.更重要的是用Laplace变换得到径向波函数的两类新的递推关系.这种递推关系是有效主量子数和角量子数之间关系,在计算原子和分子跃迁几率时有着广泛的应用. 相似文献
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The Tietz–Hua (TH) potential is one of the very best analytical model potentials for the vibrational energy of diatomic molecules. By using the Nikiforov–Uvarov method and Pekeris approximation to the centrifugal term, we have obtained the solutions of the radial Schrödinger equation for the TH potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed form. Some remarks and numerical results are also presented for some diatomic molecules. 相似文献
8.
Analytical expressions and a numerical method for calculation of distribution functions of hard spheres gij(r) based on inverting the Laplace transform for functions rgij(r) obtained from the Percus—Yevick equation are obtained. The method for calculation of radial distribution functions is applicable for any distances between hard spheres; it is verified by comparison of numerical results and Monte Carlo simulations. The application of the developed method for calculation of the radial distribution functions of metal atoms is demonstrated. Distribution functions are required to construct a universal theoretical model of equation of state capable of describing both dense multicomponent gas and condensed substances (liquid or solid phases) with high accuracy which is substantially faster than computer experiments (Monte Carlo and molecular dynamics methods). 相似文献
9.
D. A. Eisa 《等离子体物理论文集》2012,52(4):261-275
The equilibrium properties of a multi‐component plasma of charged particles that interact through the coulomb and short‐range potentials are investigated. In particular, this article presents density expansions of the reduced distribution functions for more particles, our calculations are based on the Bogoliubov‐Born‐Green‐Kirkwood‐Yvon (BBGKY) hierarchy, we used the results to calculate the binary and triplet distribution functions. We obtained the analytical form of the classical triplet distribution functions for two component plasma; one of them is based on the Kirkwood superposition approximation (KSA) which is consisting of the assumption that the potential in a set of three particles is the sum of the three pair potentials, this is equivalent to assuming that the triplet distribution function is the product of the three radial distribution functions, and the other form is calculated by integration the triplet distribution function (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
F. C. Hoh 《International Journal of Theoretical Physics》1993,32(7):1111-1133
A model for a bound quark-antiquark system is constructed from quark spinor equations and the associated pseudoscalar massless interaction potential equations in a way departing from conventional relativistic quantum mechanics. From the so-constructed covariant meson equations, linear confinement arises naturally. Nonlinear radial equations for the pseudoscalar and vector mesons in the rest frame are derived without approximation. An internal complex space is introduced for representation of the quark flavors. Quark masses are generalized to operators operating on functions in this space. A simple model is proposed for the meson internal functions and mass operators producing the squares of the average quark masses as eigenvalues. The present space-time model calls for a particle classification scheme different from the usual nonrelativistic one. When combined with the internal model, it may account for the gross structure of the meson spectra together with the form of an empirical relation. Upper limits of bare quark masses are estimated from simplified analytical solutions of the radial equations and agree approximately with the bare quark masses obtained from baryon data in a companion paper. The radial equations are solved numerically yielding estimates of the strong interaction radii of the ground state mesons. 相似文献
11.
采用从头计算的多参考组态CI方法(MRCI) 和B原子Dunnings相关调和基函数含扩散基的大基组aug-cc-pVQZ对B+2分子的基态和低激发态的势能曲线进行计算 .利用Huxley函数、Murrell-Sorbie函数和最小二乘法拟合出了解析势能函数,并以此为基础计算出光谱常数.通过比较发现:Huxley 函数比MS函数的拟合方差更小,能更好地再现分子中原子间相互作用.采用两种函数所得解析势能函数与从头计算势能曲线间的误差RMS 均远小于化学精度4.184 kJ/mol的要求,表明所得解析势能函数很好地再现了这些态中原子间的相互作用情况,可用于更广泛的研究. 相似文献
12.
Unified treatment of the bound states of the Schioberg and the Eckart potentials using Feynman path integral approach
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We obtain analytical expressions for the energy eigenvalues of both the Schioberg and Eckart potentials using an approximation of the centrifugal term.In order to determine the e-states solutions,we use the Feynman path integral approach to quantum mechanics.We show that by performing nonlinear space-time transformations in the radial path integral,we can derive a transformation formula that relates the original path integral to the Green function of a new quantum solvable system.The explicit expression of bound state energy is obtained and the associated eigenfunctions are given in terms of hypergeometric functions.We show that the Eckart potential can be derived from the Schioberg potential.The obtained results are compared to those produced by other methods and are found to be consistent. 相似文献
13.
The Hellmann potential, which is a superposition of an attractive Coulomb potential -a/r and a Yukawa potential b e-δr/r, is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov-Uvarov (NU) method, we have obtained the approximate analytical solutions of the radial Schrödinger equation (SE) for the Hellmann potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented, which show good agreement with a numerical amplitude phase method and also those previously obtained by other methods. As a particular case, we find the energy levels of the pure Coulomb potential. 相似文献
14.
A complex variable meshless method for fracture problems 总被引:4,自引:0,他引:4
CHENG Yumin & LI Jiuhong . Shanghai Institute of Applied Mathematics Mechanics Shanghai University Shanghai China . Department of Building Engineering Xi’an University of Technology Xi’an China 《中国科学G辑(英文版)》2006,49(1):46-59
1 Introduction The meshless (or meshfree) method has been a hot topic and the development trend of numerical methods for many science and engineering problems in recent years. Comparing with the conventional numerical methods, such as the finite element method and the boundary element method, the meshless method is an approximation based on nodes, and does not form a mesh to determine the shape function in the domain, in which a problem is to be solved. The meshless method has some advantages … 相似文献
15.
H.-B. Valentini 《等离子体物理论文集》1979,19(2):81-96
A system of integro-differential equations describing the velocity distribution functions of the neutral atoms and of the ions and the radial profiles of the electric potential and the particle densities in the positive column at low pressures and high degrees of ionization is derived. This system is solved for a simplified, but self-consistent, plane model. Both the initial velocity of the ions and the neutral gas depletion caused by the ionization processes are taken into account. For a cylindrical model a solution is obtained for the region near the axis. With rising neutral gas temperature the radial ion flux density is slightly increasing. The pressure tensor, the heat flux tensor, and several components of the corresponding tensor of the fourth order for the ion gas are calculated. It is shown that on the axis the radial and the azimuthal ion temperatures are smaller than the neutral gas temperature because the ions generated out of neutral atoms are retarded during the flight to the axis. 相似文献
16.
A local Schr?dinger equation (LSE) method is proposed for solving the Schr?dinger equation (SE) of general atoms and molecules without doing analytic integrations over the complement functions of the free ICI (iterative-complement-interaction) wave functions. Since the free ICI wave function is potentially exact, we can assume a flatness of its local energy. The variational principle is not applicable because the analytic integrations over the free ICI complement functions are very difficult for general atoms and molecules. The LSE method is applied to several 2 to 5 electron atoms and molecules, giving an accuracy of 10(-5) Hartree in total energy. The potential energy curves of H2 and LiH molecules are calculated precisely with the free ICI LSE method. The results show the high potentiality of the free ICI LSE method for developing accurate predictive quantum chemistry with the solutions of the SE. 相似文献
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A single-parameter form approximating the transition potential in muonic atoms is presented. The single-parameter form yields comparable results with that obtained by the Barrett form in radial moment analysis. The single parameter,β, is isotopically independent and is uniquely defined by the particular transition of a given element. 相似文献
20.
C.J. Cannon 《Journal of Quantitative Spectroscopy & Radiative Transfer》1973,13(10):1011-1021
The theory of generalized analytic functions is used to obtain an exact closed form analytical solution to a transfer problem for spectral line radiation in a multi-dimensional atmosphere. The multi-dimensional full-space and half-space Green's functions so obtained are quite general and may be used, along with the corresponding orthogonality relationships, to obtain solutions to any general multi-dimensional radiative transfer problem involving model two-level atoms. An application of the method using perturbation techniques is illustrated. 相似文献