Quantum Mayer Graphs for Coulomb Systems and the Analog of the Debye Potential

Within the Feynman–Kac path integral representation, the equilibrium quantities of a quantum plasma can be represented by Mayer graphs. The well known Coulomb divergencies that appear in these series are eliminated by partial resummations. In this paper, we propose a resummation scheme based on the introduction of a single effective potential that is the quantum analog of the Debye potential. A low density analysis of shows that it reduces, at short distances, to the bare Coulomb interaction between the charges (which is able to lead to bound states). At scale of the order of the Debye screening length ^–1 _D, approaches the classical Debye potential and, at large distances, it decays as a dipolar potential (this large distance behaviour is due to the quantum nature of the particles). The prototype graphs that result from the resummation obey the same diagrammatical rules as the classical graphs of the Abe–Meeron series. We give several applications that show the usefulness of to account for Coulombic effects at all distances in a coherent way.     

Guest Charge and Potential Fluctuations in Two-Dimensional Classical Coulomb Systems

A known generalization of the Stillinger-Lovett sum rule for a guest charge immersed in a two-dimensional one-component plasma (the second moment of the screening cloud around this guest charge) is more simply retrieved, just by using the BGY hierarchy for a mixture of several species; the zeroth moment of the excess density around a guest charge immersed in a two-component plasma is also obtained. The moments of the electric potential are related to the excess chemical potential of a guest charge; explicit results are obtained in several special cases. Unité Mixte de Recherche No. 8627—CNRS.     

含时库仑势和线性势的薛定谔方程的求解

利用Burgan等人的时空变换方法对一类特殊形式的具有含时库仑势加线性项的薛定谔方程进行了分析和计算,并进一步讨论了更普遍形式的含时势V(r,t)=–a0ξ12r+nk=1akrkξk2+1(其中ξ=at2+bt+c,a0,a1,a2,…,an,a,b,c是满足一定关系的常数)的波函数     

Potential energy shift for a screened Coulomb potential

Utilizing Hartree-Fock self-consistent field wave functions, accurate values of the potential energy shift at the nucleus due to atomic electrons have been determined for a large number of atoms. An extensive numerical table of values of the shift,V ₀, is given and comparison is made with earlier approximate results obtained from the Thomas-Fermi and Thomas-Fermi-Dirac statistical models and with estimates fromK binding energy data. In the calculation of screening corrections to Fermi functions, the Hartree-Fock results present a considerable improvement over earlier estimates from the aforementioned methods.     

一种周期库仑作用势优化法的改进

利用简单多项式基组拟合变化平缓的长程作用部分,并增加多个限定条件以提高优化势与库仑势的局部重合度,对Natoli优化法进行改进.在不增加计算复杂度的前提下,得到平均偏差明显降低的优化势;建议优化时划分r空间与k空间的准则取k_cr_c ≥ 15.在稠密液氢分子模拟中,优化法获得的能量及压力均小于Natoli法与Ewald法的结果.     

Exchange-Correlation Contribution for the Thermodynamic Functions of a Hydrogen Plasma

For a hydrogen model the exchange-correlation energy is calculated at any degree of degeneracy. The numerical data run into the T=O — RPA values, which were evaluated independently. An equation of state for hydrogen without bound states is compared with HNC-calculations in the nondegenerate limit. The influence of increasing y=m_iw/m_e — values for the agreement with limiting results derived analytically is given in detail.     

Classical Scattering in the Covariant Two-Body Coulomb Potential

The problem of two relativistically-moving pointlike particles of constant mass is undertaken in an arbitrary Lorentz frame using the classical Lagrangian mechanics of Stückelberg, Horwitz, and Piron. The particles are assumed to interact at events along their world lines at a common world time, an invariant dynamical parameter which is not in general synchronous with the particle proper time. The Lorentz-scalar interaction is assumed to be the Coulomb potential (i.e., the inverse square spacetime potential) of the spacetime event separation. The classical orbit equations are found in 1 + 1 spacetime dimensions in the hyperbolic angle coordinates for the reduced problem. The solutions to the reduced motion in these coordinates are the spacetime generalizations of the nonrelativistic Kepler solutions. and they introduce an invariant eccentricity which is a function of other known constants of the motion for the reduced problem. Solutions compatible with physical scattering are obtained by the assumption that the eccentricity is a given function of the ratio of the particle masses.     

On the Equation of State of Coulomb Systems

A quantum statistical expression is given for the pressure of multi-component plasmas which is correct up to the second cluster coefficient. The Montroll-Ward formula for the pressure is evaluated for any degree of degeneration. As an example the thermodynamic stability of an electronhole plasma is discussed.     

库仑加线性位基态解析解

应用新发展的单一轨迹积分方法求解库仑加线性位的基态量子波函数,得到基态能量和波函数的一般解析表达式,并讨论了解的收敛性.应用此方法讨论了重夸克偶素系统.     

Borromean Windows for Three-Particle Systems under Screened Coulomb Interactions

We have carried out calculations to search Borromean windows(BWs) for 11 different three-body systems interacting with screened Coulomb(Yukawa-type) potentials using Hylleraas-type wave functions within the framework of a variational approach. The critical values of the screening parameters for the ground states of the systems under consideration are reported for which the three-body systems are stable, while all the possible fragments are unbound;that is, it shows windows for Borromean binding.     

New Form for the Coulomb Potential in Complex Crystals. Part I

The Coulomb potential is constructed for a crystal with a basis by the method of the Green's functions approximated by the lattice sum of spherically symmetric electron densities of free atoms. The application of the new method with improved convergence of the lattice series in the Green's function has allowed us to obtain an additional term in the electron part of the potential, which describes attraction and can be considered as a potential of the Coulomb hole. The method was applied to calculate the potentials for carbon in the diamond lattice and for TiC solid solution in the direction of four nearest neighbors. Some typical results are presented to illustrate the capabilities of the method.     

New Form for the Coulomb Potential in Complex Crystals. Part II

Results of calculations of the Coulomb and crystal potentials of stoichiometric TiC, TiN, and TiO compounds and ordered FeCo alloy are presented. It is demonstrated that the knowledge of these potentials allows preliminary conclusions on the electronic structure of solids to be made.     

New Form for the Coulomb Potential in Complex Crystals. Part III

The present paper continues our works [1, 2] devoted to the construction of the Coulomb potential at an arbitrary point of the unit cell of crystals with a close-packed hexagonal (CPH) lattice by the Green's function method. Convergence of the real space and reciprocal lattice sums in the Green's function is investigated and the optimal convergence parameter is chosen. The method is used to construct the Coulomb potential in Ti, Co, and Zn metals. Calculations are performed for four directions. Nonmonotonic behavior of nuclear and electron components of the potential in the cell is established. The crystal potential is also calculated for these metals with allowance for the exchange interaction in the Slater approximation.     

Relativistic Scattering States of Coulomb Potential Plus a New Ring-Shaped Potential

In this paper, exact solutions of scattering states of the Klein-Gordon equation with Coulomb potential plus a new ring-shaped potential are studied under the condition that the scalar potential is equal to the vector potential. The normalized wave functions of scattering states on the “k/2π scale” and the calculation formula of phase shifts are presented. Analytical properties of the scattering amplitude are discussed.     

A New Method for the Atomic Ground-State Energy in the Screened Coulomb Potential

The new method proposed recently by Friedberg,Lee and Zhao is applied to the derivation of the atomic ground-state energy with the inclusion of the screening effect.The present results are compared with those obtained in the pure Coulomb potential and by the variational approach.The overall good results are obtained with this new method.``     

A New Method for the Atomic Ground-State Energy in the Screened Coulomb Potential

The new method proposed recently by Friedberg,Lee and Zhao is applied to the derivation of the atomic ground-state energy with the inclusion of the screening effect.The present results are compared with those obtained in the pure Coulomb potential and by the variational approach.The overall good results are obtained with this new method.     

Generalized Pseudospectral Method for Solving the Time-Dependent Schrodinger Equation Involving the Coulomb Potential

We present an accurate and efficient generalized pseudospectral method for solving the time-dependent Schrodinger equation for atomic systems interacting with intense laser fields. In this method, the time propagation of the wave function is calculated using the well-known second-order split-operator method implemented by the numerically exact, fast transform between the grid and spectral representations. In the grid representation, the radial coordinate is discretized using the Coulomb wave discrete variable representation （CWDVR）, and the angular dependence of the wave function is expanded in the Gauss-Legendre-Fourier grid. In the spectral representation, the wave function is expanded in terms of the eigenfunctions of the field-free zero-order Hamiltonian. Calculations on the high order harmonic generation and ionization dynamics of hydrogen atom in strong laser pulses are presented to demonstrate the accuracy and efficiency of the present method. This new algorithm will be found more computationally attractive than the close-coupled wave packet method using CWDVR and/or methods based on evenly spaced grids.     

Uncertainty Relation for the Radial Momentum and Radial Coordinate in the Coulomb Potential

We have obtained the uncertainty relations for arbitrary states of the hydrogen atom. It is shown that the minimal value of the uncertainty relation (Δp_rΔr → ?2) is attained for the circular Rydberg states.