Perturbation theory for fluids of rod-like molecules interacting via the Kihara potential

For systems of molecules interacting via the Kihara core potential a first-order perturbation theory is proposed. As a reference system soft convex bodies are employed with interactions given by the entire repulsive part of the original pair potential (i.e. for surface-to-surface distances smaller than that of the potential minimum). Their equilibrium behaviour is interpreted on the basis of the representative hard convex bodies-parallel convex bodies to the assumed cores with temperature-dependent thickness. The shape of the distribution function was approximated by the Verlet-Weis form. Theoretical expressions were used for the determination of the thermodynamic functions of the Kihara-molecule systems at several reduced temperatures and compared with experimental data for nitrogen.     

A uniform approximation for one-dimensional matrix elements

A general expression for one-dimensional perturbation integrals is derived, which requires no knowledge of the radial wavefunctions. It is shown to generalize and to unify all available semi-classical approximations, and, further, to reduce to a number of known results for the curve-crossing problem and to the Jackson-Mott for the Landau-Teller vibrational relaxation model.     

Calculation of the Lenz-Jensen potential using the third order approximation

The Lenz-Jensen potential was calculated using the third and fourth order approximations in the expression for the electron density, instead of the conventional first order approximation. A screening function is obtained which differs from Thomas-Fermi screening only at very large distances.     

A uniform approximation for the eigenmodes of a planar dielectric waveguide

This paper derives a new approximation for the eigenmodes of a planar waveguide. The approximation is uniformly valid at both the high and low frequency regions of the dispersion relation. It is shown that a Pade approximation of the frequency equation leads to very accurate solutions. The new approximate solution is used to compute the frequency spectrum and the results compared with the exact analytical solution. The solutions presented here are ideal for analytically studying transient wave fields by means of modal summation.     

Twofold-broken rational tori and the uniform semiclassical approximation

We investigate broken rational tori consisting of a chain of four (rather than two) periodic orbits. The normal form that describes this configuration is identified and used to construct a uniform semiclassical approximation, which can be utilized to improve trace formulae. An accuracy gain can be achieved even for the situation when two of the four orbits are ghosts. This is illustrated for a model system, the kicked top. Received 3 August 1999     

Cluster coherent potential approximation for disordered photonic crystals using photonic Wannier functions

We present an investigation of disordered photonic crystals (PhCs) based on the combination of photonic Wannier functions with the concept of the coherent potential approximation (CPA). In particular, we provide the theoretical foundation of a real-space cluster CPA that is causal, enforces the proper symmetries of the effective medium, and includes effects of multiple scattering of the same and nearby defects, which is essential for strong defects. Based on this, we present results for the density of states of disordered PhCs for different types of disorder. Our results are thus relevant to such diverse areas as random lasing and the analysis of fabricational imperfections in PhCs.     

Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation

The relation between the Wilson–Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson–Polchinski case in the study of which they fail).     

The supersymmetric WKB approximation for Hartmann potential

Using the method of supersymmetric WKB approximation, the energy spectrum of some noncentral separable potentials can be exactly obtained in r and θ dimensions. We take the Hartmann potential as an important example for its validation, and the result is consistent with that obtained by using the supersymmetric quantum mechanics and shape invariance.     

PuN基态和低激发态的分子结构与相对论有效原子实势

用Pu的三种不同相对论有效原子实势 (RECP)和密度泛函(B3LYP)方法对PuN基态和低激发态(4Σ+、6Σ+、8Σ+、10Σ+)的分子结构进行了计算,得到了相应的平衡几何构型和谐振频率.采用最小二乘法拟合得到了PuN分子的Murell-sorbie势能函数,在此基础上推导出完整的力常数和光谱数据,并与实验值作对比.结果表明:PuN的基态为X6Σ+,其余为低激发态;在三种RECP中,对于ωe的计算,60个中心电子的SDDRECP/B3LYP给出的结果与实验值符合得比较好(如X6Σ+:ωe=840.77 cm-1,ωeχe=5.73·"cm-1,De=5.880 6 eV,Re=0.176 3 nm,Be=0.408 4 cm-1,αe=3.3E-03 cm-1).计算还给出了相应的电荷布居、自旋密度、电偶极矩和能量特征等系列分子的性质.     

Optical potential in the gas approximation

Using the gas approximation the optical potential is expressed as a function of the scattering matrix of nucleon-nucleon scattering. The formalism of Green functions is used. The imaginary part of the optical potential in nuclear matter is calculated for high energies using the experimental phase shifts. In addition, a calculation of the imaginary part is made using theS-wave part of the Tabakin potential.     

Analyticity of the coherent potential approximation

A general proof is presented that the coherent potential approximation does not violate analyticity requirements.     

A uniform approximation to the scattering and propagation problem for a stratified Bi-anisotropic slab

The scattering and propagation problem for time-harmonic waves in a stratified bi-anisotropic slab is considered. Based upon the identification of the left- and right-moving modes, and on a boundedness assumption concerning the space and frequency dependence of the physical parameters, a sequence of approximate solutions which converge absolutely and uniformly to the exact solution are derived. In particular, if the magnetoelectric coupling is small and the permittivity and permeability vary slowly, the approximate solutions converge so fast that the first approximation already gives a satisfactory approximation. With the present approximation method, approximate solutions valid for all frequencies can be obtained in explicit form.     

An analytic representation for the potential of a uniform elliptic cone

In view of the fact that various gravitating and charged bodies may have singular points on their surface, the problem of the effect of these singularities in the mass distribution on the behavior of potential arises. The analytic representation for gravitational and electrostatic potentials of a uniform elliptic cone in terms of ordinary integrals is derived. Generally, these integrals are somewhat more complicated than the elliptic ones; however, they reduce to elementary functions in the case of a circular cone. The arbitrariness in the way of truncating a cone manifests itself in the possibility of adding various harmonic polynomials. However, the singularity of potential in the vicinity of the vertex of a cone is of an objective and unique character.     

Accuracy of the unitary pole approximation for the reid triplet potential

The unitary pole approximation (UPA) has been shown to be quite accurate for a central attractive potential with a soft core, such as the Reid singlet potential. We examine its accuracy for the Reid triplet soft-core potential, which includes tensor and spin-orbit forces. We compare UPA values for the t-matrix t_LL′(p, k; s) with Haftel's numerical values. Here L and L′ are angular momenta, either 0 or 2. The momenta are p and k, and we emphasize negative energy s. We find that the UPA fits Haftel's values for t₀₀ about as well as the UPA fits for the Reid singlet. The UPA is less successful for t₀₂ and t₂₂, but in general it fits Haftel's values better than does the Yamaguchi t-matrix.     

Small chain approximation for the electronic structure of polyacetylene

It is demonstrated that many properties of interest for polyacetylene chains can be predicted on the basis of Hartree-Fock calculations on short model molecules. The equilibrium geometries, energies per C₂H₂ unit, and isomerization energies converge by a chain length of six or eight carbons. The ionization potential, band gaps, and band widths converge more slowly, but their limiting values can be obtained readily by extrapolating results of calculations on chains up to a length of eight carbons.     

Coherent potential approximation for strong-coupling superconducting transition-metal alloys

Within the coherent potential approximation (CPA) a theory for strong-coupling superconducting transition-metal alloys is developed. The configurational dependence of the selfenergy-part is discussed and, in analogy to McMillan, an expression forT _c is derived for a singles band as well as for anΓ′₂₅-band. The electron-phonon coupling constantλ occuring in this expression depends explicitly on: the average component density of states,N _A (0) andN _B (0), the electron-phonon matrix elements of the components, the difference of the atomic energy levels,δ, and the phonon Green's function at zero frequency. In the limit of the pure metal this expression reduces to that developed by Appel and Kohn. It is shown that the change of the phonon density of states in an alloy due to the atomic mass differences — which is very complicated — does not influence the value ofλ.     

Quasiclassical approximation with the centrifugal potential excluded

We develop a modification of the WKB method (the modified quantization method, or MQM) for finding the radial wave functions. The method is based on excluding the centrifugal potential from the quasiclassical momentum and changing correspondingly the phase in the Bohr-Sommerfeld quantization condition. MQM is used to calculate the asymptotic coefficients at zero and at infinity. We use the examples of power-law and funnel potentials to show that MQM not only dramatically broadens the possibilities of studying the energy spectrum and the wave functions analytically but also ensures accuracy to within a few percent even when one calculates states with a radial quantum number n _r ∼1, provided that the angular momentum l is not too large. We also briefly discuss the possibility of generalizing MQM to the relativistic case (the spinless Salpeter equation). Zh. éksp. Teor. Fiz. 116, 511–525 (August 1999)     

The image potential in the weighted-density approximation

Summary We analyse the image potential of a metal surface in the weightede-density approximation and obtain an analytical expression for the position of the image plane which is independent of the surface electronic structure. We conclude that the position of the plane image given by this density functional approximation cannot be accepted as a physical result.