Multiconfiguration Hartree-Fock calculations in Cr5+, Mn6+ and Fe7+

The multiconfiguration Hartree-Fock (MCHF) method is used to calculate the excitation energies and oscillator strengths, of both the length (f _L) and velocity (f _V) forms, for 1s²2s²2p⁶3s²3p⁶3d² D→1s²2s²2p⁶3s²3p⁵3d^{2 2} P ⁰,² D ⁰,² F ⁰ transitions in Cr⁵⁺, Mn⁶⁺ and Fe⁷⁺ ions of the potassium isoelectronic sequence. Comparison is made with our earlier relevant results obtained by employing the configuration interaction (CI) method which is closely related to the MCHF method. Our present investigation demonstrates that the MCHF method is more accurate than the CI method in all ions of present consideration.     

Correct bound states of the non- linear oscillator through non-variational method: Failure of the variational method

A method for obtaining correct bound states of the non-linear oscillatorH = P ²+X ² +X ²(X ²) is described. It is shown that the variational method fails to yield correct ground state energy.     

用代数-能量自洽法研究双原子分子解析势能函数

基于计算双原子分子完全振动能谱及离解能的代数方法 (algebraic method,AM)和研究双原子分子解析势能函数的能量自洽法(energy consistent method,ECM),建立了计算双核分子体系精确解析势能函数的代数-能量自洽法(AM-ECM).应用AM-ECM方法研究了7Li+2-23Σg,KH-X1Σ+,NaLi-X1Σ+和NaLi-A1Σ+电子态的解析势能表达形式,并与其他方法的研究结果进行了比较,获得了能正确描述这些电子态在渐近区和离解区的精确解析表达结果.     

Method of Hoogenstraaten as a tool for obtaining the trap parameters of general-order thermoluminescence glow peaks

The Hoogenstraaten method is a technique that uses various heating rates for obtaining the activation energy E (eV) in the case of first-order thermoluminescence glow peaks. This method can also be used for obtaining E (eV) for all types of glow peaks regardless of their kinetics order (b). The present work shows that the intercept of the Hoogenstraaten relation, which is usually used for obtaining the frequency factor S (s ^?1) of the first-order glow peak, can be used as a very good approximation to obtain the pre-exponential factor S ^{′ ′} (s ^?1) in the case of general-order glow peaks, when one uses Hoogenstraaten’s method to obtain E (eV). In addition, the present work suggests a numerical method for obtaining the kinetics order of the general-order glow peak. The method depends on the activation energy E (eV) obtained by the Hoogenstraaten method and the above-mentioned approximation for obtaining the pre-exponential factor S ^{′ ′} (s ^?1). An independent evaluation of the suggested methods for obtaining the trap parameters, the activation energy E (eV), the pre-exponential factor S ^{′ ′} (s ^?1) and the kinetics order (b) is illustrated here by taking a numerically computed glow peak and applying a one-trap and one-recombination-center model.     

Theoretical calculations of spin-Hamiltonian parameters and defect structures for Cu2+ in trigonally-distorted tetrahedral sites of ZnO and GaN crystals

The spin-Hamiltonian (SH) parameters (g factors g _//, g ⊥ and hyperfine structure constants ⁶³ A _//, ⁶³ A ⊥, ⁶⁵ A _//, ⁶⁵ A ⊥) for Cu²⁺ ions in the trigonally-distorted tetrahedral sites of ZnO and GaN crystals are calculated from a complete diagonalization (of energy matrix) method (CDM) based on a two spin-orbit parameter model for d ⁹ ions in trigonal symmetry. In the method, the Zeeman and hyperfine interaction terms are added to the Hamiltonian in the conventional CDM. The calculated results are in good agreement with the experimental values. The calculated SH parameters are also compared with those using the traditional diagonalization method or perturbation method only within the ² T ₂ term. It appears that, for exact calculations of SH parameters of d ⁹ ions in trigonal tetrahedral clusters in crystals, the present CDM is preferable to the traditional diagonalization method or perturbation method within the ² T ₂ term. The local structures of Cu²⁺ centers (which differ from the corresponding structure in the host crystal) in ZnO : Cu²⁺ and GaN : Cu²⁺ are obtained from the calculations. The results are discussed.     

Successive approximation to determine rotational temperature

A method using successive approximation is developed for determining the rotational temperatures, when the rotational lines are overlapped. The method is applied to CH (B ² Σ ⁻ −X ² II) band as a test.     

A nonperturbative stability theory of quantum field theory models

A nonperturbative method of analysis of the stability problem of quantum field theory models is proposed. The method consists in the systematic analysis of the functional dependence on boson field B of the effective boson Lagrangian S^eff(B) consisting of the fermion term S_l^F(B), constraint term S_l^FP(B) and the boson self-interaction term S_l(B). A new heat kernel representation for S_l^F(B) is derived in which counterterms are calculated in the explicit functional form by means of the analytic renormalization method. Using these results the instabillity of Yukawa₄, four-Fermi₄, and the massive Gürsey models is demonstrated.     

A Maximum Entropy Method Based on Piecewise Linear Functions for the Recovery of a Stationary Density of Interval Mappings

Let S:[0,1]→[0,1] be a nonsingular transformation such that the corresponding Frobenius-Perron operator P _S :L ¹(0,1)→L ¹(0,1) has a stationary density f ^∗. We propose a maximum entropy method based on piecewise linear functions for the numerical recovery of f ^∗. An advantage of this new approximation approach over the maximum entropy method based on polynomial basis functions is that the system of nonlinear equations can be solved efficiently because when we apply Newton’s method, the Jacobian matrices are positive-definite and tri-diagonal. The numerical experiments show that the new maximum entropy method is more accurate than the Markov finite approximation method, which also uses piecewise linear functions, provided that the involved moments are known. This is supported by the convergence rate analysis of the method.     

密度泛函方法对SiO分子基态（X 1Σ+）势能函数的研究

利用密度泛函B3P86方法,分别选用STO-3G,D95^**,6-311G,6-311++G,6-311++G^**,cc-PVTZ基组对SiO分子基态(X¹Σ⁺)进行结构优化计算.通过比较得出,cc-PVTZ基组为对SiO分子基态(X¹Σ⁺)进行结构优化最优基组的结论.使用密度泛函B3P86方法,选用cc-PVTZ基组进 关键词： B3P86 SiO 势能函数 光谱常数     

Investigations on the g factors of the ground and excited states for Cu2+ ions in ZnO crystal

The g factors g _// and g _⊥ of the ground Γ₆(² T ₂) and excited Γ_4,5(² E), Γ₆(² E) states for trigonal Cu²⁺ centres in ZnO crystals are calculated from three theoretical methods, the complete diagonalization (of the energy matrix) method, the second-order perturbation method (PTM-I) and the simplified second-order perturbation method (PTM-II, this method was described in an earlier paper). These methods are based on the cluster approach in which the spin-orbit coupling parameters ζ, ζ′ and the orbital reduction factors k, k′ are calculated from a semi-empirical molecular orbital method. The crystal-field parameters used in the calculations are obtained from the superposition model and so the defect structure of Cu²⁺ centres in ZnO can be acquired. The calculated g factors from the three methods are in reasonable agreement with the experimental values and the defect structure of Cu²⁺ centres in ZnO is acquired. It appears that in some cases the approximate PTM can be applied in the studies of g factors of various states. The conditions that the PTM are ineffective are discussed.     

Solution of three-dimensional Faddeev equations for three-body Coulomb bound states

A new method of directly solving the three-dimensional Faddeev equations in the total-angular-momentum representation for the pure Coulomb bound-state problem is developed. The method is based on the tri-quintic Hermite spline expansion of the Faddeev components. The ground states of thee ^– e ^– e ⁺ system and thepp ^– mesic molecule are calculated.     

Lifetimes of anion vacancies and <Emphasis Type="Italic">F</Emphasis><Stack><Subscript>2</Subscript><Superscript>+</Superscript></Stack> color centers in lithium fluoride following irradiation

A method is developed for determining the mean lifetime of anion vacancies in dielectric crystals following irradiation. This method is used to study the temporal kinetics of the concentrations of vacancies and F ₂⁺ color centers in lithium fluoride crystals irradiated by ionizing radiation. It is then possible to study the dependences of the vacancy lifetime on the concentration of F ₁ color centers, temperature, and impurity content of a crystal. Vacancy and F ₂⁺ color lifetimes determined by this method are given.     

Long range interaction energies between ground and first excited state hydrogen atoms using a one centre method

A one centre method is used to evaluate the long range interaction energies, through O(R ^-10), between ground and first excited state hydrogen atoms. General pseudo spectral results for both the direct and resonant parts of the expanded second and third order interaction energies are given through any order in R ^-1. Of particular interest is an O(R ^-9) third order energy which is totally resonant in character. The advantage of the one centre method for interactions involving degenerate energy states is discussed briefly.     

Using the seventh-order numerical method to solve first-order nonlinear coupled-wave equations for degenerate two-wave and four-wave mixing

Using a new seventh-order numerical method [theO(h ⁷) method] for solving two-point boundary value problems, numerical solutions of the first-order nonlinear coupledwave equations for degenerate two-wave and four-wave mixing in a reflection geometry have been obtained. A computer program employing the Gauss-Jordan elimination technique has also been adopted to effectively solve the resultant large, sparse and unsymmetric matrix, obtained from theO(h ⁷) method and the Newton-Raphson iteration method. Numerical results from the computer calculations are presented graphically. A comparison between thisO(h ⁷) method and the shooting method, mainly from the viewpoint of computational efficiency, is also made.     

Constructing unified models based on E8 in ten dimensions

The vacuum energy is calculated for Yang-Mills (YM) system defined inD dimensional space-time ofS ¹×R ^d (D=d+1), where the possibility of the YM fields to acquire the vacuum expectation values onS ¹ is taken into account. The vacuum energy has already been obtained to the order of one-loop in many people. Here we calculate the vacuum energy inD dimensions to two-loop order. With an intention to reach higher loops, an approximation method is proposed, which is especially effective in higher dimensions. By this method, we can treat the higher-loop contributions of YM interactions as easily as we treat one-loop effect. As a check, we show reproduction of the two-loop contribution (D-dependence of the coefficient as well as the functional form) when the coupling constant is small. This approximation method is useful not only for the Kaluza-Klein theories but also for the finite temperature-density system (as a quark-gluon plasma).Minami-Ohsawa Hachioji-shi, Tokyo 92-03 Japan     

Algebraic method of determining bond length of perovskite compounds doped with Mn

An algebraic method is proposed for calculating the exponent n and constant K in the power law 10Dq=KR⁻ⁿ. By using this method, the values of n and K for the cubic perovskites KMnF₃ and RbMnF₃ are derived and then used to determine the true Mn²⁺–F⁻ bond length R in crystals of KMgF₃, KZnF₃, RbCdF₃, and CsCaF₃ doped with Mn²⁺ from the reported optical spectra. The results obtained are in good agreement with those derived from the electron paramagnetic resonance data and the extended X-ray absorption fine structure techniques. Thus, as a new theoretical method, it is valuable and convenient for the determination of the bond lengths.     

Measurement of στ product of solid state laser materials by an alternative method: Application to Nd3+ doped YVO4 crystal for 4 F 3/2→4 I 11/2 transition

In this paper an alternative approach for measurement of στ product for ⁴ F _3/2→⁴ I _11/2 transition of Nd³⁺ doped YVO₄ crystal is reported. In this method a microchip laser is formed by keeping a small piece of the sample in plane-plane resonator and a diode laser (808 nm) is used for pumping. The pump power induced thermal lensing effect is used to make the cavity stable. The cavity mode area is estimated by measuring the thermal lens focal length at the threshold and the average pump area is measured by Gaussian fit to the intensity profiles of the pump beam. The value of στ product of Nd:YVO₄ crystal obtained by this method is within 10% of the reported values. The advantage of this method is that it is a simple method for direct measurement of στ product of laser crystals.     

Sequential Cavity Method for Computing Free Energy and?Surface Pressure

We propose a new method for the problems of computing free energy and surface pressure for various statistical mechanics models on a lattice ℤ ^d . Our method is based on representing the free energy and surface pressure in terms of certain marginal probabilities in a suitably modified sublattice of ℤ ^d . Then recent deterministic algorithms for computing marginal probabilities are used to obtain numerical estimates of the quantities of interest. The method works under the assumption of Strong Spatial Mixing (SSP), which is a form of a correlation decay. We illustrate our method on the hard-core and monomer-dimer models, on which we improve several earlier estimates. For example we show that the exponential of the monomer-dimer coverings of ℤ³ belongs to the interval [0.78595,0.78599], improving best previously known estimate of [0.7850,0.7862] obtained in (Friedland and Peled in Adv. Appl. Math. 34:486–522, 2005; Friedland et al. in J. Stat. Phys., 2009). Moreover, we show that given a target additive error ε>0, the computational effort of our method for these two models is (1/ε) ^O(1) both for the free energy and surface pressure values. In contrast, prior methods, such as the transfer matrix method, require exp ((1/ε) ^O(1)) computation effort.     

弹性矩形板方程在非线性边界条件下整体解的存在唯一性

考虑了在非线性边界条件下的弹性矩形板方程.利用Galerkin方法,首先证明了该方程在非线性边界(a)及初值w⁰∈W,w¹∈W的条件下初边值问题存在唯一整体弱解w(t).其次证明了该方程在非线性边界(b)及初值w⁰∈W₁,w¹∈W₁的条件 关键词： 弹性矩形板方程 非线性边界条件 初边值问题 整体解     

Complex-scaling treatment for high-lying doubly excited resonances for screened Coulomb helium atom

This work presents an investigation on the doubly excited ¹S ^e autoionizing states of screened helium atom lying below the n = 4 threshold of the He⁺ ion. The potential generated in this system is represented by a Yukawa type potential. We have employed complex-coordinate rotation method, as it is a powerful scheme to study high lying resonances. Hylleraas type wave function is used to consider the correlation effect between all the charged particles. Our resonance parameters for the resonances lying below the He⁺ (n = 2) threshold agree well with those of the existing calculations by using the stabilization method. Resonances associated with higher thresholds are new calculations. All the present results are well converged with basis length N = 444.