Calculation of bridge function coefficients via modified Mayer-samplings

Two modified Mayer-sampling methods are described based on Transition Matrix Monte Carlo (TMMC) and overlap sampling for calculating the integrated diagrams appearing in the coefficients of the bridge function; b_n (r) constructed in terms of the total correlation function h(r) for a hard-sphere system. Calculations are performed using prescribed h(r) for reduced densities at 0.2, 0.5 and 0.8 up to the third-order expansion in density. The results from these methods compared with the generic Monte Carlo Mayer-sampling are analysed in detail. It was found that the TMMC Mayer-sampling approach shows better precision over core and tail regions of b ₂(r) and b ₃(r), and the overlap sampling method shows overall improvement in the precision of the bridge coefficients. Both methods can be straightforwardly applied to calculate higher order bridge function coefficients and to any model systems with relatively simple modifications.     

Calculation of photoelectron spectra of the trihalides of group v elements

The SCF-Xα-SW method is applied to calculate the ionization energies of the trihalides of all of the Group V elements. The calculated orbital energies agree very well with reported experimental ionization energies. The molecular-orbital orderings obtained coincide with recent experimental orbital assignments. The results are also compared with previous ab initio, semiempirical and Xα calculations for NF₃, PF₃, PCl₃ and PBr₃. The comparison indicates that the present results show improved agreement with experiment and clarify certain ambiguities in the earlier molecular-orbital assignments.     

The fifth virial coefficients of fused hard sphere fluids

The virial coefficients up toB ₅ of 34 fused hard sphere models have been computed using about (4–10)×10⁵ trial configurations of a modified Monte Carlo integration method. The principle of the conformal behaviour of hard particle systems is tested against these data. It is found that while for the fourth coefficient the principle is satisfied in all the cases, the fifth coefficients exhibit more complicated behaviour and do not conform, in general, to this principle.     

CG系数的计算

从角动量的对易关系出发,直接计算了两个角动量耦合的Clebsch-Gordan系数.     

UV photoelectron spectra of group IV alkyl hydrides

We have had occasion to measure the photoelectron spectra of some heavy group IV alkyls and alkyl hydrides. Although the ionization potentials serve primarily as a body of information which is useful in investigating trends in reactivity for processes involving electron transfer [1], they also provide a pleasing example of the simplicity with which the language of molecular orbital theory can be used to explain trends in the energies and nature of the radical cation states of a series of chemically related molecules [2].     

Morse 势中矩阵元Xνν′、Pνν′的计算

矩阵元ＸＶＶ’和ＰＶＶ’在有关量子力学问题中有相关重要的应用，本文利用广义拉盖尔多项式的正交性和分部积分的方法，推导Ｍｏｒｓｅ势中ＸＶＶ’、ＰＶＶ’的计算公式。     

Calculation and use of the coefficients in Dunham's function to determine the spectroscopic characteristics of diatomic molecules

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 52, pp. 451–454, March, 1990.     

Clebsch-Gordan coefficients for the Poincaré group

All Clebsch-Gordan coefficients for the Poincaré group are calculated by a simple global method.     

Calculation of the Kirchhoff coefficients for the Helmholtz resonator

A Helmholtz resonator is a shell Ω_shell separating a compact cavity Ω_int from a noncompact outer domain Ω_out. A small opening Ω ^δ in the shell connects the cavity with the outer domain, causing the transformation of real eigenfrequencies of the Neumann Laplacian in the cavity into the complex scattering frequencies of the full spectral problem for the Neumann Laplacian on Ω = ℝ³\Ω_shell. The Kirchhoff model of 1882, see [21], gives a convenient ansatz

Calculation of linear and nonlinear optical absorption coefficients of a spherical quantum dot with parabolic potential

In the effective mass approximation, we calculated the binding energy and wave function for the 1s-, 1p-, 1d- and 1f-states of a spherical quantum dot (QD) with parabolic potential by using a combination of quantum genetic algorithm (QGA) and Hartree-Fock-Roothaan (HFR) method. In addition, we also investigated the linear and the third-order nonlinear optical absorption coefficients as a function of the incident photon energy for the 1s-1p, 1p-1d and 1d-1f transitions. Our results are shown that the existence of impurity has great influence on optical absorption coefficients. Moreover, the optical absorption coefficients are strongly affected by the incident optical intensity, relaxation time, parabolic potential and dot radius.     

X-ray attenuation coefficients of elements and mixtures

This paper is concerned with X-ray attenuation in samples of pure elements and mixtures of elements. The emphasis is on the energy range 30–150 keV although the energy regions 10–30 and 150–1000 keV are also discussed. The approximations involved in deriving several well known formulae for the photoelectric and scattering cross-sections are described and the accuracy of these formulae is assessed. More accurate formulae are derived by reference to fundamental theory. It is shown that definitions of such quantities as effective atomic number cannot be justified from fundamental theory. The consequences of this result are explored in relation to various experimental conditions and the physical parameters of a complex medium which can be determined by X-ray transmission measurements are identified. Connections with related areas of interest in atomic physics and low energy X-ray scattering are made.     

Hyperspherical harmonics approach to the trinucleon system with Reid soft core potential: Calculation of geometrical structure coefficients

We present the full set of equations for the solution of the trinucleon problem by the hyperspherical harmonics expansion (HHE) method where nucleons interact via the Reid soft core (RSC) potential. The coupling potential matrix elements are expressed in terms of geometrical structure coefficients (GSC) and potential multipoles (PM). Introduction of GSC greatly simplifies the calculation of the potential matrix and makes the numerical algorithm efficient. A method for calculating all the twelve independent sets of GSC needed, by using the completeness property of the Jacobi polynomials has been presented. A convenient sum rule for each set of GSC has also been derived and precision of the calculated GSC has been checked by the sum rule. Such calculations of GSC are efficient and fast, in view of the complexity of the HHE equations.     

Calculation of the spin-lattice coupling coefficients in cubic symmetry

The relationships between spin-lattice coupling coefficients G₁₁, G₄₄ in cubic symmetry and the zero-field splittings in low symmetry have been put forward and hence the simple methods of calculating these coefficients from the formulae of zero-field splittings are given. According to these, the coefficient G₄₄ can be obtained very easily from two cases, one from the derivative of zero-field splitting D in trigonal symmetry with respect to the bonding angle β and another from the derivative of splitting E in rhombic symmetry with respect to the angle θ. So, one can, in a certain degree, check whether the formulae of D in trigonal field and E in rhombic field based on different mechanisms and models are consistent and reliable by comparing the formulae of G₄₄ obtained from the two cases.     

Metal-nonmetal transition in the boron group elements

Structural competition in boron group elements has been studied by means of ab initio calculations. For boron we predict a structural change alpha-B-->alpha-Ga accompanied by a nonmetal-metal transition at a pressure of about 74 GPa. For Al and Ga we find an icosahedron based elemental modification (alpha-B) 0.22 and 0.05 eV/atom, respectively, higher in energy than the corresponding metallic ground state structures. In particular, the low energy difference for Ga raises expectations into the experimental feasibility of new modifications for these elements, especially in nanosized systems.     

Calculation of geometrical coupling coefficients for the hyperspherical harmonics approach

An elegant and fast method for the calculation of geometrical structure coefficients needed for an expansion of a few-body wavefunction and interaction in hyperspherical harmonics has been proposed. A sum rule for the GSC has also been derived, which is useful for an independent check of the coefficients. The proposed method of computation is many orders of magnitude faster than conventional methods.     

氙等离子体输运性质计算

采用基于将Chapman-Enskog方法扩展到高阶近似的方法计算获得了温度范围在300—40000 K,不同压力条件下氙等离子体的黏性、热导率和电导率.热力学平衡条件下的计算结果与文献报道的实验和计算结果符合良好,验证了计算方法和结果的合理性与准确性.在此基础上,计算获得了电子温度(T e)不等于重粒子温度(T h)的热力学非平衡和化学平衡条件下氙等离子体的输运性质,并分析了输运性质随压力和热力学非平衡程度变化的原因.     

双温度氦等离子体输运性质计算

获得覆盖较宽温度和压力范围内的等离子体输运性质是进行等离子体传热和流动过程数值模拟的必要条件.本文采用Saha方程计算等离子体组分, 采用基于将Chapman-Enskog方法扩展到高阶近似的方法, 计算获得了电子温度(T_e)不等于重粒子温度(T_h)的情形下, 在300 K到40000 K的温度范围内氦等离子体的黏性、热导率和电导率. 研究结果表明压力和热力学非平衡参数(θ =T_e/T_h)对氦等离子体的输运性质有较大的影响. 在局域热力学平衡条件下,计算获得的氦等离子体输运性质和文献报道的数据符合良好.