Non-LTE spectral absorption coefficients for electronic band systems of diatomic molecules

Analytical expressions have been derived for the average non-LTE spectral absorption coefficients and the associated spontaneous spectral emission coefficients for electronic bands of anharmonic oscillators. Relatively simple differential expressions are provided for the important practical conditions under which the smeared-rotational-line approximation is applicable and for which individual rotational temperatures exist for the populations in each pair of the vibrational levels of interest. Further simplifications are given for the cases in which also vibrational temperatures exist for the populations of the two electronic states considered and in which the displacement of the band-heads from the band-centers can be neglected.     

Analytical representation of the higher virial coefficients of binary mixtures of additive hard spheres

Approximate expressions for the fourth and fifth virial coefficients of binary hard-sphere fluid mixtures are derived. The procedure used to obtain these expressions is based on that previously proposed by Wheatley [J. chem. Phys., 111, 5455 (1999)], but slightly modified. Wheatley's procedure starts from a prescribed general analytical form of the virial coefficients, from which the particular expression for each virial coefficient is obtained by imposing to the general form a number of limiting conditions. Here, we propose an alternative general expression of the virial coefficients and derive one more condition. This condition is satisfied when the fourth and fifth virial coefficients are expressed in the form we propose, but not when they are expressed in Wheatley's form. The agreement of the proposed analytical expressions with exact numerical data is excellent. The procedure can be extended to higher virial coefficients, although the lack of exact numerical data prevents any comparison.     

On coefficients of the Brody-Moshinsky type

Brody-Moshinsky coefficients of the axial type are introduced. It is shown that Brody-Moshinsky coefficients represent a particular case of Petrauskas coefficients. Analytic expressions for some sums of Petrauskas coefficients are obtained, and the examples of their application to calculating matrix elements are given. A number of analytic expressions for axial Petrauskas coefficients are presented in the Appendix.     

Perturbation of gamma-ray angular correlations following continual random reorientation of the axis of interaction

Attenuation coefficients of perturbed gamma-ray angular correlations are calculated for classical extranuclear fields which fluctuate at random both in direction and in magnitude. Explicit expressions are given for time-integral attenuation coefficients. Time-differential attenuation coefficients have been calculated numerically. The theory applies to any correlation time.     

Resonant transition radiation of solar radio bursts

We calculate the resonant transition radiation (RTR) using the most general formulas and obtain approximate analytical expressions describing the RTR dependence on the fast-particle velocity and magnetic-field intensity. Dependence of the RTR on the angle between the wave vector and the magnetic-field direction and also on the thermal velocity of background-plasma electrons is considered on the basis of approximate expressions for RTR, in which the longitudinal dielectric permittivity of the plasma is written neglecting the wave vector of transverse electromagnetic waves. The obtained dependences are combined into unified expressions for RTR coefficients. Comparison with the earlier found RTR coefficients is performed. It is shown that the obtained coefficients correspond better to the nature of the resonant transition radiation. Finally, the obtained RTR coefficients are used for interpretation of the radio emission of the solar burst of December 24, 1991. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 5, pp. 371–386, May 2007.     

Estimation of Thermal Expansion Coefficients of Rare-Earth Garnets in a Wide Temperature Range

Simple expressions were obtained for the thermal expansion coefficients of the rare-earth garnets, which allow to estimate their values in a wide temperature range in cases, when either the lattice unit cell parameters or the density of the material are known at 300 K. The expression giving the relationship between the thermal expansion and thermal conductivity coefficients for the rare-earth garnets has also been obtained. It is shown that the calculated values obtained with the use of these expressions are in a good agreement with the available experimental data for the garnets of different composition.     

A collisional approach to the calculation of time correlation functions. Transport coefficients of gases

A method of successive approximations is proposed for the evaluation of the time-correlation functions such as those that give the thermal transport coefficients of gases. The method is based on a calculation of the changes in correlations of appropriate functions of the molecular velocity which are a result of collisions in the gas. The decaying rates of the correlations are expressed as integrals of the differential collision cross section. When the first approximation is introduced in the expressions for thermal transport coefficients, results are obtained for the coefficient of binary diffusion and the viscosity and thermal conductivity of single-component systems which are identical with those of the first Chapman-Enskog solutions of the Boltzmann and Enskog equations. For the coefficients of viscosity and thermal conductivity in multicomponent systems, it is shown that the first approximation leads to expressions of the form of the Sutherland and Wassiljewa relations, respectively.     

Oscillations quantiques des coefficients de pouvoir thermoelectrique et de conductivite thermique: theorie et mesures dans Cd3As2

Quantum oscillations have been observed in the thermoelectric power and thermal conductivity coefficients of a semiconductor Cd₃As₂ single crystal. Theoretical expressions for these coefficients, taking into account the Landau level broadening, are derived in this paper. The good agreement found between the thermoelectric power measurements and the corresponding theoretical expressions for the temperature and magnetic field dependence of the quantum oscillation amplitudes and the absolute values of the amplitudes has allowed us to calculate effective mass values which are in agreement with Shubnikov-de Haas measurements.     

Properties of expansions in Legendre polynomial derivatives that show up in analysis of nonlinear vibrations of a viscous liquid drop

Analytical expressions for the coefficients of expansions of Legendre polynomial products in the first and second derivatives of the polynomials with respect to polar angles, as well as for the coefficients of expansions of derivative products in Legendre polynomials and their first derivatives, are derived. An interrelation between these expansion coefficients and a relationship between these coefficients and the Clebsch-Gordan coefficients are found. When axisymmetric nonlinear vibrations of a viscous liquid drop are investigated analytically, the toroidal component of the velocity field can be ignored, which significantly cuts the body of computation.     

Diffraction at a surface-impedance discontinuity in a closed waveguide

The Wiener-Hopf-Fock method is applied to a coaxial waveguide for which the impedance boundary conditions are given for one surface. Closed expressions are obtained for the moduli of the reflection and transmission coefficients, from which the characteristics of circular and rectangular guides may be deduced. These coefficients are expressed in formally identical ways for all closed systems. Transition to the limit of an open system is considered for a circular cylinder.     

A new approach to determining the waveguide mode index distribution

A new approach is presented to determining the profile characteristics of planar optical waveguides. The mode index value is developed into the Lagrange series in terms of mode number, which allows one to find analytical expressions for the coefficients of that series. This method is applied to evaluating the coefficients of mode index distribution for the step-index and four-layer step-index profiles.     

The operators governing quantum fluctuations of Yang-Mills multi-instantons onS 4 and their Seeley coefficients

We give explicit expressions for the Seeley coefficients of the fluctuation operator and the operator that appears in the Faddeev-Popov determinant, which arise in the calculation of quantum fluctuations around Yang-Mills multi-instantons.     

Thermal conduction and thermal diffusion in dilute polyatomic gas mixtures

A novel theoretical basis for the evaluation of the thermal conductivity and the thermal diffusion ratios of dilute polyatomic gas mixtures is derived within the semi-classical isotropic kinetic theory. New expressions for species diffusion coefficients, thermal diffusion coefficients, and thermal diffusion ratios are also obtained by using an expansion vector based upon the total energy of the molecules. Finally, practical and accurate expressions for the thermal conductivity and the thermal diffusion ratios are derived by using the recent theory of iterative transport algorithms, as developed by the authors. The resulting expressions can be used in either theoretical calculations or computational models of multicomponent flows.     

On the theory of X-ray coherent reflection from a rough surface

A solution of the problem of X-ray specular reflection from a statistically rough surface is presented. It is based on using the Green function formalism. The Kirchhoff formula is used to describe the transmission of the wave field through a rough interface. Generally, microscopically exact expressions for the coefficients of transmission through a rough surface and reflection from it are obtained by taking multiple scattering effects into account. Averaging of the obtained expressions over possible realizations of random roughness of the interface between media allows to obtain rigorous expressions for specular reflection and transmission coefficients. The behavior of exact solutions in the limiting case of infinite correlation lengths is studied. It is shown that, in this case, the obtained solution corresponds to the Debye-Waller normalization. Expressions for the reflection and transmission coefficients making it possible to carry out numerical calculations are obtained in the Bourret approximation of multiple-scattering theory.     

Vibrational relaxation and line widths in liquids dephasing by intermolecular forces

A theory of vibrational relaxation in liquids is presented in which the vibrations are loosely coupled to a bath or lattice of molecular translations and rotations by intermolecular forces. Using the second-order perturbation expressions familiar from magnetic resonance the secular contribution to the line width is calculated. Different coupling paths are considered and expressions given for the line widths in a liquid mixture in terms of number densities and diffusion coefficients valid when reorientation is slow and translation diffusional.     

Sum rules including first order quantum corrections for neutron scattering experiments on isotopic mixtures of monatomic fluids

The sum rules for neutron scattering experiments on monatomic isotopic mixtures are studied. The scattering is separated into a self part and a distinct part rather than into an incoherent part and a coherent part. Exact expressions for the moments are derived in terms of polynomials in ? ². The coefficients in these polynomials are sums of averages of hermitean operators that have a classical analogue. For the interpretation, the coefficients are approximated including first order quantum corrections.

It is argued that the separation into coherent and incoherent scattering is not justified in the presence of ‘isotopic incoherence’. Approximate expressions for the sum rules are proposed, in which combined averages (over the isotopic composition) appear of the scattering amplitudes and masses of the scattering atoms. These expressions, including first order quantum corrections to the sum rules, are not available in the literature.

The importance of correct averaging over the isotopic composition of expressions that involve scattering amplitudes and masses is discussed for the case of a maximum incoherent mixture of ³⁶Ar and ⁴⁰Ar.     

带有任意自旋粒子衰变产物的角分布

本文研究了具有任意自旋的粒子衰变为一个自旋为零,另一个自旋为1/2的粒子的角分布。给出了球谐函数展开式系数的表式。发现偶次球谐函数项的系数是和引起衰变的相互作用哈密顿量具体形式无关的。但是在球谐函数展开式的奇次项的系数却和一个参变数α有关,而α的值却反映了宇称守恒的相互作用和宇称不守恒的相互作用之间干涉作用的大小。我们给出了这些系数的极大值,发现凡是偶次项系数的极大值是随着衰变粒子自旋的增加而增加的,而奇次项系数的极大值却随着衰变粒子自旋的增加而减小。本文还给出了衰变着的粒子的密度矩阵作为展开式的系数的函数的表式。当这些展开式系数已经知道以后,用这些函数就能决定衰变前的粒子的极化状态,决定宇称守恒相互作用和宇称不守恒相互作用之间的干涉的程度。