Ab initio calculation of the spin-orbit coupling constant from gaussian lobe SCF molecular wavefunctions

The spin-orbit coupling constants of BH⁺ and CH have been calculated using ab initio molecular SCF wavefunctions with the gaussian lobe function basis set. It is demonstrated that fair agreement with experimental values can be achieved even with a relatively small basis set, provided that no terms are neglected in calculating the matrix elements.     

Evaluation of the path integrals for non-interacting electron gas in a random gaussian potential

A new method based on the direct calculation of infinite products is developed in order to evaluate the functional integrals representing the one- and two-particle canonical density matrices for the Bezák's model of a disordered solid. The present results are in agreement with those obtained by an integral transform method (Barta, Papadopoulos).     

Three-center integrals of one-electron operator of a spin-orbit interaction

A computational algorithm for three-center integrals in matrix elements of a spin-orbit interaction operator is developed. The explicit form of the integrals is derived. Empirical and calculated atomic constants of the spin-orbit interaction are compared. The effect of interatomic spacing in the atom chain on the magnitude of integrals is considered. Distinctions between one-center and multicenter approximations as well as the range of application are analyzed using planar and nonplanar compounds as examples. Siberian Physicotekhnical Institute at Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 68–78, July 2000.     

An analysis of millimeter wave quasi-optical gaussian beam radiation-perturbational expansion method

In this paper perturbational expansion of wave equation is used to analyse the Gaussian beam radiation efficiency and the near field distribution of aperture antenna. The analysis is also suitable at large angles from boresight because the Gaussian beam used here is corrected to satisfy wave equation. An approach of minimum deviation of aperture field is used to calculate the Gaussian beam radiation efficiency, and calculation results is compared with that of Wydle's[1].     

Ab initio calculation of spin-orbit coupling constants for gaussian lobe and gaussian-type wave functions

The spin-orbit coupling constants of a series of diatomic compounds containing first row atoms have been calculated using ab initio molecular wave functions with gaussian lobe and gaussian-type basis sets. In most cases, fair agreement with the experimental values has been achieved. It is pointed out that multicentre terms have almost no effect on the spin-orbit coupling constant. Furthermore, suggestions for a one-electron approximation using effective nuclear charges are presented.     

A double expansion method for calculating molecular properties

Using a form of double perturbation theory we present results of calculations on the ground state energies for the diatomic systems H₂ ⁺, HHe²⁺, H₂ and HHe⁺. For the homonuclear systems the energy values are unexpectedly good. For the heteronuclear cases the results are very encouraging and lead to optimism about the application of the method to larger systems which contain one heavy atom.     

An expansion method for calculating molecular properties IV.

The energies of the 2pσ and 2sσ states of H₂ ⁺ and HeH²⁺ and those of the a ³, A ¹, b ³, B ¹Σ⁺ states of HeH⁺ are calculated up to second order in the heavy nuclear charge. For the one-electron systems the first-order equation is solved analytically employing a special separation technique for degeneracies. The consideration of screening enables a recently proposed interchange result for the degenerate case to be tested. The results for the 2sσ states are good while those for the 2pσ states are only good at small internuclear distances.

For the two-electron systems the method employed is a single perturbation approach for two perturbations in the presence of degeneracy. The results for HeH⁺ appear to be good only at small internuclear distances. The corresponding results for the excited states of H₂ are omitted since an interesting problem arises at first order.     

Geometric approach to asymptotic expansion of Feynman integrals

We present an algorithm that reveals relevant contributions in non-threshold-type asymptotic expansion of Feynman integrals about a small parameter. It is shown that the problem reduces to finding a convex hull of a set of points in a multidimensional vector space.     

Scattering of gaussian beam by a ferrite cylinder

The scattering of a Gaussian beam by a ferrite cylinder is analyzed using two methods. The spatial pictures in the amplitude of the total Gaussian beam near the cylinder resulting from the two methods are both clarified and compared. The scattering by a ferrite cylinder coating a dielectric sleeve is also presented.     

On the spin-orbit splitting of the rare gas-monohalide molecular ground state

The spin orbit splitting of the molecular ground state of two atomsA(² P _{1/2, 3/2}) andB(¹ S ₀) is discussed. If the spin orbit matrix elements do not depend on the internuclear distance, it is sufficient to know any two of the three potentials of the ground state manifold. The third can then be calculated analytically. Data are presented for theA II 1/2 state of F+Ne; (F, Br)+(Ar, Kr, Xe); and Cl+Xe, as well as for theA I 3/2 state of HeNe⁺.     

Evaluation of the integrals of target/seabed scattering using the method of complex images

In this paper the integrals which arise in target/seabed scattering problems are examined. These are the integrals which express the propagation of a spherical harmonic term in a fluid above or below a half-space and the integrals which compute the conversion coefficients of outgoing spherical harmonics into incident spherical harmonics after a seabed reflection. A very efficient and accurate method of computing these integrals, using the method of complex images, is derived. Numerical comparisons with the exact integral expressions show the accuracy of this approach.     

Evaluation of two-photon nonlinearity by a semiclassical method

In order to discuss the two-photon nonlinearity theoretically, both photons and nonlinear materials should be treated quantum mechanically, which usually is a heavy theoretical task. Contrarily, nonlinear optics for classical light has been developed well and a detailed analysis is possible for realistic complex nonlinear systems. Here we show that the two-photon nonlinearity can be evaluated from the linear and third-order nonlinear output fields against a classical input pulse, which contains 2(-1/2) photons on average.     

Evaluation of functional integrals around a continuous set of important field configurations

For euclidean functional integrals, the relevance of configurations beyond the set of classical solutions is investigated. We propose an equation to select the important configurations and derive general expressions for their contribution to the integral. Employing a pseudoparticle picture, we perform a dilute-gas approximation and estimate finite-density corrections through a virial expansion. The methods are exemplified for the anharmonic oscillator and the double well potential.     

The spherical harmonic expansion coefficients and multidimensional integrals in theories of liquids

The Conroy integration method is re-considered and new sets of parameters are provided which permit to use as much as 150 000 sample points for twelve-fold integrals. The method is applied to various functions important in theories of liquids and compared with the approach based on the spherical harmonic expansion where it is possible.     

Approximation to the two-step diffusion profile by a series of gaussian functions

The two-step diffusion profile is approximated by a series of gaussian functions. Its accuracy is dependent upon the number of terms used in the series, but independent of the number and the spacing of exact data points.     

Electron acceleration by gaussian electromagnetic beam in a stationary magnetic field

Relativistic electron motion in the electromagnetic Gaussian beam that propagates along a stationary magnetic field is studied. It is shown that, if the cyclotron resonance conditions are initially satisfied, electrons can be efficiently accelerated over a relatively small interval at a slightly lower rate than in a plane accelerating wave.     

Estimation of molecular orientations in disordered samples by a proton-NMR-based method

We introduce a procedure on the basis of proton nuclear magnetic resonance (NMR) for investigation of the orientation state of disordered samples like amorphous or nematic polymers. Advantageous features of this method are the following: (i) disorder of the sample is not a problem (other than in the case of X-ray); (ii) the method works faster than multidimensional NMR techniques; (iii) this procedure can be implemented also at more simple and inexpensive NMR spectrometers; and (iv) for the data evaluation it will be not necessary to know the molecular geometry. The latter is possible by introducing the expressions “relative orientation distribution” and “relative orientation degree” which characterize the difference of the orientation of the current sample in comparison to a reference sample. Contrary to the absolute orientation degrees the relative ones are easily available from wide-line proton NMR spectra. The method is demonstrated by applying it to monitor the qualitatively different behavior of the director fields of two liquid-crystalline polymer samples with different molecular weights which are exposed to a suddenly switched magnetic field. A temporary asymmetry of the orientation distribution could be detected and quantified.