Structure of Regular Solutions of the Three-Body Schrödinger Equation near the Pair Impact Point

We investigate the six-dimensional Schrödinger equation for a three-body system with central pair interactions of a more general form than Coulomb interactions. Regular general and special physical solutions of this equation are represented by infinite asymptotic series in integer powers of the distance between two particles and in the sought functions of the other three-body coordinates. Constructing such functions in angular bases composed of spherical and bispherical harmonics or symmetrized Wigner D-functions is reduced to solving simple recursive algebraic equations. For projections of physical solutions on the angular bases functions, we derive boundary conditions at the pair impact point.     

Analytic properties of solution of electronic Schrödinger equation

Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 88, No. 1, pp. 31–36, July, 1991.     

Reinterpretation of the fluorescence excitation spectrum of hexafluorobiacetyl in a supersonic jet

The results of the analysis of the fluorescence excitation spectrum of trans-hexafluorobiacetyl published earlier are revised. New values of torsion frequencies and potential barriers of internal rotation of the CF₃ group in the ground and excited states of the molecule are obtained. A procedure for calculating the probabilities of torsional vibronic transitions of molecules is described. Translated fromZhurnal Struktumoi Khirnii, Vol. 38, No. 2, pp. 293–302, March–April, 1997.     

Potential function of internal rotation for isoprene from ab initio calculations and experimental data

Ab initio computations of the potential energy curve of internal rotation around the central single C---C bond of isoprene have been performed at the Hartree—Fock level with a 3·21G basis set. The similarity of the slope of the curve obtained and the potential energy curve calculated for a more complete basis set (7s3p/4s2p) [Kavana-S2ebø, J. Mol. Struct. 106 (1984) 259] is discussed. The values of the Pitzer function F(φ), its Fourier expansion coefficients, and coefficients of the potential energy expansion were calculated from data given in the above reference. The correction of the potential energy expansion coefficients was carried out from frequencies of torsional “hot” bands of isoprene and torsional overtone of its second rotational isometric form. It was shown that the isoprene second isomer is realized as a gauche-form. The potential energy expansion coefficients were obtained as follows: V₁ = 399.9, V₂ = 1330.22, V₃ = 781.8 and V₄ = −175.8 cm⁻¹.     

Interaction of antiprotons with deuterons at low energies

Approximate methods of solving the few-body problem are applied to describe the interaction of anti-protons with the deuteron. In cases available the results are compared with calculations based on solving the Faddeev equations.Submitted to the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

Proton-hydrogen reaction in an effectively two-body model

A model of total interaction between a proton incident to a hydrogen atom and the proton that is the nucleus of this atom is proposed. This interaction is assumed to be the sum of the short-range nuclear Reid potential and the long-range Thomas-Fermi potential induced by the Coulomb interaction of the electron with the nucleus of the hydrogen atom. The explicit low-energy asymptotic behavior of the cross section for the proton-hydrogen reaction leading to deuteron production is found. It is shown that this cross section increases in inverse proportion to the collision energy for the proton and hydrogen atom in its zero limit.     

Extractants selection for hyphenated electrothermal atomic absorption method

The theoretical approach for extractants selection during hyphenated atomic absorption determination of highly volatile metals (Pb, Cd), hydride- (Sb, Bi) and carbide-forming (Cr) metals using thermodynamic modelling was proposed. The calculated parameter — maximum pyrolysis temperature — can be used for selection of the extractants and chemical modifiers. Using this approach the antimony extract with Brilliant green was modified for which the 1.8-fold sensitivity and 2.6-fold repeatability decreasing while extract sampling in graphite furnace was observed. A chemical modifier — mixture of hydrazine nitrate with the palladium(II) complex with Xylenol orange — was theoretically selected and experimentally tested, which allowed to enhance the maximum pyrolysis temperature on 200°C, to eliminate extract matrix influence. Using this modifier two-fold increasing in sensitivity and 3-fold decreasing in relative standard deviation was achieved while extraction atomic absorption determination.      

Proton scattering by a hydrogen atom in an effectively two-body model

It is assumed that the total potential of proton interaction with a hydrogen atom is the sum of the short-range nuclear soft-core Reid potential and the long-range Thomas-Fermi potential. A quantum mechanical analysis of low-energy features of the phase shift and cross section for elastic proton scattering on a hydrogen atom is given for the case of zero total angular momentum. The calculations performed in the present study within a nonlinear version of the variable-phase approach ultimately revealed that, because of a long-range character of the asymptotic behavior of the Thomas-Fermi potential, the respective cross section at low energies oscillates but has a finite number of zeros.     

Extrapolation of triplet phases of proton-proton scattering to low energies

It is shown that, to correctly extrapolate the triplet phases of pp scattering to a range of energies below several megaelectronvolts, one should take into account, together with the Coulomb and nuclear interactions, the interactions of the magnetic moment of a proton with the Coulomb field and the magnetic moment of another proton. A simple method is proposed for such an extrapolation.