Renormalization group functions of the φ<Superscript>4</Superscript> theory from high-temperature expansions

It has been previously shown that calculation of the renormalization group (RG) functions of scalar ϕ⁴ theory reduces to analysis of thermodynamic properties of the Ising model. Using high-temperature expansions for the latter, RG functions of the four-dimensional theory can be calculated for arbitrary coupling constant g with an accuracy of 10⁻⁴ for the Gell-Mann-Low function β(g) and with an accuracy of 10⁻³–10⁻² for anomalous dimensions. The expansions of the renormalization group functions up to the 13th order in g ^−1/2 have been obtained.     

New approach for numerical solution of configuration-space Faddeev equations

A new computational scheme for solving the bound state configuration-space Faddeev equations is applied. The scheme is based on the spline-approximation and the adiabatic limit of Faddeev equations. An ordering of variables being in agreement with the limit was chosen. As a result the matrix of the eigenvalue problem has a sparse block structure. Calculations of the bound states of µpp, µdd, µtt mesic molecules and ¯pdd, ¯ptt antiprotonic ones, were performed. To check the method, calculations of the binding energies for such systems as the positronium ion Ps_–,³H and³He were carried out. The results are compared with the best results of other authors.     

An effective route for the synthesis of cationic palladium complexes of general formula [(Acac)PdLL]A

A series of palladium complexes of general formula [(Acac)PdL¹L²]⁺A⁻, where L¹, L² = phosphines and A = BF₄, CF₃SO₃, were synthesized. Preliminary studies show that the complexes are active in selective dimerization of styrene and addition polymerization of norbornene.     

Classical orthogonal polynomials of a discrete variable continuous orthogonality relation

Based on the general theory, we consider the continous orthogonality property for classical polynomials of a discrete variable on nonuniform lattices.     

Exact wave functions for generalized harmonic oscillators

We transform the time-dependent Schrödinger equation for the most general variable quadratic Hamiltonians into a standard autonomous form. As a result, the time evolution of exact wave functions of generalized harmonic oscillators is determined in terms of the solutions of certain Ermakov and Riccatitype systems. In addition, we show that the classical Arnold transform is naturally connected with Ehrenfest’s theorem for generalized harmonic oscillators.     

Configuration-Space Faddeev Calculation for Proton�CDeuteron Elastic Scattering Observables

A new computational method for solving the nucleon?Cdeuteron breakup scattering problem has been applied to study the elastic nucleon?Cdeuteron scattering on the basis of the configuration-space Faddeev?CNoyes?CNoble?CMerkuriev equations. The Merkuriev?CGignoux?CLaverne approach has been generalized for arbitrary nucleon?Cnucleon potentials and with an arbitrary number of partial waves. The nucleon?Cdeuteron observables at the incident nucleon energy 3?MeV have been calculated using the charge-independent AV14 nucleon?Cnucleon potential including the Coulomb force for the proton?Cdeuteron scattering. Results have been compared with those of other authors and with experimental proton?Cdeuteron scattering data.     

Isomers of astrophysical interest in neutron-deficient nuclei at masses A = 81, 85 and 86

Decay properties of neutron-deficient exotic nuclei close to A=80 have been investigated at the IGISOL facility. The studied nuclei, ⁸¹Y, ⁸¹Sr, ^81mKr, ⁸⁵Nb, ⁸⁵Zr, ⁸⁶Mo and ⁸⁶Nb, were produced by a ³²S beam from the Jyv?skyl? isochronous cyclotron on ⁵⁴Fe and ^natNi targets. The internal conversion coefficient for a 190.5 keV isomeric transition in ^81mKr has been measured and the internal transition rate has been determined. The internal transition rate has been used to estimate a neutrino capture rate on ⁸¹Br, which yields a log ft of 5.13±0.09 for the reaction ⁸¹Br( ν, e ^-)^81mKr. A new isomer with a half-life of 3.3±0.9 s has been observed in ⁸⁵Nb. The existence of an earlier reported isomer with a half-life of 56 s in ⁸⁶Nb has not been confirmed.     

Gell-Mann-Low function in QCD

The Gell-Mann—Low function in QCD β(g)(g=?²/16π², where ? is the coupling constant in the Lagrangian) is shown to behave in the strong-coupling region as β_∞ g ^α, where α≈?13 and β_∞～10⁵.     

Analytical realization of finite-size scaling for Anderson localization. Does the band of critical states exist for d > 2?

An analytical realization is suggested for the finite-size scaling algorithm based on the consideration of auxiliary quasi-1D systems. Comparison of the obtained analytical results with the results of numerical calculations indicates that the Anderson transition point splits into the band of critical states. This conclusion is supported by direct numerical evidence (Edwards, Thouless, 1972; Last, Thouless, 1974; Schreiber, 1985). The possibility of restoring the conventional picture still exists but requires a radical reinterpretation of the raw numerical data. Published in Russian in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2006, Vol. 129, No. 6, pp. 1064–1076. The text was translated by the author.