Elimination of the energy from interactions that depend on it as a resolvent

A study is made of the spectral problem (A+V(z)=z, in which the main HamiltonianA is a self-adjoint operator of fairly general nature, while the perturbationV(z)=–B(A–z)^–1 B* depends on the energyz as the resolvent of some other self-adjoint operatorA. It is assumed that the operatorB has a finite Hilbert—Schmidt norm and, in addition, that the spectra of the operatorsA andA are separated. Conditions are formulated under which it is possible to replace the perturbationV(z) by an energy-independent potentialW such that the HamiltonianH=A+W has the same spectrum (more precisely, part of the spectrum) and the same eigenfunctions as the original spectral problem. Completeness and orthogonality theorems are proved for the systems of eigenfunctions of the operatorH=A+W. A scattering theory is constructed for the HamiltonianH in the case when the operatorA has a continuous spectrum. Applications of the results to the few-body problem are discussed.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 2, pp. 281–303, August, 1995.     

Orthogonal Algebraic Polynomial Schauder Bases of Optimal Degree

For any fixed we construct an orthonormal Schauder basis for C[-1,1] consisting of algebraic polynomials with The orthogonality is with respect to the Chebyshev weight.     

Determination of the atmospheric neutrino spectra with the Fréjus detector

The combined analysis of the final event set of data on neutrino interactions inside the detector, upward going stopping muons and horizontal muons recorded in the Fréjus experiment is presented. The absolute atmospheric neutrino spectra in the energy range for electron neutrinos and for muon neutrinos are determined. Based on the parameterization of Volkova for thev ^µ a spectral index of =2.66±0.05 is obtained from the ratio of horizontal muons over upward going stopping muons and from the measurement of the energy loss of horizontal muons inside the detector. The neutrino spectra are compared with various flux calculations. They do not show any evidence for neutrino oscillations in agreement with earlier analyses of the Fréjus data.Now atUniversity of Michigan, Ann Arbor, USA     

90–120 GHz millimeter wave power head

Power-voltage and frequency characteristics of power heads for 90–120 GHz TE₁₀-mode millimeter waves are presented. Operation of the power heads is based on thermo-e.m.f. of hot charge carriers in silicon. The head has been tested both in the pulsed and continuous generation regime. The experiments were carried out in the power range of 2·10^–3–4 W. In the pulse regime, the shortest pulse duration was 1s.     

Vibrational Population of Hydrogen Molecules Excited by an RF Discharge in an Expanding Thermal Arc Plasma as Determined by Emission Spectroscopy

This work is devoted to the determination of the vibrational population of hydrogen molecules in the ground and excited electronic states from the analysis of visible spectra of the H₂ molecules excited by an RF discharge in an expanding thermal arc plasma. Comparison of the experimental results on relative electron-impact excitation cross sections for the transition H₂(X¹Σ, υ⁰ = 0)→ H₂(d³II_u, υ′) with other experiments, and with calculations based on the Franck-Condon principle, shows good agreement. This means, that for plasma under investigation: 1) in the ground electronic state H₂(d³II_u,υ′), only the lowest vibrational level with υ⁰ = 0 is significantly populated, and 2) direct electron exictation of H₂(d³II_u, υ′, υ′) state from the ground state H₂(X¹Σ, υ⁰ = 0) dominates.     

Thermodynamic properties of the spin-Peierls transition in CuGeO3

We present an investigation of the spin-Peierls transition atT _SP=14.5 K in polycrystalline CuGeO₃ through specific-heat and thermal-expansion measurements. Clear second-order phase-transition anomalies are found in both properties atT _SP, although only a small entropy of S0.1 Rn2 is released at the transition. Most of the entropy is released atT _SP<T<150 K, where the temperature dependence of the magnetic contribution to the specific heat as well as the thermal expansion exhibit extrema atT ^*40 K. These are caused by one-dimensional antiferromagnetic fluctuations along the Cu chains, possibly accompanied by structural fluctuations. Using Ehrenfest's relation, a hydrostatic pressure coefficient (T _SP/_p)_p0 (0.45±0.06) K/kbar is derived.     

Luminescence centers in porous silicon

Photoluminescence studies on porous silicon show that there are luminescence centers present in the surface states. By taking photoluminescence spectra of porous silicon with respect to temperature, a distinct peak can be observed in the temperature range 100–150 K. Both linear and nonlinear relationships were observed between excitation laser power and the photoluminescence intensity within this temperature range. In addition, there was a tendency for the photoluminescence peak to red shift at low temperature as well as at low excitation power. This is interpreted as indicating that the lower energy transition becomes dominant at low temperature and excitation power. The presence of these luminescence centers can be explained in terms of porous silicon as a mixture of silicon clusters and wires in which quantum confinement along with surface passivation would cause a mixing of andX band structure between the surface states and the bulk. This mixing would allow the formation of luminescence centers.     

Reaction studies of carbon clusters

Reaction studies of carbon clustersC _n in the rangen=8–37, produced by laser vaporisation in a supersonic nozzle, have been investigated using time-of-flight mass spectrometry. Clear differences in reaction products formed on hydrogenation are detected which show that even and odd clusters behave quite differently and furthermore thatat least two different types of even cluster appear to exist. The reactivity patterns for clusters C _n withn=16, 18 and 22 are in a different class from those withn=20, 24, 26 ..., a behaviour consistent with the existence of closed cage fullerene structures for even clusters with 20 or more carbon atoms (other thann=22).     

Shed plane leaves as a source ofα-tocopherol

A natural source of -tocopherol — shed plane leaves — has been found. The dynamics of the accumulation of a-tocopherol over the vegetation period of the plant has been studied, and a method has been developed for its isolation and quantitative determination.Deceased.Institute of the Chemistry of Plant Substances, Academy of Sciences of the Republic of Uzbekistan, Tashkent, fax (3712) 89 14 75. Translated from Khimiya Prirodnykh Soedinenii, No. 3, pp. 372–374, May–June, 1995. Original article