Dynamics of cold atoms in a quadrupole magnetic trap with an orbiting potential

We study the dynamics of atoms confined to a quadrupole magnetic trap with an orbiting potential. For typical values of the experimental parameters of the trap, the rotating magnetic field is shown to produce high-frequency modulation of atomic momenta with an amplitude comparable to the widths of the momentum distributions for the lowest oscillation states of atoms in the time-averaged potential. We find the quantum-statistical momentum and position distributions of atoms and show that at temperatures much higher than the effective vibrational temperature of the atoms in the trap the quantum-statistical momentum and position distributions are Gaussian. We also establish that at temperatures comparable to the effective vibrational temperature of the atoms the quantum-statistical momentum distribution has an annular structure in the trap’s symmetry plane, which is due to the deep modulation of the atomic momenta caused by the rotating magnetic field. Zh. éksp. Teor. Fiz. 114, 23–36 (July 1998)     

The influence of hydrostatic pressure on Raman spectra of TIS and TlInSe2

First order Raman spectra of TIS and TlInSe₂ single crystals excited with 1.064μm line of the continuously operated YAG: Nd³⁺ laser have been investigated in equilibrium conditions under various hydrostatic pressures up to 1.08 × 10⁹ and 7.06 × 10⁸ Pa, respectively. Mode parameters γ_j = (1/ν_j)(dν_j/dP) were determined for all the Raman bands observed. Comparison of a set of these parameters in both crystals showed that the character of binding interatomic forces in these crystals appeared to be similar. For both crystals the intensity of Raman bands decreased with increasing the pressure.     

Reaction center in the oxidation of amino derivatives of 2-phenylbenzimidazole in dimethylformamide

The electrochemical oxidation of amino derivatives of 2-phenylbenzimidazole on a rotating platinum disk with a ring in neutral and acidic dimethylformamide was investigated. It is shown that the investigated compounds are oxidized in two electrochemical steps that include reversible one-electron processes, as a consequence of which the potentials have thermodynamic significance and can serve as a measure of the relative reactivities of these compounds in the oxidation reaction. The imidazole ring undergoes oxidation in acidic media (HClO₄) because of protonation of the amino groups, whereas the amino group is the reaction center in neutral DMF.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 4, pp. 516–518, April, 1978.     

Linear method for the approximation of differentiable functions

This article is devoted to the problem of the approximation of functions in the metric of space L_p(0, 1), the s-th derivative of the functions being continuous and the (s + l)-th derivative belonging to the space L_q(0, 1), with p, q 1, by spline functions of order s with fixed almost uniform nodes.Translated from Matematicheskie Zametki, Vol. 7, No. 4, pp. 423–430, April, 1970.     

Higgs fields as condensates

It is shown that the Higgs-Goldstone field, which is responsible for a spontaneous symmetry breaking in gauge models, is a type of condensate.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 8–12, July, 1984.     

Direct observation of anomalous Kossel lines

Anomalous Kossel lines corresponding to the yield of X rays from a germanium crystal under the conditions of strongly asymmetric diffraction have been observed in the simplest experimental scheme with the use of characteristic Mo K _α radiation and a germanium crystal analyzer. In agreement with the results of a previous theoretical analysis, such lines are narrow collimated beams of radiation in the form of a ridge in a narrow angular range near a given direction whose intensity is one or two orders of magnitude higher than the background with a divergence of about several seconds of arc in the diffraction plane and of about 10′ along the Kossel line. The possible applications of this effect, in particular, for solving the problems of X-ray holography, are discussed.     

Growth, optical parameters, and spectroscopic properties of crystals of disordered scheelite-like molybdates NaLaxGd1 ? x(MoO4)2 (x = 0–1) activated by Tm3+ ions

Polarized optical absorption spectra in the range of 450–2000 nm have been recorded for the Czochralski-grown concentration series of single crystals of mixed scheelite-like molybdates NaLa _x Gd_{1 − x} (MoO₄)₂(x = 0–1) activated by Tm³⁺ ions. The intensity parameters Ω _t (t = 2, 4, 6) of the crystals grown were determined by the Judd-Ofelt method, and the values found were used to estimate the probabilities and emission branching ratios for a number of radiative transitions of Tm³⁺ ions. The main optical constants of an Na_0.909La_0.490Gd_0.498Tm_0.035Mo_2.020O_8.048 crystal were found and the temperature dependences of the refractive index for the ordinary and extraordinary waves were investigated in the temperature range of 293–373 K. The spectral dependences of the emission cross section for the expected ³ F ₄ → ³ H ₆ laser transition of Tm³⁺ ions in an Na_0.908La_0.301Gd_0.676Tm_0.048Mo_2.019O_8.043 crystal were measured in the spectral range of 1500–2000 nm. The gain cross section of the active medium on the ³ F ₄ → ³ H ₆ laser transition of Tm³⁺ ions in this crystal was calculated using the spectral dependences of the absorption and emission cross sections.     

On relative widths of classes of differentiable functions. II

We obtain an upper bound for the least value of the factor M for which the Kolmogorov widths d _n (W _C ^r , C) are equal to the relative widths K _n (W _C ^r , MW _C ^j , C) of the class of functions W _C ^r with respect to the class MW _C ^j , provided that j > r. This estimate is also true in the case where the space L is considered instead of C.