An invariant measure for the equationu tt −u xx +u 3=0

Numerical studies of the initial boundary-value problem of the semilinear wave equationu _tt –u _xx +u ³=0 subject to periodic boundary conditionsu(t, 0)=u(t, 2),u _t (t, 0)=u _t (t, 2) and initial conditionsu(0,x)=u ₀(x),u _t(0,x)=v ₀(x), whereu ₀(x) andv ₀(x) satisfy the same periodic conditions, suggest that solutions ultimately return to a neighborhood of the initial stateu ₀(x),v ₀(x) after undergoing a possibly chaotic evolution. In this paper an appropriate abstract space is considered. In this space a finite measure is constructed. This measure is invariant under the flow generated by the Hamiltonian system which corresponds to the original equation. This enables one to verify the above returning property.     

Probabilities of rovibronic transitions in the I 1Π g − , J 1Δ g − →C 1Π ± u systems of bands of the deuterium molecule

Probabilities of spontaneous rovibronic transitions I ¹Π _g ^? , v′ J′, J ¹Δ _g ^? , v′, J′→C ¹Π _u ^± , v″, J″ of the D₂ molecule (for vibrational and rotational quantum numbers v′=v″=0–3 and J′=1–9, J″=J′±1) have been obtained for the first time. They were determined using (1) the previously proposed nonadiabatic model, which takes into account the electron-rotational interaction of the upper levels; (2) the coefficients of expansion of wave functions of perturbed states in the Born-Oppenheimer basis, which were found from the experimental data on rovibronic terms; and (3) semiempirical b initio data on electronic transition dipole moments of the 3dπ¹Π_g→2pπ¹Π_u and 3dπδ¹Δ_g→2pπ¹Π_u transitions. The dependences of the transition probabilities on J′ for the same bands of both hydrogen isotopomers H₂ and D₂ were found to be identical. They represent monotone functions for R and P branches and functions with a maximum (minimum) for Q branches. The ratios of transition probabilities of different isotopomers for different branches of the same systems of bands and for the same branches of different systems of bands were found to be correlated. The semiempirical values obtained in the paper agree with the experimental values within the limits of the errors of their determination. The nonempirical values of transition probabilities agree with the experiment considerably worse.     

Seebeck-effect in the mixed state of Y−Ba−Cu−O

We report on measurements of the Seebeck-effect, the Nernst-effect, and the magnetoresistance in the mixed state of ac-axis oriented expitaxial film of Y–Ba–Cu–O. In contrast to conventional superconductors we find a large Seebeck-coefficientS, which is comparable in magnitude to the Nernst-effect. The broadening of the super-conducting transitions of magnetoresistance and Seebeck-effect are rather similar with respect to (1) the temperature dependence, (2) the dependence on the direction between magnetic field and crystal axis and (3) the dependence on the direction between magnetic field and driving forces. The large Seebeck-effect has to be attributed to dissipation due to normal quasiparticle-excitations, since the vortex-contribution to the Seebeck-effect is by far too small to account for the observed magnitude ofS. It is argued that such a quasiparticle contribution to the dissipation is large in the high-T _c superconductors because of the small coherence lengths and thus the small vortex cores. Another possibility is that granularity leads to dissipation proportional to the normal state transport properties. The Seebeck-voltage depends on all dissipative processes other than vortex motion, whereas the Nernst-effect depends only on the vortex motion. Therefore by measurements of thermomagnetic effects the various dissipative properties may be separated.     

Study of the K − → e − νπ 0 decay

The decay K ^? → e ^? νπ ⁰ has been studied using in-flight decays detected with the ISTRA₊ setup working at the 25-GeV negative secondary beam of the U-70 PS. About 130K events were used for the analysis. The λ ₊ parameter of the vector form factor has been measured: λ ₊=0.0293±0.0015(stat.)±0.002(syst.). The limits on the possible tensor and scalar couplings have been derived: f _T/f ₊(0)=?0.045±0.060(stat.) and f _S/f ₊(0)=?0.019 _?0.016 ^+0.025 (stat.).     

Field inversion of the sign of the hall coefficient in Hg1−xMnxTe1−ySey

In the temperature range T=77–300 K and H1–18 kOe, the dependence of the Hall coefficient (R_H) of crystals of Hg_1–xMn_xTe_1–ySe_y (0H=f(H), as well as the inversion of the sign of R_H as H increases for Hg_1–xMn_xTe_1–ySe_y (x0.1 and y=0.05) are explained by the presence in the samples of three types of charge carriers: holes, and heavy and light electrons.Chernovitskii University. Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 4, pp. 11–14, April, 1994.     

Unique features of the magnetic susceptibility of Hg1−xMnxTe1−ySey

The magnetic susceptibility of the new semimagnetic solid solutions Hg_1–xMn_xTe_1–ySe_y (0Mn = f(T) are caused by the presence within the specimen of Mn-Te-Mn-Te, Mn-Se-Mn-Se, and Mn-Te-Mn-Se type clusters, in which indirect exchange action of an antiferromagnetic character occurs among the Mn atoms by means of the Te or Se atoms.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 60–62, April, 1991.     

Effects of the dielectric discontinuity on the photodetachment of H− ion

Using the closed orbit theory, we studied the effects of dielectric discontinuity on the photodetachment of H^? ions. The photodetachment cross-section of H^? in a medium with dielectric discontinuity was derived and calculated. The results have shown that the relative dielectric constants of the medium have a significant influence on the photodetachment of H^?. If H^? is kept in a medium with a relative small dielectric constant, the photodetachment cross-section of H^? becomes oscillating only in a small region above the ionization threshold. However, if H^? is kept in a medium with a relative large dielectric constant, the oscillation in the photodetachment cross-section becomes much stronger. Besides, the distance between H^? and the dielectric dividing interface also influences the photodetachment of H^?. For a given dielectric medium, the oscillation in the cross-section decreased with increasing distance between H^? and the dielectric dividing interface. Therefore, we can control the photodetachment of a negative ion by changing the dielectric constant and the ion–interface distance. This study provides a new understanding of the photodetachment process of negative ions in the presence of a dielectric medium.     

Spectrum of the H− Ion in the s-Wave Model

 The H⁻ ion in the s-wave model has one bound state and a Rydberg series of resonances, one associated with each inelastic threshold of the electron hydrogen system. We calculate the energy of the bound state and the energies of the resonances as well as their total widths up to N = 9 and partial widths up to N = 7. Received July 5, 1999; revised February 18, 2000; accepted for publication February 22, 2000     

Comparison of semiempirical and ab initio absolute probabilities of rovibronic transitions for the I 1Π g − , J 1Δ g − →C 1Π u ± system of bands of the H2 molecule

The absolute values of probabilities of the I ¹Π _g ^? , v′, J′; J ¹ Δ _g ^? , v′, J′→C ¹Π _u ^± , v″, J″ spontaneous transitions in the H₂ molecule (for the vibrational and rotational quantum numbers v′=v″=0–3, J′=1–6, and J″=J′, J′ ±1) are calculated by using ab initio and semiempirical data on the dipole moments of the 3dπ ¹Π_g, 3dδ¹Δ_g→2pπ¹Π_u electronic transitions. In both cases, the calculations are performed both in the adiabatic approximation and with an allowance for the nonadiabatic effect of electronic-rotational interaction. The coefficients of expansion of the wave functions of perturbed rovibronic states in the Born-Oppenheimer basis functions used in the calculations were obtained in the approximation of pure precession from experimental values of the terms. It was found that the values of transition probabilities based on the ab initio calculations systematically exceed the corresponding semiempirical data by a factor of 1.2–1.9 for the I ¹Π_g→C ¹Π _u ^± transition and by a factor of 1.4–1.6 for the J ¹Δ _g ^? →C ¹Π _u ^± transition. It was established that the difference between the ab initio and semiempirical values of electronic transition moments virtually has no effect on the dependence of the transition probabilities on the vibrational quantum numbers. The discrepancies between the results of adiabatic and nonadiabatic calculations are significant and reach two orders of magnitude, which is indicative of the important role of perturbations in the probabilities of the transitions considered.     

Potential of the A 1Σ u + state of He2

The potential of the lowest excited singlet state of He₂ is calculated. The best function includes 209 configurations constructed from 10 σ basis orbitals. Excellent agreement with experimental quantities depending on the shape of the potential near the minimum (equilibrium interatomic separation, vibrational and rotational constants for the lower vibration levels) is obtained. The dissociation energy is 18 600 cm^-1, compared to the experimental 19 910±50 cm^-1. Agreement is not as good for the highest vibrational levels.     

Investigation of the character of the exchange interaction in the system Hg1−xMnxSe

A new method is proposed for determining the magnetic characteristics (magnitude and sign of the exchange interaction energy and the average size of clusters of magnetic ions) of dilute solid solutions of semimagnetic semiconductors at low temperatures based on oscillation measurements. The method makes it possible to find the magnetic characteristics of the indicated systems at temperatures between the point of the transition into the spin glass state and the temperature corresponding to the characteristic binding energy of magnetic atoms in clusters, for which standard methods based on the measurement of the magnetic susceptibility are not effective. The method is used to study the character of the exchange interaction in the system of solid solutions Hg_1–xMn_xSe as a function of their composition as well as under conditions of hydrostatic compression. To this end the oscillations of the magnetoresistance (Shubnikov-de Haas (SH) effect) in single-crystalline samples of Hg_1–xMn_xSe in the region of compositions 0.001 x 0.23 in magnetic fields H up to 65 kOe at temperatures T = (0.4–20) K and pressures up to 16 kbar were studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 29–39, November, 1989.     

Determination of the branching ratio ofρ 0→+μ− in the coherent dissociation π−→μ+μ−π− and π−→π+π−π−

In the diffraction dissociation of π^? into μ⁺μ^?π^? on a Cu nucleus at 50 GeV/c, the cross section \(\sigma _{\mu ^ + \mu ^ - \pi ^ - } \) for the 1⁺S(ρ⁰π) wave was measured. The branching ratio of ρ⁰→μ⁺μ^? could be calculated from the ratio of this and the corresponding cross sections in the diffraction dissociation of π^? into π⁺π^?π^?. The obtained value \(BR_{\rho ^0 \to \mu ^ + \mu ^ - } = (4.6 \pm 0.2_{stat^ \pm } \pm 0.2_{syst} )10^{ - 5} \) is in good agreement with the branching ratio \(BR_{\rho ^0 \to e^ + e^ - } \) , as expected ifeμ universality holds.     

SEM identification of the amorphous state of Fe−B ribbons

Based on X-ray diffraction and electron microscopy data on morphological inhomogeneities at the interfaces in Fe?B ribbons, the boundary boron concentration separating the crystal and amorphous states upon spinning (~10 at %) is established. A modulated isotropic stochastic wave structure is detected, the relaxation of which can be presented as spinodal decomposition.     

Negative Ca− and Ba− ions of large radius on the surface and in the volume of liquid helium

Negative Ca⁻ and Ba⁻ ions of large radii on the surface of and in bulk liquid helium have been studied. Our results indicate that these ions are adsorbed on the helium surface. Ions on free liquid helium surfaces have not been studied previously because it was thought impossible to confine them on the surface. Ca⁻ and Ba⁻ ions have very low binding energies, therefore, like electrons, they form a bubble of large radius in bulk helium, whose energy is higher than on the surface. The behavior of ions on the surface exhibits a number of previously unknown features owing to their large masses and strong localization in the horizontal plane. Even in the absence of confining electric field, a hole is formed under an ion due to the polarization attraction between the liquid helium and the charged ion. This hole formation reduces the ion mobility by several orders of magnitude and increases its effective mass severalfold. The critical density of electrons and ions is approximately the same on the surfaces of thin and thick helium films. Zh. éksp. Teor. Fiz. 115, 593–604 (February 1999)     

Observation of the decaya 2 − (1320)→π − η′

The reaction ^– C ^– C has been studied at 36 GeV/c. A clear signal for the decaya ₂ ^– (1320) ^– · is observed in the ^– mass spectrum. The measured ratio of branchings is BR (a ₂ ^{– –} )/BR(a ₂ ^{– –} );(3.4±0.8±0.5)·10^–2.     

Measurement of the Electric Quadrupole Moment of the 9/2− and 21/2− Isomers in 173Ta

The electric quadrupole moments of the 9/2⁻ and 21/2⁻ isomeric states of ¹⁷³Ta at 165.8 keV and 1713.2 keV, respectively, were measured as Q(9/2⁻)=2.92(15) b and Q(21/2⁻)=6.23(18) b for the first time using the TDPAD technique. A 66 MeV pulsed ¹²C ion beam from the 15UD pelletron accelerator facility of the Nuclear Science Centre at New Delhi was used in the reaction ¹⁶⁵Ho(¹²C, 4nγ)¹⁷³Ta. The experimental values of equilibrium deformations β₂(9/2⁻)=0.251(7) and β₂(21/2⁻)=0.391(7) were extracted. This revised version was published online in July 2006 with corrections to the Cover Date.     

Investigation of the behaviour of the impurity atoms in Si by μ− SR-method

The dependence of the residual polarization of negative muons in p-type Si on temperature in the 4.2–270 K range has been investigated. Measurements were carried out in external magnetic field of 0.08 T transverse to the muon spin. The impurity concentration in the sample was 2 · 10¹³ cm^–3. Muon spin relaxation was observed at temperatures below 30 K. The relaxation rate atT=30 K is equal to 0.18±0.08s^–1. The relaxation rate grows with the decrease of temperature and at 4.2 K exceeds 30s^–1. The value of the residual polarization at zero timeP(t=0) is constant within the investigated temperature range.In the rangeT<30 K data on the relaxation rate are well described by the dependence =B·T^–q, whereq=2.75. Power dependence of may evidence the essential role of the phonon mechanism in the relaxation of the electron momentum of the acceptor center.The authors express their gratitude to V.B. Brudanin and I.A. Yutlandov for providing the sample, and to Yu.B. Gurov for advices.