Partial virial theorems for atomic-molecular systems

New virial relations for three-and four-particle atomic-molecular systems are proposed. Using operators of extension or squeezing of interparticle distances, it is shown that, for all pairs of j and k particles in S states of these systems, the following partial virial relations are valid: 〈2T _jk 〉+〈 V _jk 〉=0, where 〈V _jk 〉 is the average Coulomb interaction energy for a pair of particles and 〈T _jk 〉 is a part of the average kinetic energy of the system. There are three and six such relations for three-and four-particle systems, respectively. The conventional virial theorem (〈 2T〉+〈V〉=0) for the average total kinetic and potential energies of the system (〈 T〉 and 〈V〉, respectively) corresponds to the summation of partial virial relations over all pairs of particles. It is shown by an example of variational calculations of the helium atom ⁴He²⁺ e ^? e ^? and the helium muon-electron mesoatom ⁴He²⁺μ^? e ^? that partial virial relations are a highly sensitive indicator of the accuracy of wave functions.     

Structure and phase composition of thin a-C:H films modified by Ag and Ti

The structure and phase composition of thin a-C:H and a-C:H〈M〉 films (M = Ag, Ti, or Ag + Ti) have been studied by Raman and X-ray photoelectron spectroscopy. The a-C:H〈M〉 films were prepared by ion-plasma magnetron sputtering of a combined target of graphite and metal in an Ar–CH₄ gas mixture. The Raman spectra of these films indicate that their structure is amorphous. The a-C:H〈Ag + Ti〉 films have a more graphitized structure in comparison with pure a-C:H films and films containing only one metal. It is established that carbon in the a-C:H〈Ag + Ti〉 films is in the sp ², sp ³, and C=O states, which are characteristic of the a-C:H, a-C:H〈Ag〉, and a-C:H〈Ti〉 films. In addition, there are also ether (–C–O–C–) or epoxy (?C?O–) carbon groups in the a-C:H〈Ag + Ti〉 films. It has been revealed that silver atoms in the a-C:H〈Ag〉 and a-C:H〈Ag + Ti〉 films form no chemical bonds with carbon, oxygen, and titanium. Titanium in the a-C:H〈Ti〉 and a-C:H〈Ag + Ti〉 films exists in the form of titanium IV oxide (TiO₂).     

Non-extensivity of the chemical potential of polymer melts

Following Flory’s ideality hypothesis, the chemical potential of a test chain of length n immersed into a dense solution of chemically identical polymers of length distribution P(N) is extensive in n . We argue that an additional contribution \( \delta\) \( \mu_{{{\rm c}}}^{}\)(n) ～ +1/\( \rho\) \( \sqrt{{n}}\) arises (\( \rho\) being the monomer density) for all P(N) if n ? 〈N〉 which can be traced back to the overall incompressibility of the solution leading to a long-range repulsion between monomers. Focusing on Flory-distributed melts, we obtain \( \delta\) \( \mu_{{{\rm c}}}^{}\)(n) \( \approx\) (1 - 2n/〈N〉)/\( \rho\) \( \sqrt{{n}}\) for n ? 〈N〉² , hence, \( \delta\) \( \mu_{{{\rm c}}}^{}\)(n) \( \approx\) -1/\( \rho\) \( \sqrt{{n}}\) if n is similar to the typical length of the bath 〈N〉 . Similar results are obtained for monodisperse solutions. Our perturbation calculations are checked numerically by analyzing the annealed length distribution P(N) of linear equilibrium polymers generated by Monte Carlo simulation of the bond fluctuation model. As predicted we find, e.g., the non-exponentiality parameter K _p \( \equiv\) 1 - 〈N ^p〉/p!〈N〉^p to decay as K _p \( \approx\) 1/\( \sqrt{{\langle N \rangle }}\) for all moments p of the distribution.     

One-phonon Raman spectra of carbon in composite films prepared by modification of amorphous hydrogenated carbon by copper and cobalt

One-phonon visible-range Raman spectra of a-C: H〈Cu〉 and a-C: H〈Co〉 composite films with comparable metal and carbon contents were studied in the frequency region 1200–1700 cm^?1 including the carbon sp²-bond vibrations. Broad bands G and D characteristic of unmodified a-C: H films, as well as some additional features, are observed experimentally in the spectra. By unfolding the spectra into Gaussian components, it was possible to follow the variation of Raman shifts and of contributions of individual components to the spectrum as a function of metal content and thermal annealing. The data obtained, complemented by available information on carbon sp²-coordinated systems, show that incorporation of Cu or Co favors growth and ordering of graphite-like nanoclusters in a-C: H, the effect being substantially stronger in the case of Co. It is shown that the process of metal-stimulated graphitization includes carbon bond breaking with the formation of short chainlike fragments and their linkage with the formation of aromatic-ring nanoclusters. A qualitatively similar sp²-structure rearrangement takes place under thermal annealing. For the Cu and Co concentrations studied, the linear dimensions L _a of graphite-like clusters are estimated to vary from ～0.8 nm in unannealed a-C: H to ～1.0 and ～1.2 nm in annealed a-C: H〈Cu〉 and a-C: H〈Co〉, respectively. The number of aromatic rings in these clusters is approximately estimated to increase from 12 to 16 (for Cu) and 20 (for Co).     

Bestimmung der Kernmomente des Ho165 aus der Hyperfeinstruktur des Grundzustandes im Ho I-Spektrum

In an atomic beam magnetic resonance experiment, the hyperfine interaction constantsA andB of the⁴ I _2/15-groundstate of Ho¹⁶⁵ were found to beA=800,58389 (50) MHz,B=?1667,997 (50) MHz. Using an effective value for 〈r ^?3〉, the magnetic moment of the Ho¹⁶⁵ nucleus was calculated to beμ=4·1(4)μ _n . The quadrupolement was determined by use of the 〈r ^?3〉 given byWatson andFreeman. The result isQ=2·4·10^?24 cm².     

Scaling of semi-inclusive events in <Emphasis Type="Italic">pp</Emphasis> interactions

The normalized single-particle semi-inclusive double-differential spectrum of π^t- mesons from pp interactions at 6.6–400 GeV/c and the relative concentration of π⁰ and K _S ⁰ mesons in such events of fixed multiplicity of π^? mesons are completely determined by specifying any feature of this spectrum—for example, 〈y²〉 _n or 〈E〉 _n . Therefore, a two-parameter sample of semi-inclusive events that depends on the energy and the multiplicity reduces to a one-parameter sample.     

Low-temperature plasticity and lattice dynamics of solid parahydrogen with an isotopic impurity

The low-temperature plasticity of solid polycrystalline parahydrogen doped with an isotopic impurity (deuterium) is studied. The dependences of the rate of steady-state creep in p-H₂ on the impurity concentration and stress are obtained. The deformation of p-H₂ is described with inclusion of the zero-point mean-square displacements 〈x²〉 of particles making up a crystal. The calculated and experimental values of 〈x²〉 are compared for two possible isotope molecules (HD and D₂) at three stress levels. A correlation between the 〈x²〉 values and an increase in the force constants of a p-H₂ crystal doped with the isotopic impurity is established. An increase in the mean-square displacements of p-H₂ with the tensile load is discussed. Deformation-induced purification of a p-H₂ crystal from the isotopic impurity is suggested to occur.     

New type of exact solutions to the generalized Ashkin-Teller model and anisotropic Ising model with spin 3/2

The generalized Ashkin-Teller model involving both biquadratic and bilinear interactions between the Ising subsystems (α and s) and equivalent to the anisotropic Ising model with spin 3/2 is considered. For a certain magnitude of the opposite-sign bilinear interactions along the horizontal and vertical axes of a square lattice, the exact analytic solution is obtained that describes the phase transition between the disordered (〈α 〉=〈s〉=〈αs〉=0) and the correlated ordered (〈s〉 ≠0 and 〈α〉=〈s〉=0) states.     

Composite fermions,trios, and quartets in the Fermi-Bose mixture of neutral particles

We consider the model of a Fermi-Bose mixture with strong hard-core repulsion between particles of the same sort and attraction between particles of different sorts. In this case, in addition to the standard anomalous averages of the type 〈b〉, 〈bb〉, and 〈cc〉, pairing between fermions and bosons of the type 〈bc〉 is possible. This pairing corresponds to creation of composite fermions in the system. At low temperatures and equal densities of fermions and bosons, composite fermions are further paired into quartets. At higher temperatures, trios consisting of composite fermions and elementary bosons are also present in the system. Our investigations are important in connection with the recent observation of weakly bound dimers in magnetic and optical dipole traps at ultralow temperatures and with the observation of collapse of a Fermi gas in an attractive Fermi-Bose mixture of neutral particles.     

Anomalous hall effect in a diluted <Emphasis Type="Italic">p</Emphasis>-InAs〈Mn〉 magnetic semiconductor

The dependences of the electrical resistivity and the Hall coefficient of single-crystal p-InAs〈Mn〉 bulk samples with an acceptor concentration of about 10¹⁸ cm^–3 on uniform pressure P = 4–6 GPa at T = 300 K in the region of impurity conduction are quantitatively analyzed. The anomalous Hall effect is shown to occur in p-InAs〈Mn〉. Its contribution is negative and correlates with the deionization of acceptors and an increase in the magnetic susceptibility.     

Dependence of the Daily <Emphasis Type="Italic">N</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript>F2 Values over Mid-Latitude Stations on the Solar and Geomagnetic Activity

The results of studies of the dependence of the daily electron concentration at maximum of the F2 ionospheric layer in January 2008–2015 on the solar and geomagnetic activity are presented. The solar radio emission flux density indices F_10.7 and geomagnetic activity indices A _p were averaged over 27 days, and 〈F_10.7〉₂₇ and 〈A _p 〉₂₇, respectively, were obtained. Based on the data of three stations, 27-day median (with the middle of January 15) daily N _m F2 variations were obtained for 2008–2015. Based on these data, the following paradox was discovered: in January 2014, when the values of the solar activity index F_10.7 were larger than in 2015, the dailyN _m F2 values were smaller. Averaging over four hours of local daytime (10:00–14:00 LT) gave the daily average January 〈N _m F2〉 values for each selected station for each year. To solve this paradox, a double linear regression of 〈N _m F2〉 on 〈F_10.7〉₂₇ and 〈A _p 〉₂₇ was constructed. Due to this, it was concluded that the contribution of geomagnetic activity to daily January 〈N _m F2〉 values is positive. A comparison of the mean square errors of the linear and double linear regressions for 〈F_10.7〉₂₇ and 〈F_10.7〉₈₁ showed that the use of 〈F_10.7〉₂₇ led to smaller errors than the use of 〈F_10.7〉₈₁.     

Radiation of electromagnetic waves by a dipole in an external uniform electrostatic field

Exact solution for the electromagnetic field densities E and H of a dipole of uniformly accelerated point-charges with identical masses is discussed. It is shown that, for any fixed time t and a large distance R between the center of the dipole and the fieldpoint, |E| ~ R ^?4, |H| ~ R ^?5, while for large c|t| ~ R, |E| ~ |H| ~1/R as in spherical electromagnetic waves. Nevertheless, any irreversible radiation of electromagnetic waves is absent since the wave zone does not exist.     

Determination of nuclear excitation energies from the number of evaporated particles

The mean number ?N_b〉 of particles evaporated in the interaction of ²²Ne, ³²S, and ⁵⁶Fe nuclei with photoemulsion nuclei was measured as a function of the number of alpha particles emitted within the fragmentation cone. It is found that ?N_b〉 decreases with increasing number of the alpha particles and increases with increasing number of projectile nucleons involved in the interaction with a target nucleus and that ? N_b〉 is a linear function of the excitation energy E_ex of the target-nucleus residue. The maximum experimental value of the mean number of evaporated particles is ?N_bmax〉 ? 12–13, which corresponds to E_exc ? 540 ± 60 MeV.     

Magnetization and Static Magnetic Susceptibility of Fine-Crystalline High-Temperature YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> Superconductors Synthesized by the Sol–Gel Method

A comparative study of the magnetization and static magnetic susceptibility of high-temperature superconductors (HTSC) YBa₂Cu₃O_y synthesized by two variants of the sol–gel method with different average sizes of crystallites 〈 D〉 ranging 0.4–2 μm has been performed in constant magnetic fields (Н ≤ 6 kOe). It has been shown that the different annealing temperatures and times, at which their crystal structure is formed, change both the average sizes of crystallites 〈D〉 and the sizes of the structural homogeneity regions 〈l〉 and, at the same time, the magnetic field penetration depth (λ) and the coherence length (ξ). As a result, such parameters as 〈D〉 ~ λ and 〈l〉 ~ ξ become comparable, leading to a change in the physical characteristics of HTSCs. It has also been shown that the superconducting transition temperature T_c determined from the measurements of magnetic characteristics in constant magnetic fields remains within values optimal for superconductivity (T_c ≈ 92 K) in the case of an optimal number (y) of oxygen atoms, which determine the levels of charge doping for a given compound.     

Energy spectra of developed superfluid turbulence

Turbulence spectra in superfluids are modified by the nonlinear energy dissipation caused by the mutual friction between quantized vortices and the normal component of the liquid. We have found a new state of fully developed turbulence, which occurs in some range of two Reynolds parameters characterizing the superfluid flow. This state displays both the Kolmogorov-Obukhov 5/3-scaling law E_k ∝ k^?5/3 and a new “3-scaling law” E_k ∝ k^?3, each in a well-separated range of k.     

Gottfried Sum Rule in QCD Nonsinglet Analysis of DIS Fixed-Target Data

Deep-inelastic-scattering data from fixed-target experiments on the structure function F₂ were analyzed in the valence-quark approximation at the next-to-next-to-leading-order accuracy level in the strong-coupling constant. In this analysis, parton distributions were parametrized by employing information from the Gottfried sum rule. The strong-coupling constant was found to be α _s (M²_Z) = 0.1180 ± 0.0020 (total expt. error), which is in perfect agreement with the world-averaged value from an updated Particle Data Group (PDG) report, α^PDG _s (M²_Z) = 0.1181 ± 0.0011. Also, the value of 〈x〉_u?d = 0.187 ± 0.021 found for the second moment of the difference in the u- and d-quark distributions complies very well with the most recent lattice result 〈x〉^LATTICE_u?d = 0.208 ± 0.024.     

A study of the nuclear-medium influence on transverse momentum of hadrons produced in deep-inelastic neutrino scattering

The influence of nuclear effects on the transverse momentum (p_T) of neutrino-produced hadrons is investigated using the data obtained with the SKAT propane-freon bubble chamber irradiated in the neutrino beam (with E _v =3–30 GeV) at the Serpukhov accelerator. It has been observed that the nuclear effects cause an enhancement of 〈p _T ² 〉 of hadrons produced in the target fragmentation region at low invariant mass of the hadronic system (2 < W < 4 GeV) and at low energies transferred to the hadrons (2 < ν < 9 GeV). At higher W and ν, no influence of nuclear effects on 〈p _T ² 〉 is observed. Measurement results are compared with predictions of a simple model, incorporating secondary intranuclear interactions of hadrons, which qualitatively reproduces the main features of the data.     

Electron gas induced in SrTiO<Subscript>3</Subscript>

This mini-review is dedicated to the 85th birthday of Prof. L.V. Keldysh, from whom we have learned so much. In this paper, we study the potential and electron density depth profiles in surface accumulation layers in crystals with a large and nonlinear dielectric response such as SrTiO₃ (STO) in the cases of planar, spherical, and cylindrical geometries. The electron gas can be created by applying an induction D₀ to the STO surface. We describe the lattice dielectric response of STO using the Landau–Ginzburg free energy expansion and employ the Thomas–Fermi (TF) approximation for the electron gas. For the planar geometry, we arrive at the electron density profile n(x) ∝ (x + d)^–12/7, where d ∝ D₀^–12/7. We extend our results to overlapping electron gases in GTO/STO/GTO heterojunctions and electron gases created by spill-out from NSTO (heavily n-type doped STO) layers into STO. Generalization of our approach to a spherical donor cluster creating a big TF atom with electrons in STO brings us to the problem of supercharged nuclei. It is known that for an atom with a nuclear charge Ze where Z > 170, electrons collapse onto the nucleus, resulting in a net charge Zn < Z. Here, instead of relativistic physics, the collapse is caused by the nonlinear dielectric response. Electrons collapse into the charged spherical donor cluster with radius R when its total charge number Z exceeds the critical value Z_c ≈ R/a, where a is the lattice constant. The net charge eZ_n grows with Z until Z exceeds Z* ≈ (R/a)^9/7. After this point, the charge number of the compact core Z_n remains ≈ Z*, with the rest Z* electrons forming a sparse TF atom with it. We extend our studies of collapse to the case of long cylindrical clusters as well.     

Surface Microparticles in Liquid Helium. Quantum Archimedes’ Principle

Deviations from Archimedes’ principle for spherical molecular hydrogen particles with the radius R₀ at the surface of ⁴He liquid helium have been investigated. The classical Archimedes’ principle holds if R₀ is larger than the helium capillary length L_cap ? 500 μm. In this case, the elevation of a particle above the liquid is h₊ ~ R₀. At 30 μm < R₀ < 500 μm, the buoyancy is suppressed by the surface tension and h₊ ~ R³₀/L²_cap. At R₀ < 30 μm, the particle is situated beneath the surface of the liquid. In this case, the buoyancy competes with the Casimir force, which repels the particle from the surface deep into the liquid. The distance of the particle to the surface is h_- ~ R^5/3_c/R^2/3₀ if R₀ > R_c. Here, \({R_c} \cong {\left( {\frac{{\hbar c}}{{\rho g}}} \right)^{1/5}} \approx 1\), where ? is Planck’s constant, c is the speed of light, g is the acceleration due to gravity, and ρ is the mass density of helium. For very small particles (R₀ < R_c), the distance h_ to the surface of the liquid is independent of their size, h_ = R_c.     

Low-Temperature Dynamical Transition in Lipid Bilayers Detected by Spin-Label ESE Spectroscopy

Data on neutron scattering in biological systems show low-temperature dynamical transition between 170 and 230 K manifesting itself as a drastic increase of the atomic mean-squared displacement, 〈x²〉, detected for hydrogen atoms in the nano- to picosecond time scale. For spin-labeled systems, electron spin echo (ESE) spectroscopy—a pulsed version of electron paramagnetic resonance—is also capable of detection of dynamical transition. A two-pulse ESE decay in frozen matrixes is induced by spin relaxation arising from stochastic molecular librations, and allows to obtain the 〈α²〉τ_c parameter, where 〈α²〉 is a mean-squared angular amplitude of the motion and τ_c is the correlation time lying in the sub- and nanosecond time ranges. In this work, the ESE technique was applied to spin-labeled amphiphilic molecules of three different kinds embedded in bilayers of fully saturated 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and mono-unsaturated 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) lipids. Two-pulse ESE data revealed the appearance of stochastic librations above 130 K, with the parameter 〈α²〉τ_c obeying the Arrhenius type of temperature dependence and increasing remarkably above 170–180 K. A comparison with a dry sample suggests that onset of motions is not related with lipid internal motions. Three-pulse ESE experiments (resulting in stimulated echos) in DPPC bilayers showed the appearance of slow molecular rotations above 170–180 K. For D₂O-hydrated bilayers, ESE envelope modulation experiments indicate that isotropic water molecular motions in the nearest hydration shell of the bilayer appear with a rate of ~?10⁵ s^?1 in the narrow temperature range between 175 and 179 K. The similarity of the experimental data found for three different spin-labeled compounds suggests a cooperative character for the ESE-detected molecular motions. The data were interpreted within a model suggesting that dynamical transition is related with overcoming barriers, of 10–20 kJ/mol height, existing in the system for the molecular reorientations.