Archive

Department for Astrophysics and Elementary Particles

- Rhombohedral multilayer graphene together with Bernal stacked bilayer graphene belongs to a new class of chiral two-dimensional electron systems characterized by the low energy Hamiltonian with chiral properties. The dynamical polarization function is calculated in the neutral rhombohedral multilayer with dynamically generated gap. Taking it into account, a self-consistent gap equation is derived whose solutions show that the gap is maximal in rhombohedral trilayer graphene. It is shown that the gap monotonously decreases with subsequent increase of the number of layers due to the fact that the effects of screening win over those connected with the decrease of curvature of the electron energy zones.
*V.P. Gusynin, E.V. Gorbar* - The leading radiative corrections to the axial current in the chiral separation effect are calculated in dense QED in an external magnetic field. Although in the literature there are arguments related with the chiral anomaly which determine the axial current through the topological contribution in the lowest Landau level in the free theory, it was found that the quantum electrodynamical interaction leads to nontrivial radiative corrections to the axial current. The direct calculations performed to the linear order in the external magnetic field showed that the nontrivial radiative corrections to the axial current are provided by the Fermi surface singularity in the fermion propagator at nonzero fermion density.
*E.V. Gorbar* - The confinement phase transition had a strong impact on the dynamics of the early universe. Witten noticed the possibility that part of the colored objects – quarks and gluons escape phase transition, remaining as islands of colored objects, called quark-gluon nuggets (quark nuggets – QN). We studied the evolution of the universe filled with QN, on a late period of its evolution, when inhomogeneities such as 1-t or 2-nd group galactic were already formed. In that late, nonlinear stage, the hydrodynamical approach is not applicable for the analysis. Instead, mechanical analogues were used. They describe phenomena inside the inhomogeneity cells, and provide a good means to study scalar excitations in various cosmological models. Compatibility of cosmological models containing QN with mechanical ones was proven. To do so, a model of the universe filled with dust (both baryon and dark matter), radiation and QN was studied. At a late period of the evolutions and at distances much smaller the inhomogeneity scales (about 190 Mps), our universe was strongly inhomogeneous. It is important to account for inhomogneneities in form of galactic, groups and clusters of galactic. We have assumed that radiation and QN fluctuate around some average values. These fluctuations, as well as the inhomogeneities violate the metrics, for which reason a mechanical method is preferable. It made possible to account for a small admixture of colored objects (QN) that survived after the phase transition.
*L.L. Jenkovszky* - The dynamics of the expanding universe is analyzed in terms of the quantum geometrodynamical model. It is shown that the equations of quantum theory can be reduced to the Einstein equations with an additional source of the gravitational field of quantum nature. After averaging over corresponding quantum states of the scalar field which plays the role of a surrogate of primordial matter, the classical source of the gravitational field takes the form of a barotropic fluid. The exact solution of the non-linear equation for the phase of the wave function in the model of the free scalar field is found and it is shown that the averaged free scalar field turns into the Weyssenhoff spin fluid. In the semi-classical approximation, the obtained equations coincide with the equations of the Einstein–Cartan theory. The cases when the contribution of the quantum effects into the gravitational interaction becomes significant on macroscopic scale are analyzed. It is demonstrated that, unless the whole, at least a part of such matter-energy constituents as dark matter and dark energy may have a quantum origin.
*V.V. Kuzmichev* - We review the current status of indirect search for dark-matter signatures in gamma-rays including the recently claimed line candidate at ~130 GeV. To resolve the origin of this line candidate (instrumental, astrophysical, decay/annihilation of dark-matter particles), we propose special observations of the Galactic Center using the future gamma-ray mission Gamma-400.
*D.A. Iakubovskyi, D.I. Malyshev* - We show that the current bounds on the decaying dark matter in keV region can be significantly improved using Large Observatory For X-ray Timing (LOFT) – a next-generation X-ray telescope selected by the European Space Agency as one of the space mission concepts within the “Cosmic Vision” programme with the launch possibility in the beginning of 2020th. Using special simulations that take into account the existing (Requirement) and future (Goal) characteristics of the Large Area Detector (LAD), we show that the current bounds on the decaying dark matter can be improved 10–30 times in the 1.5–30 keV range. This not only makes LOFT suitable for a number of pure astrophysical problems but also allows one to probe an interesting range of parameters of particle physics beyond the Standard Model not accessible to any other existing and planned ground and cosmic-based experiment.
*D.A. Iakubovskyi* - Using the observations of the Fermi Gamma-ray Space Telescope, we performed measurements and obtained upper limits on the emission of Cyg X-1 in the photon energy range of 0.03–300 GeV. The results are presented separately for the hard and soft spectral states of the source. In the hard state, we detected a weak steady emission in the 0.1–10 GeV range with a power-law photon index of Γ ? 2.6 ± 0.2. This measurement, even if considered to be an upper limit, strongly constrains Compton emission of the steady radio jet, present in that spectral state. If optically thin synchrotron emission of the jet is to account for the MeV tail, the value of the magnetic field in the jet has to be much above equipartition. The GeV-range measurements also strongly constrain models of hot accretion flows, most likely present in the hard state, in which γ-rays originate from the decay of neutral pions produced in collisions of energetic ions in the inner part of the flow. In the soft state, the obtained upper limits constrain electron acceleration in a non-thermal corona, present around the accretion disc. The coronal emission above 30 MeV has to be rather weak, which is most readily explained by absorption of γ-rays in pair-producing photon-photon collisions. Then, the size of the bulk of the corona is less than a few tens of the gravitational radii.
*D.I. Malyshev* - We analyzed broad multi-wavelength observations of the 2010–2011 periastron passage of the gamma-ray loud binary system PSR B1259-63. High-resolution interferometric radio observations establish extended radio emission trailing the position of the pulsar. Observations with the Fermi Gamma-ray Space Telescope reveal GeV gamma-ray flaring activity of the system, reaching the spin-down luminosity of the pulsar, around 30 days after periastron. There are no clear signatures of variability at radio, X-ray and TeV energies at the time of the GeV flare. Variability around periastron in the Hα emission line can be interpreted as the gravitational interaction between the pulsar and the circumstellar disk. The equivalent width of the Hα grows from a few days before periastron until a few days later, and decreases again between 18 and 46 days after periastron. In near infrared, we observe the similar decrease of the equivalent width of Brγ line between the 40th and 117th day after the periastron. For the idealized disk, the variability of the Hα line represents the variability of the mass and size of the disk. We discuss possible physical relations between the state of the disk and GeV emission under assumption that GeV flare is directly related to the decrease of the disk size.
*D.I. Malyshev* - We studied the properties of the diffuse γ-ray background around the Galactic plane at energies 20–200 GeV. We found that the spectrum of this emission possesses significant spatial variations with respect to the average smooth component. The positions and shapes of these spectral features change with the direction on the sky. We therefore, argue that the spectral feature around 130 GeV, found in several regions around the Galactic Center and in the Galactic plane, cannot be interpreted with confidence as a γ-ray line, but may be a component of the diffuse background and can be of instrumental or astrophysical origin. Therefore, the dark-matter origin of this spectral feature becomes dubious.
*D.I. Malyshev* - An all-sky X-ray map in hard X-rays (2–10 keV) is built with detailed treatment of systematic errors. The resulting maps in hard X-rays (XMM-Newton) and gamma-rays (Fermi) are located at a specially adapted public web interface of the VIRGO observatory at http://skyview.virgoua.org.
*D.I. Malyshev, D.O. Savchenko, D.A. Iakubovskyi* - The Bose-Einstein condensation (BEC) of magnons created by a strong pumping in ferromagnetic thin films of yttrium iron garnet used as systems of finite size is considered analytically. Such a peculiarity, typical for this magnetic material, as the presence of a minimum in the spectrum of spin waves at a finite value of the wave vector is taken into account. The definition of high temperature BEC is introduced and its characteristics are discussed. A role of boundary conditions for spin variables is analyzed, and it is shown that in the case of free spins on the boundary the magnon lattice can form in the system. The factors responsible for its appearance are discussed.
*A.I.Bugrij* - Free energy for Z(2) and Z(3) spin systems is calculated as a finite sum in relations of an iterated main eigenvalues of the transfer matrix. For the Ising model on the lattice strip of the width M=16 it is shown to be practically indistinguishable from an exact one already after 5 renormalization group (RG) iterations. Z(4) and Z(5) spin systems are investigated within the modified phenomenological RG framework. For the Z(5) model, the phase structure in the full range of the coupling constants (t1 [0,1], t2 [0,1]) is analyzed. Four fixed points'positions are found. These fixed points correspond to: 1) the standard Potts model (t1 = t2); 2) the vector Potts model where t1 and t2 relate to each other by certain parametrical dependency; 3) and 4) an extra fixed points t1 = 0.589, t2 = 0.053 and its symetric counterpart t2 = 0.589, t1 = 0.053. It is shown that the critical exonent ν in these extra fixed points tends to infinity as the lattice strip's width M increases which means these points correspond to phase transition of an infinite order. The phase flow in the vicinity of the fixed points is analyzed. Obtained approximate results reproduce an exact ones with very good precision whenever these last are available.
*V.A. Kushnir* - We have found that the boundaries affect strongly the bulk microstructure of helium-II. In particular, the formulas for the phonon energy and the ground-state energy of a system with boundaries differ from those of a closed system by the factor outside the interatomic potential (here, d is the number of noncyclic coordinates).
*M.D. Tomchenko* - We propose a novel approach to the problem of boundary conditions for scalar cosmological perturbations in a braneworld model. It consists in considering the topology of a spatially closed universe that bounds a compact set in the four-dimensional space. This space does not have any boundaries except for the brane itself; the setup is thus characterized as a multi-dimensional theory without boundaries (no-boundary). It is shown that equations for scalar perturbations effectively close on the brane in this approach if its spatial curvature is marginally small. A new additional modes of the evolution of perturbations of matter density are found, the presence of which in principle distinguishes this model from the standard cosmology based on general relativity.
*A.V. Viznyuk, Yu.V. Shtanov* - We estimated the residual magnetic field on superlarge spatial scales in the inflationary scenario in a marginally open universe. It is shown that the expected magnitude of the magnetic field on scales larger than the scale of spatial curvature cannot exceed 10–59 G in this scenario.
*Yu.V. Shtanov* - Classical solutions of the O(3) nonlinear sigma model with the parametrization of S2 sphere by orthogonal wave vectors (lattice) are found. The solutions of a set of differential equations reduce to the Liouville, sin- and sinh- Gordon equations through the Belavin-Polyakov self-dual equations. The solutions of wave-crystal type are presented also for the SO(5) nonlinear sigma model which serves as a model for high temperature superconductivity. We constructed conformal gauge- invariant tensor conservation laws for abelian p-forms gauge theory and Yang conformal gravity as bilinear forms being Hodge dual to strengths of fields and Killing conformal fields. These tensor currents exist in critical space-time dimensions where the energy-momentum tensor is traceless.
*O.I.Batsula* - We investigated the Casimir effect for charged scalar matter in a constant and homogeneous external magnetic field. In a general case, we obtained final expressions for the surface vacuum energy density and pressure at the boundary. We consider the asymptotic behavior of the vacuum-energy density and pressure in the cases of strong and weak external magnetic field. It was proved that the vacuum energy density is practically independent of the details of the boundary conditions in the case of a strong magnetic field.
*Yu.A. Sitenko, S.А. Yushchenko* - A reggeometric (Regge+geometry) model of lepton-hadron and hadron-hadron processes was developed. The new features of the model are: a) two different classes of reactions are considered on the same footing, and b) the number of the free parameters is limited, being the same in different classes of reactions: deeply-virtual Compton scattering (DVCS), exclusive diffractive production of vector mesons and in elastic hadron scattering.
*L.L. Jenkovszky* - Chiral asymmetry of the normal ground state was investigated in quantum electrodynamics at nonzero fermion density in an external magnetic field. The electron self-energy in a magnetized QED plasma to the leading perturbative order in the coupling constant and to the linear order in an external magnetic field was calculated. It is found that the chiral asymmetry of the normal ground state of the system is characterized by two new Dirac structures. One of them is the familiar chiral shift previously discussed in the Nambu--Jona-Lasinio model. The other structure is new. It formally looks like that of the chiral chemical potential, but is an odd function of the longitudinal component of the momentum, directed along the magnetic field. The origin of this new parity-even chiral structure is directly connected with the long-range character of the QED interaction. The form of the Fermi surface in the weak magnetic field is determined.
*E.V. Gorbar* - The phase diagram of a Dirac semimetal in a magnetic field at a nonzero charge density was studied. It is shown that there exists a critical value of the chemical potential at which a first-order phase transition takes place. At subcritical values of the chemical potential the ground state is a gapped state with a dynamically generated Dirac mass and a broken chiral symmetry. The supercritical phase is the normal (gapless) phase with a nontrivial chiral structure: it is a Weyl semimetal with a pair of Weyl nodes for each of the original Dirac points. The nodes are separated by a dynamically induced chiral shift. The direction of the chiral shift coincides with that of the magnetic field and its magnitude is determined by the strengths of the magnetic field, the quasiparticle charge density, and the strength of the interaction.
*E.V. Gorbar*

Department for Quantum Theory of Molecules and Crystals

- Mechanism of formation of electroluminescence is studied for a linear molecule embedded between the metallic electrodes. It is shown that an electroluminescence can appear if the photochromic group of the molecule is separated from the electrodes by covalent bonds. Electroluminescence is formed in the conditions when a difference of chemical potentials of the electrodes exceeds energy of excitation in the molecule and, additionally, an electron transfer from the donating electrode to the molecule occurs in a resonant regime. In this case, a molecular excitation is formed owing to electron hoppings between the electrodes and the molecule as well as due to an inelastic interelectrode electron tunneling accompanied by a virtual participation of the charged states of the molecule.
*V.O. Leonov, Ye.V. Shevchenko, E.G. Petrov* - Role of intramolecular exchange interaction in formation of the transient and steady-state currents in a molecular diode is clarified. It is shown that at weak exchange interaction between the unpaired electrons of an optically excited molecule and, thus, at negligible energy splitting between the excited singlet and triplet molecular states , the steady-state photocurrent is close in magnitude to the peak photocurrent, whereas the same current is suppressed when the exchange interaction is strong. The reason is that a molecule in the triplet state exhibits itself as a trap blocking an electron transfer between electrodes.
*V.O. Leonov, E.G. Petrov* - Conductance properties of a non-conjugated organic molecule that contains the localized bonds, have been studied with taken into consideration a distribution of an electron density within the molecule. It is shown that conductance properties of such molecule are determined by the electrons situated at the completely occupied molecular orbitals. As to an electron transmission along the molecule, it results from a superexchange interaction between the localized orbitals whereas a nonlinear current is associated with an interelectrode electron tunneling controlled by the noted localized orbitals. Theoretical results obtained are in a good agreement with experimental data concerning the trimethylsil-acetilene molecule with two triple and one double bonds.
*O.L. Kapitanchuk, E.G. Petrov* - A microscopic model of the non-stationary system contacting to the condensed medium is proposed. By the example of a biomolecular receptor, the role of medium fluctuations of dichotomous and trichotomous types in achieving a control of the dependent on temperature kinetic and cooperative receptor's properties is discovered. It is found out that comparing to dichotomous fluctuations the presence of trichotomous fluctuations does not influence the possibility of emerging the fact of fractal cooperativity, which is general for receptors, but due to the effect of stochastic narrowing of the width of energy levels can rather make the process of their temperature-independent desensitization several times faster.
*V.I. Teslenko* - A density matrix based theoretical description of sequential electron transmission through a single molecule sandwiched between two nanoelectrodes and placed in a nanoresonator is presented. Electroluminescence of a molecular junction has been calculated and an enhancement of the related spectra by more than three orders of magnitude could be demonstrated by changing the resonance condition between the plasmon hybrid level of the nanoresonartor and the molecular transition. A selective enhancement of different parts of the vibrational progression in the emission spectrum becomes possible by varying the distance between the nanoresonators.
*Ya.R. Zelinsky*

Department for Mathematical Methods in Theoretical Physics

- A new deformed Bose gas model is proposed based on the (deformation) structure function com¬bi¬ning q-deformation and quadratically nonlinear deformation. The model enables an effective description of the interacting gas of (2-fermion or 2-boson) composite bosons or quasi-bosons. Using certain extension of Jackson derivative, we derive the expression for the total mean number of particles, deformed virial expansion of the equation of state along with five first virial coefficients. That corres¬ponds to virial expansion of the equation of state for non-ideal gas of composite bosons with some nontrivial interac¬tion between them.
*A.M. Gavrilik, Yu.A. Mishchenko* - A multiparametric deformation of two-dimensional conformal field theory is constructed. The pole structure is found for the product of holomorphic component of the energy-momentum tensor and a primary conformal field. A realization of the deformed Virasoro algebra on conformal fields is given; the two-point correlation function of this theory is calculated.
*I. Burban* - General four-point conformal blocks of quantum conformal field theory with central charge c=1 on the Riemann sphere are expressed as the coefficients of Fourier transform of the tau-function of the Painleve VI equation with respect to one of the integration constants. On this base it is shown that for c=1 the fusion matrix (matrix of the transition between the s- and t-channel conformal blocks) coincides with the coefficient of connection which relates the asymptotic expansionsof the tau-function in the vicinity of distinct critical points. Final result for these quantities is given explicitly in terms of the ratio of two products of the Barnes G-functions with the arguments, expressed through the conformal dimensions or the monodromy data.
*N.Z. Iorgov, O. Lisovyy, Yu.V. Tykhyy*

Department for Mathematical Modelling

- The mathematical model of bank operating is built basing on the introduced concept of base bank operating model and its generating structures, namely, the lower bound dynamics of the bank investment strategy into risky and non-risky assets, the lower bound dynamics of deposit's attracting strategy to the bank accounts, and the bank repayments upper bound dynamics. The bank's capital lower bound dynamics is constructed and the estimate is obtained for the probability of bank default under favorable conditions for investment to the assets of the economy. The estimate depends on the capital value providing liquid bank's operating, the choice of investment strategy, bounds for the repayments, starting capital, and the maximum repayments.

Department for Theory of Nonlinear Processes in Condensed Matter

- The tunneling of a particle with non-zero spin through the potential barrier of the finite width, which has a chiral symmetry, is studied with the account of the spin-orbit interaction. Based on the exact solution of the Shroedinger equation, the trnasition and reflection coefficients are calculated and it is shown that such barriers posses a property of spin selectivity. This means that non-magnetic barriers can lead to a spin current in the absence of their mirror symmetry. These expressions are used to describe quantitatively the experiments on the transfer of photoelectrons through the layers of DNA moleculers on a substrate.
*O.O. Eremko, V.M. Loktev* - The propagation is studies of a soliton (fluxon) in a two-dimensional Josephson contact with a strip-like in-homogeneity , which belongs to the class of a short-cuts and is a line oriented perpendicular to the propagation of fluxons. The radiation , caused by scattering of a fluxon on in-homogeneity, is calculated and shown to have a resonant dependence on the fluxon velocity. which is qualitatively different from the case of point-like impurity, for which such a dependence is a monotonously increasing function.
*Ya.O. Zolotaryuk* - The effect of electron temperature on absorption and scattering of light by metallic nanoparticles during the excitation of a surface plasmon, is studied. Expressions for the tensors of electroconductivity and polarizability at finite electron temperatures are obtained. Electroconductivity and shape of resonance of the surface plasmon are obtained for a spherical metallic nanoparticle. These results allow to describe various kinetic phenomena in such spherical particles, place in a dielectric medium.
*M.I. Grigorchuk*

Department for Computational Methods in Theoretical Physics

- Two types of nanocrystal arrangement have been found to exist in the binary layered crystal system with isomorphic inclusions: on the layer surface and along the linear structural defects of the host crystal. Within the model proposed it is shown that the excitation energy transfer to nanocrystals of the first type is realized by the electron-hole and exciton mechanisms while to those of the second type the electron-hole mechanism prevails. Calculation of the energetic characteristics involving the electron-phonon interaction allowed us to identify the 4H crystal modification of impurity nanoinclusions.
*N.V. Gloskovs'ka* - Superconductive properties of recently obtained MgB2 nanoparticles are studied. Within a two-level model, the two-gap superconductivity of a nanosize system is investigated. The equations for the two gaps and the condensation energy of such a system are obtained for the first time.
*S.P. Kruchinin* - The propensity of the fullerenes' void to form the dimers of the noble gas atoms is shown for the first time; e. g., the He-He bond length in He2@C60 is equal to 1.936 Å. To experimentally detect the aforementioned endofullerenes, we obtain, by means of vdW-corrected time-dependent density functional formalism, the UV absorption spectrum of He2@C60 which exhibits a well-defined absorption peak at ~360 nm and a broad absorption between 450 and 650 nm.
*E.S. Kryachko* - It is shown that the manifestations of monomeric cooperativity observed in the functioning of some enzymes (hexokinases, oxidases, transporters and others), especially in recent experiments on single molecules, can be hardly explained quantitatively or qualitatively within modified Michaelis-Menten schemes. Instead, they are readily apparent from a nonlinear sorption theory we have developed.
*L.N. Christophorov*

Department for Synergetics

- The peculiarity of the interaction between particles immersed into a smectic liquid crystal with a layered structure was obtained. Such a structure of a liquid crystal imposes restrictions on possible deformations of the layer displacement ﬁeld. Previous studies neglect this fact and give improper results for the interaction potential within one molecular layer. Was shows that such restrictions yield an interaction potential substantially diﬀerent from those of previous studies. Oscillatory behavior, which was not present in the potentials of previous studies, might give rise to superstructures of immersed particles with ﬁnite interparticle distance.
*O.M. Tovkach, B.I. Lev* - General description of a cellular structure formation in a system of interacting particles has been proposed. Analytical results are presented for such structures in colloids, systems of particles immersed into a liquid crystal and gravitational systems. It is shown, that physical nature of formation of cellular structures in all systems of interacting particles is identical. In all cases a characteristic of the cellular structure,depending on strength of the interaction, concentration of particles and temperature,can be obtained.
*B.I. Lev* - The influence of refraction on statistical properties of output stream of excitatory neuron with delayed feedback was studied within rigorous mathematical framework. It is proven that even in the refraction presence the output stream cannot be represented as Markov of any finite order.
*A.K. Vidybida, K.G. Kravchuk* - Generalization of a disordered metal's theory has been proposed when scattering of quasiparticles by impurities is caused with a retarded interaction. It was shown that in this case Anderson's theorem was violated in the sense that embedding of the impurities in s-wave superconductor increases its critical temperature. The increasing depends on parameters of the metal, impurities and their concentration. At a speciﬁc relation between the parameters the critical temperature of the dirty superconductor can essentially exceed critical temperature of pure one up to room temperature. Thus the impurities catalyze superconductivity in an originally low-temperature superconductor.
*C.V. Grigorishyn, B.I. Lev* - Autocatalytic processes were found in a mathematical model. They influence on a self organization and a cyclic recurrence in dynamics of Crebs cycle. A phase-parametric diagram of bifurcation cascade transition into a chaotic regime was obtained, which has Feigenbaum scenario. The fractal behavior of the cascade was investigated.
*V.J. Grytsay* - In the simplest realization of Brownian motion, a colloidal sphere moves randomly in an isotropic fluid; its mean squared displacement (MSD) grows linearly with time t. Brownian motion in an orientationally ordered fluid—a nematic—is anisotropic, with the MSD being larger along the axis of molecular orientation, called the director. We found that at short time scales, the anisotropic diffusion in a nematic becomes anomalous, with the MSD growing slower or faster than t; these states are respectively termed subdiffusion and superdiffusion. The anomalous diffusion occurs at time scales that correspond to the relaxation times of director deformations around the sphere. Once the nematic melts, the diffusion becomes normal and isotropic. Our experiment shows that the deformations and fluctuations of long-range orientational order profoundly influence diffusive regimes.
*B.I. Lev*

Department for Structure of Atomic Nuclei

- We formulated a general approach to construct phase portraits of a quantum system in the Fock-Bargmann space. The method was applied to the free motion of a 1D quantum particle, to the motion in the field of a Gaussian potential, and to the two-cluster system α+d. The phase portrait of the state of a quantum system characterized by the energy E is the density distribution over phase trajectories in this state. We have shown that the phase portraits provide an additional important information about quantum systems, as compared to the wave functions in the coordinate or momentum representation. The density distribution for a bound state is localized in a small area of the phase space, and all phase trajectories are finite. The phase portrait for the states of the continuum spectrum contains both infinite and finite trajectories. As the energy E increases, the contribution of the finite trajectories is reduced, and the infinite trajectories are condensed around the classical phase trajectories. Hence, the Fock-Bargmann space provides a natural description of the quantum-classical correspondence and allows us to establish, at which energy the quantum phase trajectories approach their classical limit.
*Yu.A. Lashko, G.F. Filippov, V.S. Vasilevsky, M. D. Soloha-Klymchak* - The structure of
^{10}В nucleus is investigated. For this aim, a microscopic three-cluster model is involved. The nucleus^{10}В is modeled as a three-cluster system, which consists from two alpha-particles and deuteron. This configuration has minimal threshold energy among other three-cluster channels, and allows one to take into account the dominant two-cluster channels of the^{10}В decay. Effects of the interacting cluster size and parameters of nucleon-nucleon interaction on the bound states are studied in detail. It is shown, that spin-orbital components of the potential have a large impact on the energy and relative position of the bound states. The spectroscopic factors for virtual decay of the^{10}В ground and excited states on three clusters α+α+d are calculated. They determine measure of clusterization and effects of the Pauli principle on the energy level. It is also demonstrated how shape and size of the nucleus depends on energy of the excited state.*V.S Vasilevsky, A.V. Nesterov, T.P. Kovalenko*

Department for Theory of Nuclei and Quantum Field Theory

- A possibility of the generation of a magnetic field by a cosmic string appearing in the aftermath of the deconfinement-confinement phase transition in early Universe is considered. We find the theoretical estimates of the magnetization of the surrounding plasma owing to its interaction with the magnetic field of the cosmic string.
*Yu.A. Sitenko* - Based on the quantum T-matrix formalism for description of the interaction of a charged particle and a complex, the inhomogeneous integral Lippmann-Schwinger equation with the Coulomb interaction that takes consistently virtual multiple scattering into account has been analytically solved and the general formula for all the electric multipole polarizabilities of the hydrogeh-like atom has been derived.
*V.F. Kharchenko* - The influence of the mass difference between charged and neutral ?-mesons on the low-energy characteristics of nucleon-nucleon interaction in the
^{1}S_{0}spin-singlet state was studied within the framework of the effective-range approximation. By making use of the latest experimental results on the nd breakup reaction we obtain the following values for the neutron-neutron scattering length and effective range: a_{nn}=-16.59fm, r_{nn}=2.83fm.*V.O. Babenko, M.M. Petrov* - Model of an Ohmic contact as a piece of metal of the finite capacitance attached to a quantum Hall edge was proposed. It is shown that charged quantum Hall edge states may have weak coupling to neutral excitations in an Ohmic contact.
*I.P. Levkivskyi*