Bogolyubov Institute for Theoretical Physics
of the National Academy of Sciences of Ukraine

Department of Applied Problems in Theoretical Physics
  • The structure of the mirror nuclei 14С and 14O is studied within a five-particle model (three alpha-particles plus two extra nucleons). The interaction potentials are proposed to have data fit with the experimental energy and radius of 14С nucleus, as well as with the energy of 14O. Within the variational approach in Gaussian representation, we obtain the ground state wave functions of the abovementioned five-particle systems. The charge r.m.s. radius of 14O nucleus is predicted. The charge density distributions and elastic formfactors are found.
    B.E. Grinyuk, D.V. Piatnytskyi
  • Some quasi-relativistic equations are found to have similar expansions in 1/c up to the fourth order to within the terms removable by additional unitary transformations. The expansions of these equations contain only the terms proportional to е2, while expansions of the Breit and Salpeter equations contain the terms ~ е4.
    A.I. Turovsky
  • The structure of mirror nuclei 10Bе and 10С is studied within a four-particle model (two alpha-particles plus two extra nucleons). Interaction potentials between a nucleon and an alpha-particle, as well as that between alpha-particles are proposed with non-local repulsive terms - in order to take into account the Pauli principle in a phenomenological way, and to reach a concordance with the experimental data. In the framework of variational calculations, the four-particle problem is solved with controlled accuracy, and the main structure characteristics of 10Bе and 10С nuclei are explained: the charge form factors and density distributions are predicted, the pair correlation functions and the momentum distributions both of extra nucleons and of alpha-particles in these nuclei are studied.
    B.E. Grinyuk, I.V. Simenog
  • On the basis of variational principle, with complete account of pair correlations, the repulsive δ-potentials are shown to be inefficient (i.e. they do not make any influence on the spectrum and other physical observables) at a dimension of the space greater than or equal to 2. The proved theorem refutes the existing misconception about a possible treating of the δ-potentials within the perturbation theory.
    I.V.Simenog, B.E.Grinyuk, M.V.Kuzmenko
  • Symmetric and antisymmetric terms have been obtained in the framework of the variational approach for two-dimensional Coulomb systems of symmetric trions XXY. Stability diagrams and certain anomalies arising in the 2D space are explained qualitatively in the framework of the Born-Oppenheimer adiabatic approximation. The asymptotics of energy terms at large distances obtained for an arbitrary space dimensionality are analyzed, and some approximation formulas for 2D terms are proposed. An anomalous dependence of multipole moments on the space dimensionality has been found in the case of a spherically symmetric field. The main results obtained for the 2D and 3D problems of two Coulomb centers are compared.
    I.V. Simenog, V.V. Mikhnyuk, Yu.M. Bidasyuk
  • Structure characteristics are studied for the four-cluster nuclei consisting of two alpha- particles and two nucleons. These nuclei two spatial configurations to be the "cross" and "tetrahedron" are ascertained. The main structure functions of 10Be and 10C nuclei are obtained, and specific modes of behaviour are revealed for the charge form factors, momentum distributions, and pair correlation functions.
    B.E. Grinyuk, I.V. Simenog
  • The thresholds of stability diagrams are constructed for a three-particle system with the total angular momentum equal to unity. The analysis of the thresholds behaviour, as well as their scaling law in the vicinity of the Efimov effect is carried out for systems with the zero and unity angular momenta. The "traps" effect is revealed for the energy levels of the Efimov series.
    Yu.M. Bidasyuk, I.V. Simenog
  • For quantum systems of particles with an interaction in the form of a superposition of smooth and delta-type potentials in two- and three-dimensional spaces, it is proved with complete account of pair correlations that the attractive delta-potentials cause the collapse of a system, whereas the repulsive delta-potentials give no contribution into all spectral characteristics of the system. Thus, the delta-potentials are shown to be efficient only for one-dimensional systems.
    I.V. Simenog, B.E. Grinyuk, M.V. Kuzmenko
  • Halo-nuclei 6Не and 6Li are studied within a model of α-particle plus two extra nucleons, and nuclei 10Bе and 10С are explored within a four-cluster model with two α-particles and two extra nucleons. New versions of the αα-interaction involving local and non-local potentials are proposed. The density distributions, pair correlation functions, and form factors are calculated. The dependence of the form factors on the momentum transferred is explained.
    B.E. Grinyuk, I.V. Simenog
  • The asymptotics of the density distributions and the pair correlation functions of 3H and 3He nuclei are obtained. The experimental momentum distributions of nucleons and the charge form factors are explained.
    D.V. Piatnytskyi, I.V. Simenog
  • The energy dependence of the Woods--Saxon-type interaction potential for the 13С + 16О scattering is studied with regard for the bulk and surface absorptions. It is found that the potential is of quasimolecular form.
    I.V. Simenog
  • The density distributions of particles, mass and charge form factors, and two-particle correlation functions are calculated and analyzed for a number of reference atomic and molecular three-particle systems. The asymptotic behavior of the density distributions and the form factors are studied. The form factors of three-particle systems are shown to decrease according to a power law universal for all the Coulomb systems.
    M.V. Kuzmenko, I.V. Simenog
  • Possibilities of the determination of a symmetry of energy states obtained by means of stochastic variational calculations without preliminary symmetrization of the states are studied for the systems of three and four charged particles. Some local and integral computational schemes are proposed to determine a posteriori the permutational symmetry of bound states.
    I.V. Simenog, M.V. Kuzmenko, V.M. Khryapa