List of Departments
Topmost Scientific Results

- Department of Astrophysics and Elementary Particles
- Department of High-Density Energy Physics
- Department of Theory of Quantum Processes in Nanosystems
- Department of Mathematical Methods in Theoretical Physics
- Department of Theory of Nonlinear Processes in Condensed Matter
- Department of Synergetics
- Department of Theory of Nuclei and Quantum Field Theory
- Department of Computer Maintenance

Department of Theory of Nuclei and Quantum Field Theory

- With the use of the path integral formalism for finite-temperature field theory, we find the persisting vector and axial currents that are generated in quantum chiral fermionic systems. The role of the explicit violation of chiral symmetry by fermion mass is elucidated. For the case of quantum fermionic systems in the backround of an arbitrary smooth magnetic field, we show that the chiral magnetic effect is substantiated on equally the same footing as the chiral separation effect is. Both effects remain unaltered if chiral symmetry is violated by mass.
*Y.A. Sitenko* - The generalization of the classical Padй-approximant method in the context of summing up and approximating divergent series in the perturbation theory of quantum field theory and quantum mechanics has been proposed, developed, and thoroughly investigated. This is demonstrated using the pertinent example of the quantum anharmonic oscillator, highlighting its significance and relevance in contemporary research. The suggested generalization is based on the averaging of suitably chosen Padй approximants, utilizing a properly selected weight function. This method ensures the accurate asymptotic behavior at infinity of the computed physical quantities as the coupling constant increases, in contrast to the conventional application of Padй approximations.
*V.A. Babenko, N.M. Petrov* - New approach to the description and determination of electrical multipole polarization of deuteron, particularly for quadrupole and octupole electrical polarization of deuteron. Mellin integral transformation was applied to Yamaguchi model and also to models with another potential of interaction. An analytical expression for the case of three particles with negative energy is obtained.
*V.F. Kharchenko* - The thermodynamic properties of the interacting bosonic system of particles and antiparticles at high temperatures and densities were studied within the framework of scalar and thermodynamic mean-field models. Conservation of the isospin (charge) density in the system is assumed. The influence of attraction and repulsion interactions on the thermodynamic properties of the system, especially on the possibility of Bose condensate formation, was studied. It is shown that under "weak" attraction, the boson system has a phase transition of the second order, which occurs every time the dependence of the particle density crosses the critical curve or even touches it. It was established that with a "strong" attractive interaction, the system forms a Bose condensate during a phase transition of the first order. Despite the presence of a non-zero total charge, these condensed states are characterized by a zero chemical potential. It was concluded that such states of the condensate cannot be described by the Grand Canonical Ensemble, where a certain non-zero value of the charge corresponds to a non-zero value of the chemical potential. When the system is in the condensate phase, the impossibility of using the chemical potential as a free thermodynamic variable is explained by the fact that the chemical potential must be written in the condition of condensate formation and therefore its value is fixed.
*D.V. Anchishkin* - New basis is proposed for variational calculations of a few-particle system bound states. For an N-particle system with pairwise interactions, the matrix elements of the Hamiltonian are found in an explicit form. A modified version of the basis invariant with respect to spatial translations is considered too. As an example, the
^{12}C nucleus is considered as a system consisting of three α-particles, and the convergence of the method is studied.*B.E. Grinyuk* - The current Hubble tension problem, the "third" from the historical point of view, is analyzed in the framework of quantum cosmological approach based on the quantum Bohm potential formalism. It is found that there arises a new summand in the expression for the total energy density, introducing of a novel element into the standard cosmological model. The additional energy density component that has a quantum origin may act similarly to early dark energy modifying the early expansion rate before recombination while leaving the late evolution of the universe unchanged. A characteristic feature of the proposed cosmological model is the existence of a "coasting period" (similarly to the Lemaоtre and Eddington-Lemaоtre models) in the epoch of matter-radiation equality, when the evolution of the scale factor slows down.
*V.E. Kuzmichev, V.V. Kuzmichev* - A set of nuclear reactions relevant to the cosmological lithium problem, with recent experimental data, is investigated using a microscopic many-cluster and many-channel model. Specifically, reactions arising from deuteron collisions with nuclei
^{7}Li and^{7}Be are studied in detail. Calculations employ the algebraic version of the resonating group method, incorporating realistic wave functions of nuclei in ingoing and exit channels. It is established that reactions proceed in states allowing for head-on collisions. The calculated astrophysical S-factors of the considered reactions are shown to be in fairly good agreement with available experimental data, predicting their behavior in the energy range dominant during the first seconds of our Universe's nucleosynthesis.*V. S. Vasilevsky, Yu. A. Lashko, V.I. Zhaba*

- The influence of a topological defect in the form of the Abrikosov-Nielsen-Olesen vortex that is known in cosmology and astrophysics under the name of a cosmic string on quantum systems has been studied. A magnetic field is found to be induced in the ground state of relativistic quantum bosonic matter surrounding the cosmic string. The dependence of the total induced ground state magnetic flux on the string flux and tension, as well as on the transverse size of the string, is determined.
*Yu.A. Sitenko* - The Ter-Martirosyan-Skornyakov equation is simplified using the Mellin integral transformation. An analytical expression for the case of three particles with negative energy is obtained. Simple analytical expressions of the Coulomb transition matrix of a two-particle system with a repulsive potential are obtained based on the analytical solution of the Lippmann-Schwinger equation.
*V.F. Kharchenko* - A sufficient criterion for a possibility of the spatial collapse effect in an infinite system of Bose particles is established on the basis of the variational principle with the use of Jastrow correlation factors in the wave function. Using the obtained criterion, we show that in hypothetical nuclear matter, if it consisted of α-particles, spatial collapse would take place under the assumption of any αα-interaction potential from the known set of Ali-Bodmer ones.
*B.E. Grinyuk* - The structure functions of the first excited state of mirror nuclei
^{14}C and^{14}O are studied within the five-cluster model (three α-particles plus two extra nucleons) on the ground of variational calculations with the use of Gaussian bases. It is shown that the first excited 0+ state as compared to the ground state reveals itself in a change of the spatial structure of the two-nucleon subsystem moving in the field of the^{12}C cluster. Root mean square radii and relative distances between particles are calculated. Density distributions and electric form factors (both elastic and transition ones) are studied. Pair correlation functions and momentum distributions of particles for the excited state of these nuclei are found. For all the obtained structure functions, a comparison is carried out with the corresponding functions of the ground state. Two main configurations in the ground state and excited one of^{14}C and^{14}O nuclei are revealed.*V.S.Vasilevsky, B.E. Grinyuk*

- A theory for the inducing of magnetic field in the vacuum of quantized fermion field in the background of a cosmic string of nonzero transverse size is elaborated. The dependence of the induced vacuum magnetic field strength on the string flux and tension, as well as on the transverse size of the string and on the distance from the string, is unambiguously determined.
*Cor.-member of the NAS of Ukraine Yu.A. Sitenko* - Conditions under which a quantum particle can be described using classical quantities are studied. The wavefunction of a quantum particle submitted to a potential field for which all quantum effects vanish, even if Planck's constant is non negligible, is investigated. This problem is equivalent to the problem of the motion of a particle in a refringent medium. In these media, quantum particles have classical momenta, while their wave properties are described by the wave-optics equation. In the 1D case, the particle cannot be found in the region near the origin, since the index of refraction tends to infinity there. For the 3D case with central symmetry, the wave properties are determined by a function, that has a resonance of width of the order of the de Broglie wavelength.
*V.E. Kuzmichev, V.V. Kuzmichev* - A three-cluster model of the
^{9}_{Λ}Be hypernucleus composed of two alpha-particles and Λ-hyperon has been developed. Input parameters of the model reproduce the experimental binding energy of the binary subsystem^{5}_{Λ}He . A good agreement between the calculated energies of the excited^{9}_{Λ}Be states and the available experimental data has been obtained.*A.V. Nesterov, Yu.A. Lashko, V.S. Vasilevsky*

- Temperature dependences of the tunneling rate through the screened Coulomb barrier are calculated for pp-, pd-, pt-, dd-, and dt-reactions at room temperatures, and an increase of a few orders of magnitude is demonstrated for the probability of the fusion reactions at only hundreds degrees of the temperature growth.
*B.E. Grinyuk* - We have adapted a microscopic three-cluster model, which has been developed in nuclear structure laboratory for investigation of atomic nuclei, to studying light hypernuclei. The model has been applied to analyzing the structure of the
^{9}_{Λ}Be hypernucleus, which was considered as a three-cluster system comprising of two alpha particles and a Λ-hyperon. Within the present model, the spectrum of bound and resonance states in the^{9}_{Λ}Be hypernucleus and phase shifts of elastic and inelastic scattering of a Λ-hyperon on^{8}Ве nucleus and of an alpha-particle on the_{Λ}^{5}Нe hypernucleus have been studied in detail. It was shown that cluster polarization generates a number of resonant states, most of which are very narrow with a width of less than 100 keV. There is a fairly good agreement between our results and the available experimental data, as well as the results obtained within alternative microscopic and semi-microscopic models.*V.S. Vasilevsky, Yu. A. Lashko, A.V, Nesterov* - The effects of Coulomb interaction in the formation of bound and resonant states of mirror light nuclei
^{7}Li-^{7}B,^{8}Li-^{8}B,^{9}Be-^{9}B,^{11}B-^{11}C have been studied in detail. The resonant states with strong, weak and moderate effects of Coulomb interaction have been revealed. It was shown that the Coulomb shift is maximal for bound states because the bound states are more compact than the resonant ones.*V.S. Vasilevsky* - A new position-momentum uncertainty relation, which takes into account gravitational interaction of massive particles and generalizes the known relation that was previously proposed in various theoretical models, is obtained. Gravitational corrections to mean-square deviations of position and momentum are written explicitly. It is shown that the minimum length and the minimum momentum depend on the energy of particle relative motion.
*V.E. Kuzmichev, V.V. Kuzmichev*

- The theory of polarization of the vacuum of quantized fermion field in the presence of a topological defect is constructed.
*Corr. Member of the NAS of Ukraine Yu.A. Sitenko* - Using the method of stereographic projection of the three-dimensional momentum space onto the four-dimensional unit sphere, the analytical solution of the two-particle Lippmann-Schwinger integral equation with the Coulomb interaction at the negative energy has been performed. For the first time, the analytical expressions for the three-dimensional Coulomb transition matrix at the energies that correspond to the fractional values of the interaction parameter have been obtained.
*V.F. Kharchenko* - The simple semi-phenomenological model which describes the charge independence and charge symmetry breaking of the pion-nucleon coupling constant has been proposed. The model has simple physical meaning and suggests directly proportional dependence of the pion-nucleon coupling constants on the masses of interacting nucleons and pions. On the basis of the proposed model we have found that the charged pion-nucleon coupling constant exceeds the neutral pion-nucleon coupling constant by about 7% indicative of a substantial charge independence breaking of nuclear forces in the pion-nucleon coupling constant.
*V.A. Babenko, N.M. Petrov*

- The continuum model for long-wavelength charge carriers, originating in the tight-binding approximation for the nearest-neighbour interaction of atoms in the crystalline lattice, is applied to consider quantum ground-state effects of electronic excitations in Dirac materials with two-dimensional monolayer honeycomb structures warped into nanocones by a disclination. The magnetic flux circulating in the angular direction around the nanocone apex and the pseudomagnetic flux directed orthogonally to the nanocone surface are shown to be induced in the ground state.
*Corr. Member of the NAS of Ukraine Yu.A. Sitenko* - New analytical expressions for the three-dimensional Coulomb matrix of transition are derived for energies corresponding to the integral and semi-integer value of the Sommerfeld parameter.
*V.F. Kharchenko* - Within the framework of a nonperturbative quantum theory of gravitation, based on the quantum generalization of the Hamilton-Jacobi equation of general relativity, it is shown that during the evolution of the early universe the cosmological parameters, i.e., the matter-energy density, the pressure, and the deceleration parameter, may fluctuate between positive and negative values under the influence of quantum corrections to the energy density.
*V.E. Kuzmichev* - Simple relations connecting the strange s-quark mass to the splittings of the light hyperon masses are obtained on the basis of the phenomenological quark model compatible with the quantum chromodynamics (QCD). The value of strange s-quark mass, calculated in the proposed approach, is in good agreement with the modern evaluations and calculations of this quantity, obtained by the lattice QCD methods.
*V.A. Babenko, N.M. Petrov* - An alternative way of light nuclei synthesis in the stellar environment through a triple collision of nuclei and the excitation of a narrow resonance state is studied in detail. It is shown that the long-lived resonance state which is a key element of synthesis of carbon ‒ the Hoyle-analog state ‒ exists also in the light nuclei
^{9}Be,^{9}B,^{11}B and^{11}C. Such resonance states are generated by collisions of two alpha-particles with neutrons, protons, tritons, and nuclei^{3}He, respectively. The Hoyle-analog states are not observed in the nucleus^{10}B consisting of two alpha-particles and a deuteron.*V.S. Vasilevsky, Y.A. Lashko, G.F. Filippov* - Structure characteristics of the lowest excited state of the mirror nuclei
^{14}С and^{14}О are studied within a five-particle model (three α-particles plus two extra nucleons) in terms of the variational approach with the Gaussian bases. The charge radius of^{14}О is calculated, and it is explained why this radius is smaller than that of^{14}С nucleus, although^{14}О contains two extra protons instead of two extra neutrons in^{14}С. Both elastic and transition electrical form-factors of^{14}C and^{14}O nuclei are calculated.*V. S. Vasilevsky, B. E. Grinyuk, D. V. Piatnytskyi* - Within the discrete representation of the harmonic oscillator basis, eigenvalues and eigenfunctions of the potential energy matrix are investigated for a particle in the field of central spherical square-well potentials, Gaussian potential, Yukawa potential and exponential potential. For all the potentials considered, the eigenfunctions of the potential energy operator in the discrete representation are shown to be harmonic oscillator basis functions. In the momentum representation the eigenfunctions of the potential energy operator are proved to be spherical Bessel functions.
*Y.A. Lashko*

- We consider quantum ground state effects in Dirac materials with two-dimensional monolayer structures warped into nanocones by a disclination; the nonzero size of the disclination is taken into account, and a boundary condition at the edge of the disclination is chosen to ensure self-adjointness of the Dirac-Weyl Hamiltonian operator. In the case of carbon, silicium and germanium nanocones, we show that the quantum ground state effects are independent of the disclination size and find circumstances when they are independent of the boundary parameter.
*Yu.A. Sitenko* - On the basis of Schwinger representation for the Coulomb Green function the possibility of the analytical solution of the Lippmann-Schwinger equation for the three-dimensional Coulomb transition matrix at negative energies has been established in the case of the repulsive interaction and the integer values of Coulomb parameter as well as in the case of repulsive and attractive interactions and half-integer values of Coulomb parameter (1/2 and -1/2, respectively).
*V.F. Kharchenko* - We considered a set of three-cluster systems (
^{4}He,^{7}Li,^{7}Be,^{8}Be,^{10}Be) within a microscopic model which involves the hyperspherical harmonics to represent intercluster motion. We selected such three-cluster systems which have at least one binary channel. Our aim is to study whether the hyperspherical harmonics are able and under what conditions to describe two-body channel or they are suitable for describing three-cluster continuum only. The main result of the present investigations is that to describe the nondemocratic two-cluster decay or bound states below the two-cluster threshold one needs to use a rather restricted set of the hyperspherical harmonics and hyperradial excitations as well. It was demonstrated that the eigenstates of the three-cluster hamiltonian have correct asymptotic behaviour both for bound states below two-cluster threshold and states in two-cluster continuum.*Yu.A. Lashko, G.F. Filippov, V.S. Vasilevsky* - On the basis of a simple phenomenological model, by assumption of the one-pion exchange mechanism for the nuclear forces, we establish relations between different pion-nucleon coupling constants that characterize the nucleon-nucleon interaction. The charge independence breaking effect in the pion-nucleon coupling constants is entirely explained by the mass difference between the charged and neutral pions and by the mass difference between the proton and the neutron as well.
*V.A. Babenko, N.M. Petrov*

- We study the influence of boundaries on chiral effects in hot dense relativistic spinor matter in a strong magnetic field which is orthogonal to the boundaries. It is shown that the chiral magnetic effect disappears, whereas the chiral separation effect becomes dependent not only on chemical potential, but on temperature and on a boundary condition as well. These points at a significant role of boundaries for physical systems with hot dense magnetized spinor matter, i.e. compact astrophysical objects (neutron stars and magnetars), relativistic heavy-ion collisions, novel materials known as the Dirac and Weyl semimetals.
*Yu.A. Sitenko* - New approach to the description of the off-shell Coulomb scattering amplitude that is based on using the Fock's method of the stereographic projection of the momentum space onto the four-dimensional unit sphere has been worked out. New analytical expressions for the partial-wave off-shell Coulomb transition matrices for particles with the repulsive interaction at the ground-state energy have been derived.
*V.F. Kharchenko* - Charge independence breaking (CIB) in the pion-nucleon coupling constant and the nucleon-nucleon scattering length is considered on the basis of the Yukawa meson theory. The CIB effect in these quantities is almost entirely explained by the mass difference between the charged and the neutral pions. Therewith charge splitting of the pion-nucleon coupling constant is almost the same as charge splitting of the pion mass.
*V.A. Babenko, N.M. Petrov* - The structure functions of the mirror nuclei
^{14}С and^{14}O are studied within a model "three alpha-particles plus two extra nucleons". The charge density distributions, form factors, pair correlation functions, and the momentum distributions of particles are found for these nuclei. Two spatial configurations are revealed in the ground state of^{14}С and^{14}O nuclei. The unknown experimental charge r.m.s. radius of^{14}O nucleus is predicted.*B.E. Grinyuk, D.V. Piatnytskyi* - Theoretical analysis of bound and resonance states in
^{10}Be nucleus is performed within a microscopic three-cluster model. This nucleus is represented as three-cluster system comprised of two alpha particles and a dineutron. The latter is two neutrons correlated in the space, which form a pseudo-bound state. The processes of elastic and inelastic scattering of alpha particles from^{6}He and dineutron from^{ 8}Be are also investigated. Within the present model, nuclei^{6}Не and^{8}Ве are considered as two-cluster systems, which consist of alpha particle and dineutron and two alpha particles, respectively. One of main aims of the present investigation is to study how cluster polarization of nuclei^{6}Не and^{8}Ве affects the structure of bound and resonance states in^{10}Ве and elastic and inelastic processes as well. It is shown that nuclei^{6}Не and^{8}Ве are substantially changed their size and shape when they interact with alpha particle and dineutron, respectively. It is also shown that the cluster polarization strongly changes a mutual attraction of clusters in the compound system and leads to larger energy of bound states and smaller energy and width of resonance states of the three-cluster system. Within the present model, we obtain good agreement of theoretical results with available experimental data for discrete and continuous spectrum states in^{10}Ве.*Yu.A. Lashko, G.F. Filippov, V.S. Vasilevsky*