The alpha-decays of even-even isotopes of actinides and superheavy nuclei to the ground 0(+) and first 2(+) states of their daughter nuclei are studied. The conditions for the maximum intensity of alpha-decay from the ground state to the lowest 2(+) state are analyzed in detail based on existing experimental data. The decays to the first 2(+) states reach their maximum intensity relative to those to corresponding ground states of daughter nuclei at N-D = 136, due to the corresponding increasing Q(alpha)(2(+)). This correlates with relatively strong negative octupole deformation of daughter nucleus and is also accompanied by decreasing E(2(+)). For the alpha-decays of heavy nuclei up to Og, the half-lives and population probabilities of the 0(+) and 2(+) states of the daughter nucleus are described and predicted employing the preformed cluster model.

The quantum-mechanical description of the collective angular motion in a system of two touching fission fragments is proposed. The main peculiarities of excitation spectrum and the structure of the wave functions are investigated. As found, the angular motion approximately corresponds to independent vibrations of fragments around the pole-to-pole configuration. The model allows us to explain the experimentally observed lack of correlation between the angular momenta of fission fragments. Additionally the correlation between angular momentum and fragment mass is primarily linked to the change of fragments deformation. The saw-tooth behavior of angular momentum distribution with respect to the fragment mass is well explained.

The non-Markovian dynamics of a two-dimensional charged harmonic oscillator linearly coupled to a neutral bosonic heat bath is investigated in a linear-polarized electric field. The analytical expressions for the time-dependent and asymptotic magnetic moment are derived for the Markovian and non-Markovian dynamics. It is predicted that the liner-polarized electric field generates strong orbital currents and magnetization in a symmetric harmonic oscillator embedded into anisotropic heat bath. The role of the mixed dissipative kernel in magnetization is analyzed.

Spontaneous fission and α decay from the ground state of nuclei 248No and 252Rf are studied within the dinuclear system model. All these decay processes are considered as the evolution of a nucleus in the charge (mass) asymmetry coordinate. For the even–even and even–odd nobelium and rutherfordium isotopes, the available experimental spontaneous fission and α -decay half-lives of the ground state are effectively described.

Carbon burning is crucial for the fate of massive stars and element creation in the Universe. Its understanding at stellar energies is a great theoretical challenge, as carbon fusion is a multidimensional quantum tunneling process affected by resonances whose origin is not fully understood yet. Simplified quantum dynamical coupled-channels calculations are presented, suggesting that clustering in the intermediate nuclear molecule is a source of fusion resonances.

Evolution of occupation number is studied for a bosonic oscillator (with one and two degrees of freedom) linearly fully coupled to fermionic and bosonic heat baths. The lack of equilibrium in this oscillator is discussed in the light of the creation of an energy source. The connection of such a system with known nonlinear self-oscillating systems is shown.

Comparative analysis of the complete fusion reactions ^12C + ^12C, ^12C + ^13 C and ^13C + ^13 C at extremely low energies is performed using the Extended Quantum Diffusion Approach. The theoretical calculations are compared with the available experimental data, and the results are discussed for future experiments. The study reveals the presence of a maximum in the astrophysical S-factor for these reactions.

Fusion reactions with stable and radioactive isotopes of light nuclei are indicated to control the crustal composition, nucleosynthesis, and heating mechanism during nuclear burning in neutron stars. The role of isospin asymmetry and proton-/neutron-skin thickness in the fusion excitation function and its related astrophysical S factor is investigated for the reactions involving O-12,O-14-20,O-22,O-24,O-25,O-28 isotopes at sub-barrier energies of astrophysical interest. The calculations are performed in an extended quantum diffusion framework. Among many examined potentials, the only potentials based on the Skyrme-BSk19 and M3Y-Reid nucleon-nucleon interactions successfully reproduce the experimental O-16+ O-16, C-12+ O-16, S-36+ Ca-48, and Ca-48+ Ca-48 fusion data, over the whole considered energy range. The height, radius, and curvature of the Coulomb barrier for the interactions involving proton-rich 12,15O isotopes are found to impede the near- and above-barrier fusion cross section and the corresponding S factor relative to the O-16+ O-16 reaction. However, the relatively small reduced mass and proton-skin thickness act to enhance fusion at deeply sub-barrier energies. For the interactions involving neutron-rich O(N > 8) isotopes, the fusion enhancement due to the produced Coulomb barrier is supported by relatively large Q values and neutron-skin thicknesses, against the increase of reduced masses. The neutron transfer is indicated to hinder the fusion in some A1O+ A(2)O (A(2) >= A1 + 4) reactions at sub-barrier energy.

The theory of open quantum systems is applied to study galvano-, thermo-magnetic, and magnetization phenomena in axial symmetric two-dimensional systems. Charge carriers are considered as quantum particles interacting with the environment through a one-body (mean-field) mechanism. The dynamics of charge carriers is affected by the average collision time that takes effectively into account two-body effects. The functional dependencies of the average collision time on the external uniform magnetic field, concentration and temperature are phenomenologically treated. Analytical expressions are obtained for the tensors of electric and thermal conductivity and/or resistivity. The developed theory is applied to describe the Shubnikov-de Haas oscillations and quantum Hall effect in graphene and GaAs/AlxGa1−xAs heterostructure. The dependencies of magnetization and thermal conductivity on the magnetic field are also predicted.

Non-Markovian dynamics of a charged particle in a two-dimensional harmonic oscillator linearly coupled to a neutral bosonic heat bath is investigated in an external uniform magnetic field and two perpendicular time-dependent electric fields. The analytical expressions for the time-dependent and asymptotic angular momentum are derived for the Markovian and non-Markovian dynamics. The dependence of the angular momentum on the frequency of the electric field, cyclotron frequency, collective frequency, and anisotropy of the heat bath is studied. The angular momentum (or magnetization) of a charged particle can be ruled by varying the frequency of the electric field.

For the neutron -induced fission of nuclei 235,238U, the evolution of the shape of fission -fragment neutron multiplicity distribution with increasing excitation energy is explored within the improved scission -point model. For a wide range of incident neutron energies, the dependence of an average number of neutrons emitted per a fission event on the excitation energy is studied.

Spontaneous fission and alpha decay from K-isomeric states are studied within the dinuclear system model. All these processes are considered as evolution of a nucleus in the charge (mass) asymmetry coordinate. For even-even and even-odd actinides and superheavy nuclei, the spontaneous fission and alpha-decay half-lives of K-isomeric states are calculated and compared with the available experimental data. The origin of the hindrance of spontaneous fission from the high-K isomeric states is explained.

The correlation between the spin-orbit strength and effective mass at saturation density is demonstrated for various Skyrme energy-density functionals without tensor force. This correlation can be used to reduce the number of parameters in these functionals. The role of the spin-orbit interaction is considered together with the tensor force, which has a similar effect on the observable nuclear characteristics. The use of the relation obtained between the spin-orbit strength and the effective mass in the calculations of binding energies, spin-orbit splitting, and charge radii does not spoil the description of experimental data.

We employ a statistical approach to investigate the influence of axial asymmetry on the nuclear level density and entropy along the fission pathways of a superheavy nucleus, explicitly focusing on the $^{296}$Lv isotope. These pathways are determined within multidimensional deformation spaces. Our analysis reveals a significant impact of triaxiality on entropy. Additionally, suppressing shell effects can alter the fission scenario depending on the available excitation energy. We derive the deformation-dependent level density parameter, which plays a crucial role in estimating the survival probability of a superheavy nucleus. Furthermore, we utilize a set of master equations to obtain the time-dependent fission probabilities and calculate the ratio of decay probabilities for both axial and triaxial paths.

The probabilities of $xn$-, $pxn$-, and $αxn$-evaporation channels in excited superheavy nuclei were evaluated using the Monte Carlo method. The calculations utilized microscopically determined nuclear level densities and were compared with results obtained from the phenomenological Jackson formula. Effective temperatures derived from the microscopic approach were incorporated into the Jackson formula for different evaporation channels at low and moderate excitation energies. Additionally, an analytical formula was introduced to estimate the average kinetic energy of emitted particles in multi-step processes.

Within the improved scission-point fission model, it is shown that the average neutron number per proton is not the same in fission fragments and is not equal to that in a fissioning nucleus. For the induced fission of U-238, Pu-240, Cm-244, and Cf-250, the dependencies of the fission-fragment neutron-excess ratio on the shell structure and excitation energy of fragment are studied.

Background: Calculations of the structure of the low-lying states of nuclei with Z = 97-109 play an important role in understanding the properties of nuclei belonging to the new region of the nuclide chart, which is available now for experimental study.Purpose: To calculate quasiparticle-phonon structure and the reduced gamma-transition probabilities for the excited states with excitation energies below 1 MeV for odd-proton nuclei with Z = 97-109.Methods: The quasiparticle-phonon model, which takes into account the quasiparticle-phonon interaction of different multipolarities, is used as a basis for the calculations.Results: The quasiparticle-phonon structure and the gamma-reduced transition probabilities of odd-proton nuclei 263,265,267,269Mt, 259,261,263,265Bh, 255,257,259,261,263Db, 251,253,255,257,259,261Lr, 249,251,253,255Md, 245,247,249,251Es, and 243,245,247Bk are calculated. The alpha-decay chains starting from 263,265,267,269Mt are analyzed.Conclusion: The structure of the nuclear states with excitation energies below 1 MeV in the considered nuclei is mainly exhausted by the one-quasiparticle component. However, in some isotopes the quasiparticle-phonon admixtures plays an important role to destroy the smooth isotopic dependence of energy of the states. The nuclei in the alpha-decay chains starting from 263,265,267,269Mt have up to two alpha-decay lines. The number of alpha-decay lines could be different in the alpha-decay chain and in the direct production of the nucleus.

For the electromagnetic-induced fission of even 222-230Th isotopes, the effect of the transition from a symmetric fission mode to an asymmetric one on the charge/mass, total kinetic energy, neutron multiplicity distributions, and probability for a given neutron multiplicity per fission event is explored within an improved scission-point model. The simultaneous description all these observables and correlations between them are presented.