arXiv subjects
Publications and source records attributed to S. V. Lukyanov.
An expression for the two-particle relaxation time of collective excitations on a distorted Fermi surface in the diffusion approach to kinetic theory is obtained. The general case of momentum-dependent diffusion and drift coefficients is considered. The temperature dependence of the obtained expression is established.
The influence of the diffuse surface layer of a finite nucleus on the mean square radii and their isotopic shift is investigated. We present the calculations within the Gibbs-Tolman approach using the experimental values of the nucleon separation energies. Results are compared with that obtained by means of direct variational method based on Fermi-like trial functions.
The neutron skin and halo distributions in medium and heavy nuclei are calculated within the extended Thomas-Fermi approximation. Calculations are carried out for the effective Skyrme-like forces using the direct variational method. The analytical expression for the isovector shift of the rms radii $Δr_{np}$ as a sum of skin- and halo-like terms is obtained. The contribution of halo and skin terms to $Δr_{np}$ are found to be approximately equal.
We suggest the diffuse approach to the relaxation processes within the kinetic theory for the Wigner distribution function. The diffusion and drift coefficients are evaluated taking into consideration the interparticle collisions on the distorted Fermi surface. Using the finite range interaction, we show that the momentum dependence of the diffuse coefficient $D_{p}(p)$ has a maximum at Fermi momentum $p=p_{F}$ whereas the drift coefficient $K_{p}(p)$ is negative and reaches a minimum at $p\approx p_{F}$. For a cold Fermi system the diffusion coefficient takes the non-zero value which is caused by the relaxation on the distorted Fermi-surface at temperature $T=0$. The numerical solution of the diffusion equation was performed for the particle-hole excitation in a nucleus with $A=16$. The evaluated relaxation time $τ_{r}\approx 8.3\cdot 10^{-23}\mathrm{s}$ is close to the corresponding result in a nuclear Fermi-liquid obtained within the kinetic theory.
The diffusion approximation to the relaxation on the distorted Fermi surface in a Fermi liquid is considered. The dependence of the relaxation time on the multipolarity of a Fermi surface deformation is established. The time evolution of the non-equilibrium particle-hole excitations is studied.
The radii of nucleon distribution, bulk density, and neutron skin in nuclei beyond the β-stability line are studied within the direct variational method. We evaluate the partial equation of state of finite nuclei and demonstrate that the bulk density decreases beyond the beta stability line. We show that the growth of the neutron skin in unstable nuclei does not obey the saturation condition because of the polarization effect. The value of the neutron-skin thickness Δr_{np}=\sqrt{ }-\sqrt{ } is caused by the different radii (skin effect) and only slightly by the different shapes (halo effect) of neutron and proton distributions. The relative contribution of both effects depends on the competition between the symmetry energy, and the spin-orbit and Coulomb interactions. The calculations of the isovector shift of the nuclear radius Δr_{np} show its primarily linear dependence on the asymmetry parameter X=(N-Z)/A.
We redefine the surface tension coefficient for a nuclear Fermi-liquid drop with a finite diffuse layer. Following Gibbs-Tolman concept, we introduce the equimolar radius R_e of sharp surface droplet at which the surface tension is applied and the radius of tension surface R_s which provides the minimum of the surface tension coefficient σ. This procedure allows us to derive both the surface tension and the corresponding curvature correction (Tolman length) correctly for the curved and diffuse interface. We point out that the curvature correction depends significantly on the finite diffuse interface. This fact is missed in traditional nuclear considerations of curvature correction to the surface tension. We show that Tolman's length ξis negative for nuclear Fermi-liquid drop. The value of the Tolman length is only slightly sensitive to the Skyrme force parametrization and equals ξ=-0.36 fm.
The radii of nucleon distribution and neutron skin in nuclei beyond the β-stability line are studied within the extended Thomas-Fermi approximation. We show that the growth of neutron skin in unstable nuclei does not obey the saturation condition because of the neutron coat. The neutron coat indicates the possibility of giant neutron halo which is growing with moving away from the beta stability line. We demonstrate the presence of strong shell oscillations in the charge radius R_C and the relation of R_C to the isospin shift of neutron-proton chemical potentials Δλ=λ_n-λ_p for nuclei beyond the beta-stability line at fixed value of mass number A.
We consider the energy weighted sums (EWS) for isovector giant dipole resonances (IVGDR) in finite nuclei within Landau kinetic theory. The dependence of both IVGDR energy, $E_{IVGDR}$, and the EWS enhancement factor, $κ(A)$, on the mass number $A$ occurs because of the boundary condition on the moving nuclear surface. The values of $E_{IVGDR}A^{1/3}$ and $κ(A)$ increase with $A$. The obtained value of the enhancement factor is about 10% for light nuclei and reaches approximately 20% for heavy nuclei. A fit of the enhancement factor to the proper experimental data provides a value for the isovector Landau amplitude of $F'_1\simeq 1.1$.
We investigate the collective response function and the energy-weighted sums (EWS) $m_k$ for isovector mode in hot nuclei. The approach is based on the collisional kinetic theory and takes into consideration the temperature and the relaxation effects. We have evaluated the temperature dependence of the adiabatic, $E_1=\sqrt{m_1/m_{-1}}$, and scaling, $E_3=\sqrt{m_3/m_1}$, energy centroids of the isovector giant dipole resonances (IVGDR). The centroid energy $E_3$ is significantly influenced by the Fermi surface distortion effects and, in contrast to the isoscalar mode, shows much weaker variation with temperature. Taking into account a connection between the isovector sound mode and the corresponding surface vibrations we have established the $A$-dependence of the IVGDR centroid energy which is in a good agreement with experimental data. We have shown that the enhancement factor for the "model independent" sum $m_1$ is only slightly sensitive to the temperature change.
We investigate the collective response function and the energy-weighted sums m_k for isovector mode in hot nuclei. The approach is based on the collisional kinetic theory and takes into consideration the temperature and the relaxation effects. Taking into account a connection between the isovector sound mode and the corresponding surface vibrations we have established the A-dependence of the enhancement factor for the isovector sum rule in a good agreement with experimental data. We have shown that the enhancement factor for the "model independent" sum m_1 is only slightly sensitive to the temperature change.
Model independent, $m_1$, adiabatic, $m_{-1}$, and high-energy, $m_3$, energy weighted sums for the isoscalar and isovector nuclear excitations are investigated within the framework of the kinetic theory adopted to the description of a two-component nuclear Fermi-liquid. For both the adiabatic and scaling approaches, the connection of the EWS $m_{-1}$ and $m_3$ to the nuclear stiffness coefficients and the first- and zero-sound velocity is established. We study the enhancement factor $κ_{I}$ in the energy weighted sum $m'_1$ for the isovector excitations and provide the reasonable explanation of the experimental exceeding of the 100% exhaustion of sum $m'_1$ for the isovector giant dipole resonances. We show the dependence of the enhancement factor $κ_{I}$ on the nuclear mass number $A$ and analyse its dependence on the Landau's isovector amplitude $F'_1$.
The validity of small damping approximation (SDA) for the quasi-classical description of the averaged properties of nuclei at high temperatures is studied within the framework of collisional kinetic theory. The isoscalar collective quadrupole vibrations in hot nuclei are considered. We show that the extension of the SDA, by accounting for the damping of the distribution function $δf$ in the collision integral reduces the rate of variation with temperature of the Fermi surface distortion effects. The damping of the $δf$ in the collision integral increases significantly the collisional width of the giant quadrupole resonance (GQR) for small enough values of the relaxation time. The temperature dependence of the eigenenergy of the GQR becomes much more weaker than in the corresponding SDA case.
The contribution of thermal fluctuations to the widths of isoscalar giant multipole resonances (GMR) in heated nuclei is studied. Starting from the collisional kinetic equation, it is shown that an additional contribution to the nuclear friction and the corresponding GMR widths arises due to the nonlinear dissipativity effect. It is also shown that the magnitude of the contributions of the thermal fluctuations to the nuclear friction coefficient and the GMR widths do not exceed 20%.
Two important ingredients of nuclear shell-structure, kinetic energy and spin-orbit splitting, are studied as a function of orbital angular momenta \ell and binding energies, when binding energies of neutrons decrease towards zero. If we use the standard parameters of the Woods-Saxon potential in βstable nuclei and approach the limit of zero binding energy from 10 MeV, the spin-orbit splitting for n=1 orbitals decreases considerably for \ell=1, while for \ell > 2 little decreasing is observed in the limit. In contrast, the kinetic energy decreases considerably for \ell \simleq 3. The smaller the \ell values of orbitals, the larger the decreasing rate of both kinetic energy and spin-orbit splitting. The dependence of the above bservation on the diffuseness of potentials is studied.
Finite size effects in the equilibrium phase space density distribution function are taken into account for alculations of the relaxation of collective motion in finite nuclei. Memory effects in the collision integral and the diffusivity and the quantum oscillations of the equilibrium distribution function in momentum space are considered. It is shown that a smooth diffuse (Fermi-type) equilibrium distribution function leads to a spurious contribution to the relaxation time. The residual quantum oscillations of the equilibrium distribution function eliminates the spurious contribution. It ensures the disappearance of the gain and loss terms in the collision integral in the ground state of the system and strongly reduces the internal collisional width of the isoscalar giant quadrupole resonances.