Searcharxiv⌕ Search

arXiv subjects

A. G. Magner

Publications and source records attributed to A. G. Magner.

At least 37 records · Page 2Linked to original sources
arXiv2018

Velocity and absorption coefficient of sound waves in classical gases

Velocity and absorption coefficient of the plane sound waves in classical gases are obtained by solving the Boltzmann kinetic equation. This is done within the linear response theory as a reaction of the single-particle distribution function to a periodic external field. The nonperturbative dispersion equation is derived in the relaxation time approximation and solved numerically. The obtained theoretical results demonstrate an universal dependence of the sound velocity and scaled absorption coefficient on variable $ωτ$, where $ω$ is the sound frequency and $τ^{-1}$ is the particle collision frequency. In the region of $ωτ\sim 1$ a transition the frequent- to rare-collision regimes takes place. The sound velocity increases sharply, and the scaled absorption coefficient has a maximum -- both theoretical findings are in agreement with the data.

physics.flu-dyn↗
arXiv2018

A simple approach to the chaos-order contributions in nuclear spectra

The simple one-parameter nearest neighbor-spacing distribution (NNSD) is suggested for statistical analysis of nuclear spectra. This distribution is derived within the Wigner-Dyson approach in the linear approximation for the level repulsion density of quantum states. The obtained NNSD gives the individual information on the Wigner and Poisson contributions in agreement with that of the statistical experimental distributions of collective states in deformed nuclei. Using this NNSD, one finds that the symmetry breaking due to the fixing of projections of the angular momentum of collective states enhances a chaos as a shift of the NNSD from the Poisson to Wigner distribution behavior.

nucl-th↗
arXiv2018

New data on $0^+$ states in $^{158}$Gd

Excited states in the deformed nucleus $^{158}$Gd have been studied in the (p,t) reaction by using the Munich Tandem and Q3D spectrograph. 30 new excited 0$^+$ states (three tentative) have been assigned up to the 4.3 MeV excitation energy. The total number of 34 excited 0$^+$ states (four tentatively assigned) in a deformed nucleus, close to a complete level scheme, offers a new opportunity to test nuclear models and obtain more information on the structure of these special states.

nucl-ex↗
arXiv2018

Viscosity of a classical gas: The rare-collision versus the frequent-collision regime

The shear viscosity $η$ for a dilute classical gas of hard-sphere particles is calculated by solving the Boltzmann kinetic equation in terms of the weakly absorbed plane waves. For the rare-collision regime, the viscosity $η$ as a function of the equilibrium gas parameters -- temperature $T$, particle number density $n$, particle mass $m$, and hard-core particle diameter $d$ -- is quite different from that of the frequent-collision regime, e.g., from the well-known result of Chapman and Enskog. An important property of the rare-collision regime is the dependence of $η$ on the external ("non-equilibrium") parameter $ω$, frequency of the sound plane wave, that is absent in the frequent-collision regime at leading order of the corresponding perturbation expansion. A transition from the frequent to the rare-collision regime takes place when the dimensionless parameter $nd^2 (T/m)^{1/2} ω^{-1}$ goes to zero.

cond-mat.stat-mech↗
arXiv2018

Ultrasonic waves in classical gases

The velocity and absorption coefficient for the plane sound waves in a classical gas are obtained by solving the Boltzmann kinetic equation, which describes the reaction of the single-particle distribution function to a periodic external field. Within the linear response theory, the nonperturbative dispersion equation valid for all sound frequencies is derived and solved numerically. The results are in agreement with the approximate analytical solutions found for both the frequent- and rare-collision regimes.

cond-mat.stat-mech↗
arXiv2018

Nucleon matter equation of state, particle number fluctuations, and shear viscosity within UrQMD box calculations

Properties of equilibrated nucleon system are studied within the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) transport model. The UrQMD calculations are done within a finite box with periodic boundary conditions. The system achieves thermal equilibrium due to nucleon-nucleon elastic scattering. For the UrQMD equilibrium state, nucleon energy spectra, equation of state, particle number fluctuations, and shear viscosity $η$ are calculated. The UrQMD results are compared with both, statistical mechanics and Chapman-Enskog kinetic theory, for a classical system of nucleons with hard-core repulsion.

nucl-th↗
arXiv2017

Statistical analysis of excitation energies in the actinide and rare-earth nuclei

Statistical analysis of distributions of the collective states in the actinide and rare-earth nuclei is performed in terms of the nearest neighbor spacing distribution (NNSD). Several approximations, such as the linear approach to the level repulsion density and that suggested by Brody to the NNSDs were applied for the analysis. We found an intermediate character of the experimental spectra between the order and the chaos for a number of the rare-earth and actinide nuclei. They are more close to the Wigner distribution for energies limited by 3 MeV, and to the Poisson distribution for data including higher excitation energies and higher spins. The latter is in agreement with the theoretical calculations. These features are confirmed by the cumulative distributions, where the Wigner contribution dominates at smaller spacings while the Poisson one is more important at larger spacings.

nucl-th↗
arXiv2017

Semiclassical catastrophe theory of simple bifurcations

The Fedoriuk-Maslov catastrophe theory of caustics and turning points is extended to solve the bifurcation problems by the improved stationary phase method (ISPM). The trace formulas for the radial power-law (RPL) potentials are presented by the ISPM based on the second- and third-order expansion of the classical action near the stationary point. A considerable enhancement of contributions of the two orbits (pair of consisting of the parent and newborn orbits) at their bifurcation is shown. The ISPM trace formula is proposed for a simple bifurcation scenario of Hamiltonian systems with continuous symmetries, where the contributions of the bifurcating parent orbits vanish upon approaching the bifurcation point due to the reduction of the end-point manifold. This occurs since the contribution of the parent orbits is included in the term corresponding to the family of the newborn daughter orbits. Taking this feature into account, the ISPM level densities calculated for the RPL potential model are shown to be in good agreement with the quantum results at the bifurcations and asymptotically far from the bifurcation points.

math.DS↗
arXiv2017

Semiclassical approaches to nuclear dynamics

The extended Gutzwiller trajectory approach is presented for the semiclassical description of nuclear collective dynamics, in line with the main topics of the fruitful activity of V.G. Solovjov. Within the Fermi-liquid droplet model, the leptodermous effective surface approximation was applied to calculations of energies, sum rules and transition densities for the neutron-proton asymmetry of the isovector giant-dipole resonance and found to be in good agreement with the experimental data. By using the Strutinsky shell correction method, the semiclassical collective transport coefficients such as nuclear inertia, friction, stiffness, and moments of inertia can be derived beyond the quantum perturbation approximation of the response function theory and the cranking model.The averaged particle-number dependence of the low-lying collective vibrational states are described in good agreement with basic experimental data, mainly due to an enhancement of the collective inertia as compared to its irrotational flow value. Shell components of the moment of inertia are derived in terms of the periodic-orbit free-energy shell corrections. A good agreement between the semiclassical extended Thomas-Fermi moments of inertia with shell corrections and the quantum results is obtained for different nuclear deformations and particle numbers. Shell effects are shown to be exponentially dampted out with increasing temperature in all the transport coefficients.

nucl-th↗
arXiv2016

Shear viscosity of nuclear matter

Shear viscosity $η$ is calculated for the nuclear matter described as a system of interacting nucleons with the van der Waals (VDW) equation of state. The Boltzmann-Vlasov kinetic equation is solved in terms of the plane waves of the collective overdamped motion. In the frequent-collision regime, the shear viscosity depends on the particle-number density $n$ through the mean-field parameter $a$, which describes attractive forces in the VDW equation. In the temperature region $T=15 - 40$~MeV, a ratio of the shear viscosity to the entropy density $s$ is smaller than 1 at the nucleon number density $n =(0.5 - 1.5)\,n^{}_0$, where $n^{}_0=0.16\,$fm$^{-3}$ is the particle density of equilibrium nuclear matter at zero temperature. A minimum of the $η/s$ ratio takes place somewhere in a vicinity of the critical point of the VDW system. Large values of $η/s\gg 1$ are, however, found in both the low-density, $n\ll n^{}_0$, and high-density, $n>2n^{}_0$, regions. This makes the ideal hydrodynamic approach inapplicable for these densities.

nucl-th↗
arXiv2016

Shells, orbit bifurcations and symmetry restorations in Fermi systems

The periodic-orbit theory based on the improved stationary-phase method within the phase-space path integral approach is presented for the semiclassical description of the nuclear shell structure, concerning the main topics of the fruitful activity of V. G. Solovjov. We apply this theory to study bifurcations and symmetry breaking phenomena in a radial power-law potential which is close to the realistic Woods-Saxon one up to about the Fermi energy. Using the realistic parametrization of nuclear shapes we explain the origin of the double-humped fission barrier and the asymmetry in the fission isomer shapes by the bifurcations of periodic orbits. The semiclassical origin of the oblate-prolate shape asymmetry and tetrahedral shapes is also suggested within the improved periodic-orbit approach. The enhancement of shell structures at some surface diffuseness and deformation parameters of such shapes are explained by existence of the simple local bifurcations and new non-local bridge-orbit bifurcations in integrable and partially integrable Fermi systems. We obtained good agreement between the semiclassical and quantum shell-structure components of the level density and energy for several surface diffuseness and deformation parameters of the potentials, including their symmetry breaking and bifurcation values.

nucl-th↗
arXiv2015

Slope-dependent nuclear-symmetry energy within the effective surface approximation

The effective-surface approximation is extended taking into account derivatives of the symmetry-energy density per particle with respect to the mean particle density. The isoscalar and isovector particle densities in this extended effective-surface approximation are derived. The improved expressions of the surface symmetry energy, in particular, its surface tension coefficients in the sharp-edged proton-neutron asymmetric nuclei take into account important gradient terms of the energy density functional. For most Skyrme forces the surface symmetry-energy constants and the corresponding neutron skins and isovector stiffnesses are calculated as functions of the Swiatecki derivative of the nongradient term of the symmetry-energy density per particle with respect to the isoscalar density. Using the analytical isovector surface-energy constants in the framework of the Fermi-liquid droplet model we find energies and sum rules of the isovector giant-dipole resonance structure in a reasonable agreement with the experimental data, and they are compared with other theoretical approaches.

nucl-th↗
arXiv2014

Semiclassical shell-structure moment of inertia within the phase-space approach

The moment of inertia for nuclear collective rotations was derived within the semiclassical approach based on the cranking model and the Strutinsky shell-correction method by using the non-perturbative periodic-orbit theory in the phase space variables. This moment of inertia for adiabatic (statistical-equilibrium) rotations can be approximated by the generalized rigid-body moment of inertia accounting for the shell corrections of the particle density. A semiclassical phase-space trace formula allows to express quite accurately the shell components of the moment of inertia in terms of the free-energy shell corrections for integrable and partially chaotic Fermi systems, in good agreement with the quantum calculations.

nucl-th↗
arXiv2014

Semiclassical treatment of symmetry breaking and bifurcations in a non-integrable potential

We have derived an analytical trace formula for the level density of the Hénon-Heiles potential using the improved stationary phase method, based on extensions of Gutzwiller's semiclassical path integral approach. This trace formula has the correct limit to the standard Gutzwiller trace formula for the isolated periodic orbits far from all (critical) symmetry-breaking points. It continuously joins all critical points at which an enhancement of the semiclassical amplitudes occurs. We found a good agreement between the semi- classical and the quantum oscillating level densities for the gross shell structures and for the energy shell corrections, solving the symmetry breaking problem at small energies.

nucl-th↗
arXiv2014

Isovector dipole-resonance structure within the effective surface approximation

The nuclear isovector-dipole strength structure is analyzed in terms of the main and satellite (pygmy) peaks within the Fermi-liquid droplet model. Such a structure is sensitive to the value of the surface symmetry-energy constant obtained analytically for different Skyrme forces in the leptodermous effective surface approximation. Energies, sum rules and transition densities of the main and satellite peaks for specific Skyrme forces are qualitatively in agreement with the experimental data and other theoretical calculations.

nucl-th↗
arXiv2013

A semiclassical collective response of heated, asymmetric and rotating nuclei

The Landau Fermi-liquid and extended Gutzwiller periodic-orbit theories are presented for the semiclassical description of collective excitations in nuclei, which are close to main topics of the fruitful activity of S.T. Belyaev. Static susceptibilities show the ergodicity of Fermi liquids. Transport coefficients (nuclear friction and inertia) as functions of the temperature for the hydrodynamic and zero-sound modes are derived within the response theory by using the Fermi-liquid droplet model, in agreement with the shell model for large temperatures. The surface symmetry binding-energy constants are obtained as functions of Skyrme force parameters in the approximation of a sharp edged proton-neutron asymmetric nucleus.The energies and sum rules of the isovector dipole giant resonances are in fairly good agreement with the experimental data. An analysis of the specific structure of these resonances in terms of a main, and satellite peaks, in comparison with the experimental data and microscopic theoretical models, might turn out to be of importance for a better understanding of the values of the surface symmetry-energy constant. The semiclassical collective moment of inertia is derived analytically beyond the quantum perturbation approximation of the cranking model for any potential well as a mean field. It is shown that this moment of inertia can be approximated by its rigid-body value for the rotation with a given frequency within the ETF and more general periodic orbit theories in the nearly local long-length approximation. Its semiclassical shell-structure components are derived in terms of the periodic-orbit free-energy shell corrections. We obtained good agreement between the semiclassical and quantum shell-structure components of the moment of inertia for several critical bifurcation deformations for the harmonic oscillator mean field.

nucl-th↗
arXiv2013

Semiclassical trace formula for the two-dimensional radial power-law potentials

The trace formula for the density of single-particle levels in the two-dimensional radial power-law potentials, which nicely approximate the radial dependence of the Woods-Saxon potential and quantum spectra in a bound region, was derived by the improved stationary phase method. The specific analytical results are obtained for the powers 4 and 6. The enhancement phenomena near the bifurcations of periodic orbits are found to be significant for the description of the fine shell structure. It is shown that the semiclassical trace formulas for the shell corrections to the level density and energy reproduce the quantum results with good accuracy through all the bifurcation (symmetry breaking) catastrophe points, where the standard stationary-phase method breaks down. Various limits (including the harmonic oscillator and the spherical billiard) are obtained from the same analytical trace formula.

nlin.SI↗