arXiv subjects

A. I. Levon

Publications and source records attributed to A. I. Levon.

At least 19 recordsLinked to original sources

arXiv2026

Rotating neutron stars within the macroscopic effective-surface approximation

The macroscopic model for a neutron star (NS) as a finite perfect fluid at the equilibrium is extended to rotating systems by incorporating the linear perturbation expansion over a small frequency $ω$ near Schwarzschild outer-inner gravitational metric within the effective-surface (ES) approach. The NS angular momentum $I$ and moment of inertia (MI) for a slow stationary azimuthal rotation around the symmetry axis are calculated by using the Kerr metric approach in spherical coordinates, and compared with Boyer-Lindquist (outer) and Hogan (inner) metric results. The volume and gradient-surface terms of the macroscopic NS energy density $\mathcal{E}(ρ)$ (Equation of State) are taken into account at the leading order of the leptodermic parameter $a/R \ll 1$, where $a$ is the ES crust thickness and $R$ is the NS effective radius. The analytical macroscopic NS MI expressions, $Θ= \mathrm{d}I/\mathrm{d}ω= \tildeΘ/(1-\mathcal{T}_{tφ})$, have been obtained in terms of the statistically averaged MI, $\tildeΘ$, and its time and azimuthal-angle $t,φ$ correlation, $\mathcal{T}_{tφ}$, as sums of the volume and surface components. The MI $Θ$ is changed significantly as function of the effective radius $R$ because of a strong gravity. We found the additional constraint for the NS radius to smaller accessible ranges which is due mainly to the $t,φ$ correlations and surface contributions. The adiabaticity conditions for applicability of the linear perturbation theory is carried out for several neutron stars with a strong gravity and relatively large rotation periods.

gr-qc↗

arXiv2026

Macroscopic approaches to rotating neutron stars

The macroscopic model for a neutron star (NS) as a perfect liquid drop at equilibrium is extended to rotating systems with a small frequency $ω$ within the effective-surface (ES) approach. The gradient surface terms of the NS energy density $\cal{E}(ρ)$ in the Equation of State are taken into account along with the volume components at the leading order over the leptodermic parameter $a/R << 1$, where $a$ is the ES crust thickness and $R$ is the mean NS radius. The macroscopic NS angular momentum at small frequencies $ω$ is used for calculations of the adiabatic moment of inertia (MI) within the Kerr metric approach in the outer Boyer-Lindquist and inner Hogan coordinate forms. The NS MI, $Θ=\tildeΘ/(1-\cal{G}_{tφ})$, was obtained in terms of the statistically averaged MI, $\tildeΘ$, and its time and azimuthal-angle correlation, $\cal{G}_{tφ}$, as the sums of volume and surface components. The MI $Θ$ depends dramatically on the effective radius $R$ due to strong gravitation and surface effects. We found significant additional rotational constraints on the radius $R$ due to the correlation term $\cal{G}_{tφ}$ and surface contributions. With these contributions, the adiabaticity condition is better fulfilled for a stronger gravitation in many well-known neutron stars.

astro-ph.HE↗

arXiv2025

Leptodermic corrections to the TOV equations and nuclear astrophysics within the effective surface approximation

The macroscopic model for a neutron star (NS) as a liquid drop at the equilibrium is used to extend the Tolman-Oppenheimer-Volkoff (TOV) equations taking into account the gradient terms responsible for the system surface. The parameters of the Schwarzschild metric in the spherical case are found with these surface corrections to the known leading (zero) order of the leptodermic approximation $a/R<<1$, where $a$ is the NS effective-surface (ES) thickness, and $R$ is the effective NS radius. The energy density $\mathcal{E}$ is considered in a general form including the functions of the particle number density and of its gradient terms. The macroscopic gravitational component $Φ(ρ)$ of the energy density is taken into account in the simplest form as expansion in powers of $ρ-\overlineρ $, where $\overlineρ$ is the saturation density, up to second order, in terms of its contributions to the separation particle energy and incompressibility. Density distributions $ρ$ across the NS ES in the normal direction to the ES, which are derived in the simple analytical form at the same leading approximation, was used for the derivation of the modified TOV (MTOV) equations by accounting for their NS surface corrections. The MTOV equations are analytically solved at first order and the results are compared with the standard TOV approach of the zero order.

gr-qc↗

arXiv2025

Neutron stars as a dense liquid drop at equilibrium within the effective surface approximation

The macroscopic model is formulated for a neutron star (NS) as a perfect liquid drop at the equilibrium. We use the leptodermic approximation $a/R\ll 1$, where $a$ is the crust thickness of the effective NS surface (ES), and $R$ is the mean radius of the ES curvature. Within the approximate Schwarzschild metric solution to the general relativity theory equations for the spherically symmetric systems, the macroscopic gravitation is taken into account in terms of the total separation particle energy and incompressibility. Density distribution $ρ$ across the ES in the normal direction to the ES was obtained analytically for a general form of the energy density $\mathcal{E}(ρ)$. For the typical crust thickness, and effective radius, one finds the leading expression for the density $ρ$. NS masses are analytically calculated as a sum of the volume and surface terms, taking into account the radial curvature of the metric space, in reasonable agreement with the recently measured masses for several neutron stars. We derive the simple macroscopic equation of state (EoS) with the surface correction. The analytical and numerical solutions to Tolman-Oppenheimer-Volkoff equations for the pressure are in good agreement with the volume part of our EoS.

nucl-th↗

arXiv2023

Nuclear level density in the statistical semiclassical micro-macroscopic approach

Level density $ρ$ is derived for a finite system with strongly interacting nucleons at a given energy E, neutron N and proton Z particle numbers, projection of the angular momentum M, and other integrals of motion, within the semiclassical periodic-orbit theory (POT) beyond the standard Fermi-gas saddle-point method. For large particle numbers, one obtains an analytical expression for the level density which is extended to low excitation energies U in the statistical micro-macroscopic approach (MMA).The interparticle interaction averaged over particle numbers is taken into account in terms of the extended Thomas-Fermi component of the POT. The shell structure of spherical and deformed nuclei is taken into account in the level density. The MMA expressions for the level density $ρ$ reaches the well-known macroscopic Fermi-gas asymptote for large excitation energies U and the finite combinatoric power-expansion limit for low energies U. We compare our MMA results for the averaged level density with the experimental data obtained from the known excitation energy spectra by using the sample method under statistical and plateau conditions. Fitting the MMA $ρ$ to these experimental data on the averaged level density by using only one free physical parameter - inverse level density parameter K - for several nuclei and their long isotope chain at low excitation energies U, one obtains the results for K. These values of K might be much larger than those deduced from neutron resonances. The shell, isotopic asymmetry, and pairing effects are significant for low excitation energies.

nucl-th↗

arXiv2023

Paring correlations within the micro-macroscopic approach for the level density

Level density $ρ(E,N,Z)$ is calculated for the two-component close- and open-shell nuclei with a given energy $E$, and neutron $N$ and proton $Z$ numbers, taking into account pairing effects within the microscopic-macroscopic approach (MMA). These analytical calculations have been carried out by using the semiclassical statistical mean-field approximations beyond the saddle-point method of the Fermi gas model in a low excitation-energies range. The level density $ρ$, obtained as function of the system entropy $S$, depends essentially on the condensation energy $E_{\rm cond}$ through the excitation energy $U$ in super-fluid nuclei. The simplest super-fluid approach, based on the BCS theory, accounts for a smooth temperature dependence of the pairing gap $Δ$ due to particle number fluctuations. Taking into account the pairing effects in magic or semi-magic nuclei, excited below neutron resonances, one finds a notable pairing phase transition.Pairing correlations sometimes improve significantly the comparison with experimental data.

nucl-th↗

arXiv2022

Microscopic-macroscopic level densities for low excitation energies

Level density $ρ(E,{\bf Q})$ is derived within the micro-macroscopic approximation (MMA) for a system of strongly interacting Fermi particles with the energy $E$ and additional integrals of motion ${\bf Q}$, in line with several topics of the universal and fruitful activity of A.S. Davydov. Within the extended Thomas Fermi and semiclassical periodic orbit theory beyond the Fermi-gas saddle-point method we obtain $ρ\propto I_ν(S)/S^ν$, where $I_ν(S)$ is the modified Bessel function of the entropy $S$. For small shell-structure contribution one finds $ν=κ/2+1$, where $κ$ is the number of additional integrals of motion. This integer number is a dimension of ${\bf Q}$, ${\bf Q}=\{N, Z, ...\}$ for the case of two-component atomic nuclei, where $N$ and $Z$ are the numbers of neutron and protons, respectively. For much larger shell structure contributions, one obtains, $ν=κ/2+2$. The MMA level density $ρ$ reaches the well-known Fermi gas asymptote for large excitation energies, and the finite micro-canonical combinatoric limit for low excitation energies. The additional integrals of motion can be also the projection of the angular momentum of a nuclear system for nuclear rotations of deformed nuclei, number of excitons for collective dynamics, and so on. Fitting the MMA total level density, $ρ(E,{\bf Q})$, for a set of the integrals of motion ${\bf Q}=\{N, Z\}$, to experimental data on a long nuclear isotope chain for low excitation energies, one obtains the results for the inverse level-density parameter $K$, which differs significantly from those of neutron resonances, due to shell, isotopic asymmetry, and pairing effects.

nucl-th↗

arXiv2022

Level density within a micro-macroscopic approach

Statistical level density $ρ(E,A)$ is derived for nucleonic system with a given energy $E$, particle number $A$ and other integrals of motion in the micro-macroscopic approximation beyond the standard saddle-point method of the Fermi gas model. This level density reaches the two limits; the well-known Fermi gas grand-canonical ensemble limit for a large entropy $S$ related to large excitation energies, and the finite micro-canonical limit for a small combinatorical entropy $S$ at low excitation energies. The inverse level density parameter $K$ as function of the particle number $A$ in the semiclassical periodic orbit theory, taking into account the extended Thomas-Fermi and Strutinsky shell corrections, is calculated and compared with experimental data.

nucl-th↗

arXiv2021

Shell-structure and asymmetry effects in level densities

Level density $ρ(E,N,Z)$ is derived for a nuclear system with a given energy $E$, neutron $N$, and proton $Z$ particle numbers, within the semiclassical extended Thomas-Fermi and periodic-orbit theory beyond the Fermi-gas saddle-point method. We obtain $~~ρ\propto I_ν(S)/S^ν$,~~ where $I_ν(S)$ is the modified Bessel function of the entropy $S$, and $ν$ is related to the number of integrals of motion, except for the energy $E$. For small shell structure contribution one obtains within the micro-macroscopic approximation (MMA) the value of $ν=2$ for $ρ(E,N,Z)$. In the opposite case of much larger shell structure contributions one finds a larger value of $ν=3$. The MMA level density $ρ$ reaches the well-known Fermi gas asymptote for large excitation energies, and the finite micro-canonical limit for low excitation energies. Fitting the MMA $ρ(E,N,Z)$ to experimental data on a long isotope chain for low excitation energies, due mainly to the shell effects, one obtains results for the inverse level density parameter $K$, which differs significantly from that of neutron resonances.

nucl-th↗

arXiv2021

Semiclassical shell-structure micro-macroscopic approach for the level density

Level density $ρ(E,A)$ is derived for a one-component nucleon system with a given energy $E$ and particle number $A$ within the mean-field semiclassical periodic-orbit theory beyond the saddle-point method of the Fermi gas model. We obtain $~~ρ\propto I_ν(S)/S^ν$, with $I_ν(S)$ being the modified Bessel function of the entropy $S$. Within the micro-macro-canonical approximation (MMA), for a small thermal excitation energy, $U$, with respect to rotational excitations, $E_{\rm rot}$, one obtains $ν=3/2$ for $ρ(E,A)$. In the case of excitation energy $U$ larger than $E_{\rm rot}$ but smaller than the neutron separation energy, one finds a larger value of $ν=5/2$. A role of the fixed spin variables for rotating nuclei is discussed. The MMA level density $ρ$ reaches the well-known grand-canonical ensemble limit (Fermi gas asymptotic) for large $S$ related to large excitation energies, and also reaches the finite micro-canonical limit for small combinatorial entropy $S$ at low excitation energies (the constant "temperature" model). Fitting the $ρ(E,A)$ of the MMA to the experimental data for low excitation energies, taking into account shell and, qualitatively, pairing effects, one obtains for the inverse level density parameter $K$ a value which differs essentially from that parameter derived from data on neutron resonances.

nucl-th↗

arXiv2019

Excitation of monopole pairing vibrations in two-neutron transfer reaction: a semiclassical approach

For studying the collective pairing excitations of nuclei, the two-nucleon transfer reactions in superfluid nuclei (the pairing gap of the ground state is not zero), in particular, the (p,t) reaction, are of the greatest interest. A simple model of monopole pairing excitations in superfluid nuclei on the basis of the semiclassical time-dependent Hartree-Fock-Bogolyubov theory in the limit of small amplitudes is considered. Using the anomalous density response function, the monopole pairing mode in the energy region of double pairing gap and the variation of the pairing gap associated with this mode are found. The ratio of the spectroscopic factor for the excitation of monopole pairing vibrations in the (p,t) reaction in even superfluid nuclei to the spectroscopic factor for the transfer of two neutrons to the ground state of the daughter nucleus (the relative spectroscopic factor) is estimated. For this, it is assumed that the relative spectroscopic factor is proportional to the pairing gap variation associated with the monopole pairing vibrations in agreement with the corresponding quantum expression. Numerical estimate of the relative spectroscopic factors for superfluid nuclei of the rare-earth and actinide regions shows that the spectroscopic factor for the two-neutron transfer, leading to the excitation of the monopole pairing vibrations, does not exceed several percent of the spectroscopic factor for the transfer of two neutrons to the ground state. This semiclassical estimate is in agreement with the experimental rations of the cross sections for the excitation of 0+states in the energy region of double pairing gap to the cross sections for the excitation of the ground states for superfluid nuclei of the rare-earth and actinide regions.

nucl-th↗

arXiv2019

High-resolution study of excited states in 158Gd with (p,t) reactions

The excitation spectra in the deformed nucleus 158Gd have been studied with high energy resolution by means of the (p,t) reaction using the Q3D spectrograph facility at the Munich Tandem accelerator. The angular distributions of tritons were measured for more than 200 excited states seen in the triton spectra up to 4.3 MeV. A number of 36 excited 0+ states (five tentative), have been assigned by comparison of experimental angular distributions with the calculated ones using the CHUCK code. Assignments for levels with higher spins are the following: 95 for 2+ states, 64 for 4+ states, 14 for 6+ states and about 20 for negative parity states. Sequences of states which can be treated as rotational bands are selected. The analysis of the moments of inertia defined for these bands is carried out. This high number of excited states in a deformed nucleus, close to a complete level scheme, constitutes a very good ground to check models of nuclear structure. The large ensembles of states with the same spin-parity offer unique opportunities for statistical analysis. Such an analysis for the 0+, 2+ and 4+ states sequences, for all K-values and for well-determined projections K of the angular momentum is performed. The obtained data may indicate on a K symmetry breaking. Experimental data are compared with interacting boson model (IBM) calculations using the spdf version of the model. The energies of the low-lying levels, the transition probabilities in the first bands and the distribution in transfer intensity of the 0+ states are calculated and compared with experiment.

nucl-ex↗

arXiv2019

Two-neutron transfer reactions and quantum-chaos measure of nuclear spectra

A new statistical interpretation of the nuclear collective states is suggested and applied recently in rare earths and actinide nuclei by the two-neutron transfer reactions in terms of the nearest neighbor-spacing distributions (NNSDs). Experimental NNSDs were obtained by using the complete and pure sequences of the collective states through an unfolding procedure. The two-neutron transfer reactions allow to obtain such a sequence of the collective states that meets the requirements for a statistical analysis. Their theoretical analysis is based on the linear approximation of a repulsion level density within the Wigner-Dyson theory. This approximation is successful to evaluate separately the Wigner chaos and Poisson order contributions. We found an intermediate behavior of NNSDs between the Wigner and Poisson limits. NNSDs turn out to be shifted from a chaos to order with increasing the length of spectra and the angular momentum of collective states. Perspectives for the statistical analysis of the symmetry breaking of states with the fixed projection of angular momenta $K$ are discussed.

nucl-th↗

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↗

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↗

arXiv2016

Spectroscopy of 232U in the (p,t) reaction: More information on 0+ states

The excitation spectra in the deformed nucleus 232U have been studied by means of the (p,t) reaction, using the Q3D spectrograph facility at the Munich Tandem accelerator. The angular distributions of tritons were measured for 162 excitations seen in the triton spectra up to 3.25 MeV. 0+ assignments are made for 13 excited states by comparison of experimental angular distributions with the calculated ones using the CHUCK3 code. Assignments up to spin 6+ are made for other states. Sequences of states are selected which can be treated as rotational bands. Moments of inertia have been derived from these sequences, whose values may be considered as evidence of the two- or one-phonon nature of these 0+ excitations. Experimental data are compared with interacting boson model (IBM) and quasiparticle-phonon model (QPM) calculations.

nucl-ex↗

arXiv2013

0+ states and collective bands in 228Th studied by the (p,t) reaction

The excitation spectra in the deformed nucleus 228Th have been studied by means of the (p,t)-reaction, using the Q3D spectrograph facility at the Munich Tandem accelerator. The angular distributions of tritons were measured for about 110 excitations seen in the triton spectra up to 2.5 MeV. Firm 0+ assignments are made for 17 excited states by comparison of experimental angular distributions with the calculated ones using the CHUCK3 code. Assignments up to spin 6+ are made for other states. Sequences of states are selected which can be treated as rotational bands and as multiplets of excitations. Moments of inertia have been derived from these sequences, whose values may be considered as evidence of the two-phonon nature of most 0+ excitations. Experimental data are compared with interacting boson model and quasiparticle-phonon model calculations and with experimental data for 229Pa.

nucl-ex↗