arXiv subjects

A. G. Magner

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

At least 19 recordsLinked to original sources

arXiv2025

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 $\omega$ 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 $\mathcal{E}(\rho)$ (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, $\Theta = \mathrm{d}I/\mathrm{d}\omega = \tilde{\Theta}/(1-\mathcal{T}_{t\varphi})$, have been obtained in terms of the statistically averaged MI, $\tilde{\Theta}$, and its time and azimuthal-angle $t,\varphi$ correlation, $\mathcal{T}_{t\varphi}$, as sums of the volume and surface components. The MI $\Theta$ 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 $t,\varphi$ 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↗

arXiv2025

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 $\omega $ within the effective-surface (ES) approach. The gradient surface terms of the NS energy density $\cal{E}(\rho)$ 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 $\omega$ 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, $\Theta=\tilde{\Theta}/(1-\cal{G}_{t\varphi})$, was obtained in terms of the statistically averaged MI, $\tilde{\Theta}$, and its time and azimuthal-angle correlation, $\cal{G}_{t\varphi}$, as the sums of volume and surface components. The MI $\Theta$ 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 $\cal{G}_{t\varphi}$ 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

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↗

arXiv2024

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 $\Phi(\rho)$ of the energy density is taken into account in the simplest form as expansion in powers of $\rho-\overline{\rho} $, where $\overline{\rho}$ is the saturation density, up to second order, in terms of its contributions to the separation particle energy and incompressibility. Density distributions $\rho$ 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↗

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↗

arXiv2023

Particle-number fluctuations near the critical point of nuclear matter

The equation of state with quantum statistics corrections is used for particle number fluctuations $ω$ of isotopically symmetric nuclear matter with interparticle van der Waals and Skyrme local density interactions. The fluctuations, $ω\propto 1/\mathcal{K}$, are analytically derived through the isothermal incompressibility $\mathcal{K}$ at first order over a small quantum-statistics parameter. Our approximate analytical results appear to be in good agreement with the results of accurate numerical calculations. These results are also close to those obtained by using more accurate Tolman and Rowlinson expansions of the incompressibility $\mathcal{K}$ near the critical point. A more general formula for fluctuations $ω$, improved at the critical point, was obtained for a finite particle-number average $\langle N \rangle$ by neglecting, for simplicity, small quantum statistics effects. It is shown that for a large dimensionless parameter, $α\propto \mathcal{K}^2\langle N \rangle/\mathcal{K}^{\prime\prime} $, where $\mathcal{K}^{\prime\prime}$ is the second derivative of the incompressibility $\mathcal{K}$ as function of the average particle density $n$, far from the critical point ($α\gg 1$), one finds the traditional asymptote, $ω\propto 1/\mathcal{K}$, for the fluctuations $ω$. For a small parameter, $α\ll 1$, near the critical point, where $\mathcal{K}=0$ and $α=0$, one obtains another asymptote of $ω$. These fluctuations, having a maximum near the critical point as function of the average density $n$, for finite values of $\langle N \rangle$ are finite and relatively small, in contrast to the results of the traditional calculations.

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

Quantum statistics effects near the critical point in systems with different inter-particle interactions

Equation of state with quantum statistics corrections is derived for systems of the Fermi and Bose particles by using their van der Waals (vdW) and effective density-dependent Skyrme mean-field interactions. First few orders of these corrections over the small quantum statistics parameter, $\varepsilon \approx \hbar^3 n(mT)^{-3/2}g^{-1}$, where $n$ and $T$ are the particle number density and temperature, $m$ and $g$ the mass and degeneracy factor of particles, are analytically obtained. For interacting system of nucleon and $α$ - particles, a small impurity of $α$ - particles to a nucleon system at leading first order in both $α$-particle and nucleon small parameters $\varepsilon$ does not change much the basic results for the symmetric nuclear matter in the quantum vdW consideration. Our approximate analytical results for the quantum vdW and Skyrme mean-field approaches are in a good agreement with accurate numerical calculations.

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↗

arXiv2021

Semiclassical and quantum shell-structure calculations of the moment of inertia

Shell corrections to the moment of inertia (MI) are calculated for a Woods-Saxon potential of spheroidal shape and at different deformations. This model potential is chosen to have a large depth and a small surface diffuseness which makes it resemble the analytically solved spheroidal cavity in the semiclassical approximation. For the consistent statistical-equilibrium collective rotations, the MI is obtained within the cranking model in an approach which goes beyond the quantum perturbation approximation based on the non perturbative energy spectrum. For the calculation of the MI shell corrections $δΘ$, the Strutinsky smoothing procedure is used to obtain the average occupation numbers of the particle density generated by the resolution of the Woods-Saxon eigenvalue problem. One finds that the major-shell structure of $δΘ$, as determined in the adiabatic approximation, is rooted, for large as well as for small surface deformations, in the same inhomogenuity of the distribution of single-particle states near the Fermi surface as the energy shell corrections $δE$. This fundamental property is in agreement with the semiclassical results $δΘ\propto δE$ obtained analytically within the non perturbative periodic orbit theory for any potential well, in particular for the spheroidal cavity, and for any deformation, even for large deformations where bifurcations of the equatorial orbits play a substantial role. Since the adiabatic approximation, $ω\ll Ω$, with $\hbar Ω$ the distance between major nuclear shells, is easily obeyed even for large angular momenta typical for high-spin physics at large particle numbers, our model approach seems to represent a tool that could be useful for the description of such nuclear systems.

nucl-th↗

arXiv2020

Quantum statistics effects and fluctuations of particle numbers near the critical point of nuclear matter

Equation of state with quantum statistics corrections is derived for a multi-component gas of particles interacting through the repulsive and attractive van der Waals (vdW) forces up to first few orders over a small parameter $δ\approx \hbar^3 n(mT)^{-3/2}[g(1- bn)]^{-1}$, where $n$ and $T$ are the particle number density and temperature, $m$ and $g$ the particle mass and degeneracy factor. The parameter $b$ corresponds to the vdW excluded volume. For interacting system of Fermi nucleon and Bose $α$ particles, a small impurity of $α$ particles to the nucleon system at leading first order in both $α$ particle and nucleon small parameters $δ$ does not change much the basic results for the symmetric nuclear matter. The particle number fluctuations $ω$ determined by the isothermal in-compressibility $\mathcal{K}(n,T)$ can be obtained analytically at the same first order quantum-statistics approximation for symmetric nucleon matter. Our approximate analytical results appear to be in good agreement with the accurate numerical calculations.

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

Surface corrections to the moment of inertia and shell structure in finite Fermi systems

The moment of inertia for nuclear collective rotations is derived within a semiclassical approach based on the Inglis cranking and Strutinsky shell-correction methods, improved by surface corrections within the nonperturbative periodic-orbit theory. For adiabatic (statistical-equilibrium) rotations it was approximated by the generalized rigid-body moment of inertia accounting for the shell corrections of the particle density. An improved phase-space trace formula allows to express the shell components of the moment of inertia more accurately in terms of the free-energy shell correction. Evaluating their ratio within the extended Thomas-Fermi effective-surface approximation, one finds good agreement with the quantum calculations.

nucl-th↗

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↗

arXiv2019

Effects of quantum statistics near the critical point of nuclear matter

Effects of quantum statistics for nuclear matter equation of state are analyzed in terms of the recently proposed quantum van der Waals model. The system pressure is expanded over a small parameter $δ\propto n(mT)^{-3/2}[g(1-bn)]^{-1}$, where $n$ and $T$ are, respectively, the particle number density and temperature, $m$ and $g$ the particle mass and degeneracy factor. The parameter $b$ corresponds to the van der Waals excluded volume. The corrections due to quantum statistics for the critical point values of $T_c$, $n_c$, and the critical pressure $P_c$ are found within the linear and quadratic orders over $δ$. These approximate analytical results appear to be in a good agreement with exact numerical calculations in the quantum van der Waals model for interacting Fermi particles: the symmetric nuclear matter ($g=4$) and the pure neutron matter ($g=2$). They can be also applied to the system of interacting Bose particles like the matter composed of $α$ nuclei.

nucl-th↗