arXiv subjects

A. V. Afanasjev

Publications and source records attributed to A. V. Afanasjev.

At least 19 recordsLinked to original sources

arXiv2026

Optimized basis of covariant density functional theory: point coupling functionals and excited states

The present investigation focuses on the improvement of the accuracy of the description of physical observables of interest in moderately sized fermionic basis within the framework of covariant density functional theory. It extends previous study of Ref. [1] to point coupling (PC) covariant energy density functionals (CEDFs) and to excited states. Using as a benchmark the solutions corresponding either to infinite fermionic basis or those extrapolated to such a basis it is shown that the optimization of oscillator frequency $\hbarω_0$ of the harmonic oscillator (HO) basis leads to a substantial improvement in the description of different physical observables in the fermionic basis truncated at $N_F$. Globally optimized scaling factors $f_{opt}(A)$ of the oscillator frequency and the sizes $N_F^{\varepsilon}$ of the HO bases providing the required accuracy $\varepsilon$ in the calculations of the binding energies are generated for the PC functionals. The optimization of the basis also significantly improves the accuracy of the description of potential energy curves, defining the fission barriers and fission isomers in actinides and superheavy nuclei, provided that the size of the basis is at least equal to $N_F=20$. The optimization of the HO basis improves the accuracy of the description of the energies of bound single-particle states: the only exceptions are weakly bound neutron states with low orbital momenta $l=0$, 1 and 2. It is demonstrated for the first time that the halo densities of neutron halo nuclei generated in the coordinate space calculations are well reproduced in the calculations with very large fermionic HO bases.

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arXiv2026

Basis truncation, statistical errors, and systematic uncertainties in relativistic approaches to nuclear response

Although there exists a clear and, in principle, exact theoretical formulation for the equation of motion for the response of a correlated fermionic system, its numerical implementations for atomic nuclei require feasible approximations. One of the widely accepted approximations is a truncated harmonic oscillator (HO) basis, whose wave functions are used to expand the solutions obtained with realistic interactions. In this work, we extend previously employed HO basis truncated at $N_F$ = 20 fermionic shells to $N_F$ = 50 and perform a systematic study of the effects of such basis increase on nuclear resonances. The relativistic random phase approximation (RRPA) and its extension by the particle-vibration coupling dubbed as relativistic time-blocking approximation (RTBA) are applied to the description of the monopole, dipole, quadrupole, and octupole resonances in $^{48}$Ca, $^{78}$Ni, and $^{132}$Sn, and the RRPA studies are extended to $^{70}$Ca and $^{208}$Pb. A considerable sensitivity of the strength distributions to the HO basis size is found, especially for low-spin resonances in the light neutron-rich nuclei. The effects of the HO basis extension to $N_F$ = 50 are analyzed and linked to the involvement of proton and neutron continuum states and proton quasi-bound states in the strength formation. The obtained results point to the importance of the HO basis completeness and continuum effects in the nuclear response calculations and evaluation of the associated parameters of the nuclear equation of state. Statistical errors and systematic uncertainties in the RRPA strength functions are analyzed. They are found to be substantial for the monopole response, but significantly smaller for the dipole, quadrupole, and octupole ones. Neither of them shows a pronounced mass dependence, and statistical errors are generally smaller than systematic uncertainties.

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arXiv2025

Global optimization of harmonic oscillator basis in covariant density functional theory

The present investigation focuses on the improvement of the accuracy of the description of binding energies within moderately sized fermionic basis. Using the solutions corresponding to infinite fermionic basis it was shown that in the case of meson exchange (ME) covariant energy density functionals (CEDFs) the global accuracy of the description of binding energies in the finite $N_F=16-20$ bases can be drastically (by a factor ranging from $\approx 3$ up to $\approx 9$ dependent on the functional and $N_F$) improved by a global optimization of oscillator frequency of the basis. This is a consequence of the unique feature of the ME functionals in which with increasing fermionic basis size fermionic and mesonic energies approach the exact (infinite basis) solution from above and below, respectively. As a consequence, an optimal oscillator frequency $\hbarω_0$ of the basis can be defined which provides an accurate reproduction of exact total binding energies by the ones calculated in truncated basis. This leads to a very high accuracy of the calculations in moderately sized $N_F=20$ basis when mass dependent oscillator frequency is used: global rms differences $δB_{rms}$ between the binding energies calculated in infinite and truncated bases are only 0.025 MeV and 0.031 MeV for the NL5(Z) and DD-MEZ functionals, respectively. Optimized values of the oscillator frequency $\hbarω_0$ are provided for three major classes of CEDFs, i.e. for density dependent meson exchange functionals, nonlinear meson exchange ones and point coupling functionals.

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arXiv2025

Recent progress in global optimizations of covariant energy density functionals

The recent progress on global optimizations of covariant energy density functionals (CEDFs) and global calculations of binding energies within the covariant density functional theory (CDFT) has been analyzed and reviewed. Recently developed anchor-based optimization approach of Ref. [1] allows global optimizations of CEDFs at a reasonable numerical cost. Moreover, it permits such optimizations in a very large fermionic basis with a proper extrapolation to an infinite one. This allows to accurately estimate global calculation errors due to use of truncated fermionic basis and neglect of some contributions to binding energies (such as total electron binding energy)

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arXiv2025

Crust composition and the Shallow Heat Source in KS 1731-260

The presence of a strong shallow heat source of unknown origin in accreting neutron star crusts has been inferred by analyzing X-ray observations of their cooling in quiescence. We model the cooling of KS 1731-260 using realistic crust compositions and nuclear heating and cooling sources from detailed nuclear reaction network calculations. We find that the required strength of the shallow heat source in KS 1731-260 is reduced by more than a factor of 3 compared to previous analysis, a 5-sigma difference that alleviates the need for exotic solutions. Our analysis also suggests the existence of an impure nuclear pasta layer in the inner crust of KS 1731-260 though future observations will provide more stringent constraints. In addition, we obtain constraints on the dominant surface burning modes of KS 1731-260 over its history.

astro-ph.HE↗

arXiv2025

Further steps towards next generation of covariant energy density functionals

The present study aims at further development of covariant energy density functionals (CEDFs) towards more accurate description of binding energies across the nuclear chart. For the first time, infinite basis corrections to binding energies in the fermionic and bosonic sectors of the covariant density functional theory have been taken into account in the fitting protocol within the covariant density functional theory. In addition, total electron binding energies have been used in the conversion of atomic binding energies into nuclear ones. Their dependence on neutron excess has been investigated for the first time across the nuclear chart within atomic approach. These factors have been disregarded in previous generation of covariant energy density functionals but their neglect leads to substantial global calculation errors for physical quantities of interest. For example, these errors for binding energies are of the order of 0.8 MeV or higher for the three major classes of covariant energy density functionals.

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arXiv2025

Calculation of the correlation, relativistic and QED corrections to the total electron binding energy in atoms and their nuclear charge dependence

We present relativistic many-body calculations of total electron binding energy of neutral atoms up to element $Z=120$. Binding energy for ions may be found by subtracting known ionization potentials. Accuracy of the results for $17 105$ there). We fit numerical results for binding energies by analytical function of $Z$. We also calculate numerical values and determine dependence on $Z$ of the correlation corrections, Dirac and Breit relativistic corrections and quantum electrodynamics (QED) corrections.

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arXiv2025

Fast rotation of nuclei with extreme isospin in the vicinity of neutron and proton drip lines

The analysis of the present understanding of collective rotation in very neutron-rich nuclei is presented. It is shown that collective rotation can lead to the increase of stability of rotational states with increasing spin. The detailed investigation of rotational excitations in very proton-rich nuclei confirms this conclusion and indicate that experimental studies of such features are more feasible in the nuclei near proton drip line. They also show that rotational bands which are proton quasi-bound at zero or low spins can be transformed into proton bound ones at high spin by collective rotation of nuclear systems. This is due to strong Coriolis interaction which acts on high-$j$ or strongly mixed M orbitals and drives the highest in energy occupied single-particle states into negative energy domain. These physical mechanisms lead to a substantial extension of the nuclear landscape beyond the spin zero proton drip line. In addition, a new phenomenon of the formation of giant proton halos in rotating nuclei emerges: it is triggered by the occupation of strongly mixed M intruder orbitals.

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arXiv2025

Clusterization aspects in the states of non-rotating and fast rotating nuclei

The understanding of clustering aspects at the ground state of nuclei and in fast rotating ones within the framework of covariant density functional theory has been reviewed and reanalyzed. The appearance of many exotic nuclear shapes in nuclear chart can be inferred from combined analysis of nodal structure of the densities of the single-particle states and the evolution of such states in the Nilsson diagram with deformation and particle number. Such analysis which is supported by fully self-consistent calculations allows to predict the existence of nuclear configurations with specific shape or cluster properties at ground state and at high spin. For example, it indicates that in a given shell with principal quantum number $N$ only the lowest in energy two-fold degenerate deformed state can contribute to the formation of linear chain $α$ cluster structures.

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arXiv2024

Towards accurate nuclear mass tables in covariant density functional theory

The current investigation focuses on detailed analysis of the anchor based optimization approach (ABOA), its comparison with alternative global fitting protocols and on the global analysis of the truncation of basis effects in the calculation of binding energies. It is shown that ABOA provides a solution which is close to that obtained in alternative approaches but at small portion of their computational time. The application of softer correction function after few initial iterations of ABOA stabilizes and speeds up its convergence. For the first time, the numerical errors in the calculation of binding energies related to the truncation of bosonic and fermionic bases have been globally investigated with respect of asymptotic values corresponding to the infinite basis in the framework of covariant density functional theory (CDFT). These errors typically grow up with the increase of the mass and deformation of the nuclei. To reduce such errors in bosonic sector below 10 keV for almost all nuclei with proton number $Z<120$ one should truncate the bosonic basis at $N_B=28$ instead of presently used $N_B=20$. The reduction of the errors in binding energies due to the truncation of the fermionic basis in CDFT is significantly more numerically costly. For the first time it is shown that the pattern and the speed of the convergence of binding energies as a function of the size of fermionic basis given by $N_F$ depend on the type of covariant energy density functional. The use of explicit density dependence of the meson-nucleon coupling constants or point couplings slows down substantially the speed of convergence of binding energies as a function of $N_F$. A new procedure for finding the asymptotic values of binding energies is suggested in the present paper: it allows better control of numerical errors.

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arXiv2023

Impact of Pycnonuclear Fusion Uncertainties on the Cooling of Accreting Neutron Star Crusts

The observation of X-rays during quiescence from transiently accreting neutron stars provides unique clues about the nature of dense matter. This, however, requires extensive modeling of the crusts and matching the results to observations. The pycnonuclear fusion reaction rates implemented in these models are theoretically calculated by extending phenomenological expressions and have large uncertainties spanning many orders of magnitude. We present the first sensitivity studies of these pycnonuclear fusion reactions in realistic network calculations. We also couple the reaction network with the thermal evolution code dStar to further study their impact on the neutron star cooling curves in quiescence. Varying the pycnonuclear fusion reaction rates alters the depth at which nuclear heat is deposited although the total heating remains constant. The enhancement of the pycnonuclear fusion reaction rates leads to an overall shallower deposition of nuclear heat. The impurity factors are also altered depending on the type of ashes deposited on the crust. These total changes correspond to a variation of up to 9 eV in the modeled cooling curves. While this is not sufficient to explain the shallow heat source, it is comparable to the observational uncertainties and can still be important for modeling the neutron star crust.

astro-ph.HE↗

arXiv2023

Anchor-based optimization of energy density functionals

A new anchor-based optimization method of defining the energy density functionals (EDFs) is proposed. In this approach, the optimization of the parameters of EDF is carried out for the selected set of spherical anchor nuclei the physical observables of which are modified by the correction function which takes into account the global performance of EDF. It is shown that the use of this approach leads to a substantial improvement in global description of binding energies for several classes of covariant EDFs. The computational cost of defining a new functional within this approach is drastically lower as compared with the one for the optimization which includes the global experimental data on spherical, transitional and deformed nuclei into the fitting protocol.

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arXiv2023

Differential charge radii: self-consistency and proton-neutron interaction effects

The analysis of self-consistency and proton-neutron interaction effects in the buildup of differential charge radii has been carried out in covariant density functional theoretical calculations without pairing interaction. Two configurations of the $^{218}$Pb nucleus, generated by the occupation of the neutron $1i_{11/2}$ and $2g_{9/2}$ subshells, are compared with the ground state configuration in $^{208}$Pb. The interaction of added neutron(s) and the protons forming the $Z=82$ proton core is responsible for a major contribution to the buildup of differential charge radii. It depends on the overlaps of proton and neutron wave functions and leads to a redistribution of single-particle density of occupied proton states which in turn modifies the charge radii. Self-consistency effects affecting the shape of proton potential, total proton densities and the energies of the single-particle proton states provide only secondary contribution to differential charge radii. The buildup of differential charge radii is a combination of single-particle and collective phenomena. The former is due to proton-neutron interaction, the impact of which is state dependent, and the latter reflects the fact that all occupied proton single-particle states contribute to this process. The neglect of either one of these aspects of the process by ignoring proton-neutron interaction and self-consistency effects as it is done in macroscopic+microscopic approach or by introducing the core as in spherical shell model introduces uncontrollable errors and restricts the applicability of such approaches to the description of differential charge radii.

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arXiv2022

Bubble nuclei: single-particle versus Coulomb interaction effects

The detailed investigation of microscopic mechanisms leading to the formation of bubble structures in the nuclei has been performed in the framework of covariant density functional theory. The main emphasis of this study is on the role of single-particle degrees of freedom and Coulomb interaction. In general, the formation of bubbles lowers the Coulomb energy. However, in nuclei this trend is counteracted by the quantum nature of the single-particle states: only specific single-particle states with specific density profiles can be occupied with increasing proton and neutron numbers. A significant role of central classically forbidden region at the bottom of the wine bottle potentials in the formation of nuclear bubbles (via primarily the reduction of the densities of the $s$ states at $r=0$) has been revealed for the first time. Their formation also depends on the availability of low-$l$ single-particle states for occupation since single-particle densities represent the basic building blocks of total densities. Nucleonic potentials disfavor the occupation of such states in hyperheavy nuclei and this contributes to the formation of bubbles in such nuclei. Additivity rule for densities has been proposed for the first time. It was shown that the differences in the densities of bubble and flat density nuclei follow this rule in the $A\approx 40$ mass region and in superheavy nuclei with comparable accuracy. This strongly suggests the same mechanism of the formation of central depression in bubble nuclei of these two mass regions. Nuclear saturation mechanisms and self-consistency effects also affect the formation of bubble structures. The detailed analysis of different aspects of bubble physics strongly suggests that the formation of bubble structures in superheavy nuclei is dominated by single-particle effects.

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arXiv2022

The impact of isospin dependence of pairing on fission barriers in the fission cycling regions

A systematic analysis of the ground state and fission properties of actinides and superheavy nuclei important for the $r$ process modeling has been performed within the framework of covariant density functional theory for the first time in Ref. [1]. A brief review of the results related to the heights of primary fission barriers and systematic uncertainties in their prediction is presented. In addition, new results on the potential impact of the isospin dependence of pairing on fission barriers in fission cycling regions is provided for the first time.

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arXiv2022

Model for independent particle motion

Independent particle model in nuclear physics assumes that the nucleon in the nucleus moves in the average (mean field) potential generated by all other nucleons. This chapter gives a short overview of basic features of the independent particle motion in atomic nuclei and its theoretical realization in the framework of shell models for spherical, deformed and rotating nuclei as well as in more sophisticated approaches such as microscopic+macroscopic model and density functional theories. Independent particle motion of nucleons leads to global and single-particle consequences. The global ones manifest themselves in the shell structure and its consequences for global structure of nuclear landscape, the existence of superheavy nuclei and the superdeformation at high spin are briefly reviewed. The latter shows itself in the single-particle properties such as energies, alignments and densities; their manifestations are illustrated on specific examples.

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arXiv2021

Charge radii, moments and masses of mercury isotopes across the N = 126 shell closure

Combining laser spectroscopy in a Versatile Arc Discharge and Laser Ion Source, with Penning-trap mass spectrometry at the CERN-ISOLDE facility, this work reports on mean-square charge radii of neutron-rich mercury isotopes across the $N = 126$ shell closure, the electromagnetic moments of $^{207}$Hg and more precise mass values of $^{206-208}$Hg. The odd-even staggering (OES) of the mean square charge radii and the kink at $N = 126$ are analyzed within the framework of covariant density functional theory (CDFT), with comparisons between different functionals to investigate the dependence of the results on the underlying single-particle structure. The observed features are defined predominantly in the particle-hole channel in CDFT, since both are present in the calculations without pairing. However, the magnitude of the kink is still affected by the occupation of the $1i_{11/2}$ and $2g_{9/2}$ orbitals with a dependence on the relative energies as well as pairing.

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arXiv2021

Global performance of covariant density functional theory in description of charge radii and related indicators

A short review of existing efforts to understand charge radii and related indicators on a global scale within the covariant density functional theory (CDFT) is presented. Using major classes of covariant energy density functionals (CEDFs), the global accuracy of the description of experimental absolute and differential charge radii within the CDFT framework has been established. This assessment is supplemented by an evaluation of theoretical statistical and systematic uncertainties in the description of charge radii. New results on the accuracy of the description of differential charge radii in deformed actinides and light superheavy nuclei are presented and the role of octupole deformation in their reproduction is evaluated. Novel mechanisms leading to odd-even staggering in charge radii are discussed. Finally, we analyze the role of self-consistency effects in an accurate description of differential charge radii.

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