arXiv subjects

B. Osei

Publications and source records attributed to B. Osei.

6 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 $\hbar\omega_0$ 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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arXiv2025

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

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

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 $\hbar\omega_0$ 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 $\delta B_{rms}$ 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 $\hbar\omega_0$ 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

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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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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