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Recent progress in global optimizations of covariant energy density functionals

A. V. Afanasjev, B. Osei, A. Dalbah

TL;DR

The paper addresses the challenge of achieving high-accuracy global binding-energy predictions within covariant density functional theory by examining the limitations of traditional fits and the slow basis convergence that hinders global optimization. It presents anchor-based optimization (ABOA) with extrapolation to infinite fermionic basis as a practical route to global CEDF calibrations, and it emphasizes careful treatment of total electron binding energies (TEBE) and basis corrections to quantify true global errors via $\Delta B_{rms}^{tot} = \Delta B_{rms} \pm \delta B_{rms}^{negl}$. The authors identify that, even with ABOA and large bases, global calculation errors remain non-negligible (on the order of tens of keV for basis corrections and up to ~MeV without TEBEs or infinite-basis corrections), and they demonstrate that the Z-class functionals DD-MEZ, NL5(Z), and PC-Z offer the best global performance, approaching but not yet reaching non-relativistic benchmarks. The work highlights the necessity of including beyond-mean-field corrections and improving single-particle energies (via tensor interactions and $\delta$-meson terms) to enhance spectroscopic fidelity, thereby advancing the reliability of CDFT-based global mass predictions for nuclear physics and astrophysics applications.

Abstract

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)

Recent progress in global optimizations of covariant energy density functionals

TL;DR

The paper addresses the challenge of achieving high-accuracy global binding-energy predictions within covariant density functional theory by examining the limitations of traditional fits and the slow basis convergence that hinders global optimization. It presents anchor-based optimization (ABOA) with extrapolation to infinite fermionic basis as a practical route to global CEDF calibrations, and it emphasizes careful treatment of total electron binding energies (TEBE) and basis corrections to quantify true global errors via . The authors identify that, even with ABOA and large bases, global calculation errors remain non-negligible (on the order of tens of keV for basis corrections and up to ~MeV without TEBEs or infinite-basis corrections), and they demonstrate that the Z-class functionals DD-MEZ, NL5(Z), and PC-Z offer the best global performance, approaching but not yet reaching non-relativistic benchmarks. The work highlights the necessity of including beyond-mean-field corrections and improving single-particle energies (via tensor interactions and -meson terms) to enhance spectroscopic fidelity, thereby advancing the reliability of CDFT-based global mass predictions for nuclear physics and astrophysics applications.

Abstract

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)

Paper Structure

This paper contains 6 sections, 1 equation, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. The status of global calculations
  3. New generation of covariant energy density functionals
  4. Global calculation errors
  5. Unresolved issues in global mass calculations
  6. Conclusions

Figures (3)

  • Figure 1: The differences $B_{th}-B$ between calculated ($B_{th}$) and experimental ($B$) nuclear binding energies for the DD-MEZ functional. Positive (negative) value of this difference means that calculated nucleus is less (more) bound than experimental one.
  • Figure 2: The summary of existing global mass calculations which satisfy the condition $\Delta B_{rms} \leq 3.0$ MeV. The labels A, B, C, D, E, F, G are used for references NL5Z-DDMEZ-PCZ, TA.23, RHB-e-e-continuum.22, YWZL.21, LLLYM.15, AGC.16 and AARR.14, respectively. Red, blue and black colors are employed for the DDME, NLME and PC functionals, respectively. See text for details.
  • Figure 3: (left panels) The differences $B^{th} - B$ between calculated ($B^{th}$) and experimental $(B)$ nuclear binding energies obtained with indicated functionals. Note that only the nuclei which satisfy the condition $|B^{th} - B| \geq 2.5$ MeV are shown here. (right panels) The calculated quadrupole deformations $\beta_2$ of the nuclei shown on respective left panels.