Further steps towards next generation of covariant energy density functionals

A. Dalbah; A. Taninah; A. V. Afanasjev; B. Osei; U. C. Perera; V. A. Dzuba; V. V. Flambaum

REVIEW 4 major objections 7 minor 1 cited by

Further steps towards next generation of covariant energy density functionals

T0 review · 4 major / 7 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper claims that earlier covariant nuclear mass fits carried a hidden systematic error of about 0.8 MeV because they ignored infinite-basis corrections and total electron binding energies, and shows that a corrected fitting protocol…

desk verdict A real methodological step in CEDF fitting, but the headline 0.8 MeV error is an indirect model-difference measure, not a clean attribution. read the letter →

arxiv 2507.17082 v2 pith:C2ZRYR3F submitted 2025-07-22 nucl-th

B. Osei , A. V. Afanasjev , A. Taninah , A. Dalbah , U. C. Perera , V. A. Dzuba , V. V. Flambaum This is my paper · ORCID

classification nucl-th

keywords covariantdensityfunctionaltheorynuclearbindingenergiesmasstablesinfinitebasiscorrectionselectronanchor-basedoptimizationrelativisticHartree-Bogoliubovenergyrmsdeviations

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Accurate nuclear masses are the main calibration target for covariant density functional theory, but the paper says that previous global fits of those functionals were aiming at a slightly wrong quantity: the experimental table gives atomic binding energies, not nuclear ones, and the numerical equations were solved in a truncated basis. The paper shows that these two omissions are not small, producing a hidden global error of about 0.8 MeV or more in binding energies across the nuclear chart. It removes the omissions by subtracting total electron binding energies and by adding extrapolated infinite-basis corrections to the fit data, producing three new functionals DD-MEZ, NL5(Z) and PC-Z. The best of these, DD-MEZ, reaches 1.557 MeV rms deviation over 882 even-even nuclei when a Wigner term is included, with the remaining numerical error near 0.025 MeV. If the paper is right, no high-precision covariant mass fit can afford to leave these corrections out.

What carries the argument

The load-bearing object is the correction function $\Delta B_{\rm cor}(Z,N) = B_{\rm el}(Z) + \Delta B^F_\infty(Z,N)$ used to generate pseudodata for the fit. $B_{\rm el}(Z)$ is the total energy needed to strip all electrons from an atom with $Z$ protons, converting the experimental table's atomic binding energies into nuclear ones. $\Delta B^F_\infty$ is the difference between the binding energy computed in an infinite fermionic basis and in the truncated $N_F=20$ basis used in practice; since infinite bases are numerically impossible, the paper extrapolates from runs with up to $N_F=40$ (and $N_F=60$ without pairing), benchmarks the extrapolation on test nuclei to better than 15 keV for DD-MEZ and 10 keV for NL5(Z), and iterates the correction inside the anchor-based optimization until it stabilizes below 8 keV. The bosonic sector is handled more directly by using $N_B=40$ full shells instead of the standard $N_B=20$, which brings the bosonic basis error below 10 keV everywhere. This combination turns the fitted parameters into quantities defined against infinite-basis, purely nuclear binding energies.

What would settle it

Run the new functionals on deformed actinide and superheavy nuclei such as 240Pu and 290Lv in fermionic bases of 56 or 60 shells without pairing and with a converged bosonic basis, then compare the resulting binding energies with the extrapolated pseudodata; if the differences cluster systematically above about 100 keV, the extrapolation and the 0.8 MeV error estimate would need revision.

Watch

Extended reading notes

Core claim

The central claim is that the accuracy budget of covariant energy density functionals is controlled, at the level of around 0.8 MeV, by three protocol details that are not part of the nuclear interaction: the truncation of the harmonic-oscillator basis in the fermionic and bosonic sectors, and the use of atomic rather than nuclear binding energies as fit targets. To remove them, the paper fits to pseudodata $B_{\rm pseudo}(Z,N) = B_{\rm AME}(Z,N) - [B_{\rm el}(Z) + \Delta B^F_\infty(Z,N)]$, where $B_{\rm el}$ is the total electron binding energy and $\Delta B^F_\infty$ is an extrapolated correction from the truncated fermionic basis to the infinite limit. The correction is redetermined iteratively inside the anchor-based optimization, with convergence judged by the global rms change between rounds falling below 8 keV. On this basis the paper constructs new functionals in all three classes, DD-MEZ, NL5(Z) and PC-Z, and reports the first evaluation of the global calculation error of earlier fits: about 0.77 MeV for DD-MEY, 0.84 MeV for NL5(Y), and more than 1 MeV for the point-coupling class. DD-MEZ improves the rms deviation from 1.802 MeV to 1.601 MeV (1.557 MeV with Wigner energy) while shrinking its own numerical error to roughly 0.025 MeV. The conclusion is that the older fits were not just less convenient but systematically biased, and that convergence to the infinite-basis limit plus the electron correction is a prerequisite for sub-MeV covariant mass tables.

Load-bearing premise

The headline error estimate depends on the extrapolation that turns finite-basis calculations into infinite-basis binding energies being accurate to tens of keV across the whole chart, including the heavy, deformed, and superheavy nuclei where the paper's own basis runs do not fully converge.

Editorial extensions

If this is right

Previous covariant mass tables based on meson-exchange functionals should be treated as carrying a hidden global error of about 0.8 MeV on top of their reported rms deviations, which changes how their agreement with experiment is interpreted.
The corrected DD-MEZ functional becomes the best covariant mean-field functional for global binding energies, reaching an rms deviation of 1.557 MeV over 882 even-even nuclei when a Wigner term is included, with a residual numerical error near 0.025 MeV.
The iterative procedure shows that infinite-basis corrections must be recomputed after each refit: a one-shot correction map can be off by almost 90 keV globally and by up to about 0.4 MeV in heavy nuclei, so static correction tables are not reliable.
Within the experimentally known region, total electron binding energies can be treated as a function of proton number alone, because their isotopic variation stays below about 1 keV even in superheavy chains.
For point-coupling functionals, the harmonic-oscillator basis converges too slowly to define infinite-basis corrections in actinides and superheavy nuclei; the new PC-Z fit therefore covers only part of the chart and still carries a global error above 1 MeV.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the paper is right, a similar audit would be worth doing for non-relativistic mass fits that also rely on truncated harmonic-oscillator bases: part of their reported agreement with experiment may likewise come from absorbing basis and electron-conversion errors into fitted parameters rather than removing them.
The Y-versus-Z parameter shifts in the paper suggest a testable prediction: the difference between old and new functionals should be concentrated in shell-correction regions, especially around 208Pb and the actinides, where single-particle level ordering most strongly changes binding energies.
The iterative correction procedure implies that infinite-basis corrections cannot be tabulated once and reused for a different functional; reusing another functional's correction map can introduce errors of a few hundred keV in heavy nuclei.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a genuine technical advance—first CEDF fits that include infinite basis corrections in both fermionic and bosonic sectors and subtract total electron binding energies from AME data—but the paper's headline number, 0.8 MeV global error, is an indirect measure. It comes from comparing two independently optimized functionals (Y vs Z), not from an ablation of the three new ingredients. The referee should push for an isolation of those effects.

What is new and good: the iterative ABOA procedure for defining basis corrections is clearly described, with convergence checks at NF=40/60 and NB=40/120 that are meaningful. The PC-Z limitation is admitted up front: the correction function cannot be defined for actinides and superheavy nuclei, and the fit is biased accordingly. The atomic calculations behind the electron binding energies are state of the art, and the demonstration that isotope shifts in Bel are <1 keV justifies using Z-only values. The new functionals themselves are new, with tables of parameters and nuclear matter properties. That is all solid.

The soft spot: Eq. (10) and Fig. 9 define δB_negl as the rms difference between Y and Z binding energies. The Y and Z fits differ in more than the new protocol: AME2016 vs AME2020 (853 vs 882 nuclei), the charge-radius expression (full Eq. (1) for Z, truncated for Y), and possibly the anchor set. The paper says the AME update 'does not play a principal role' but gives no sensitivity test. Parameter shifts are large for density-dependent couplings, so part of the 0.8 MeV may be normal functional re-fitting, not the specific physics. The abstract's '0.8 MeV or higher for three major classes' is also ahead of the evidence: Section VI E explicitly says PC errors cannot be accurately quantified, and the PC-Z fit is biased. The PC comparison gives >1 MeV but the authors themselves call it a conservative estimate.

There is also a self-referential aspect: the corrections come from the same group's atomic tables and are defined through the functionals being fitted. The iterative scheme converges (89 keV -> 16 keV -> 8 keV rms), so this is not fatal, but it is worth noting.

The citation pattern is dominated by the group's own ABOA papers and atomic calculations, but that is appropriate here since the work builds directly on them.

Who this is for: anyone fitting CEDFs or using CDFT mass tables. It deserves peer review, but the referee should require an ablation or at least a sensitivity analysis that separates the effects of AME update, charge-radius expression, and the basis/Bel corrections. The abstract should be softened for the PC class.

Recommendation: send for peer review with revision.

Referee Report

4 major / 7 minor

Summary. The paper presents three modifications to the fitting protocol of covariant energy density functionals (CEDFs): (i) inclusion of infinite-basis corrections to binding energies in both fermionic and bosonic sectors, (ii) subtraction of total atomic electron binding energies when converting AME atomic binding energies into nuclear ones, and (iii) use of the full charge-radius formula with spin-orbit terms for anchor nuclei. New functionals DD-MEZ, NL5(Z), and PC-Z are fitted within the anchor-based optimization approach and compared with previous DD-MEY, NL5(Y), and PC-Y fits. The authors report that neglect of the basis corrections and electron binding energies in earlier fits produces a global calculation error δB_negl of about 0.8 MeV for the DDME and NLME classes, and larger than 1.0 MeV for the PC class, while the new Z functionals have δB_negl of about 25–30 keV. The new DD-MEZ functional yields ΔB_rms = 1.601 MeV over 882 even–even nuclei, improving to 1.557 MeV when a Wigner term is added.

Significance. If the central claim is correct, it identifies a hidden systematic error of ~0.8 MeV in previous CDFT mass tables, comparable to the reported rms deviations and thus potentially affecting conclusions drawn from those tables. The paper is also significant for introducing the first chart-wide calculations of infinite-basis corrections in both sectors, for analyzing the neutron-excess dependence of electron binding energies, and for providing new global fits that reach the best mean-field accuracy among CEDFs. The convergence benchmarks (NF = 40/60, NB = 40/120) and the iterative ABOA procedure for defining basis corrections are well documented and could be reused by other groups. The main weakness is that the 0.8 MeV error estimate is derived from a Y-vs-Z functional comparison that does not isolate the three protocol changes, so the causal attribution is not fully established.

major comments (4)

[Sec. VI E, Eq. (10), Fig. 9] The quantity δB_negl^rms defined in Eq. (10) and displayed in Fig. 9 is computed as rms[B(Y) − B(Z)], i.e., as a difference between two independently optimized functionals. However, the Y and Z fits differ not only in the treatment of basis truncation and electron binding energies but also in the AME evaluation (2016 vs 2020; 853 vs 882 even–even nuclei), in the anchor data values taken from those evaluations, and in the charge-radius expression (full Eq. (1) including spin-orbit terms for Z, first three terms only for Y). The statement in Sec. VI E that the AME update “does not play a principal role” is an assertion with no supporting ablation or sensitivity analysis. Large parameter changes for density-dependent couplings (e.g., c_ω ratio 1.439 in Table V) suggest that the observed 0.8 MeV differences may partly reflect shallow-minimum parameter shifts or data-set changes rather than the physics corrections. To support the central claim, the authors should provide controlled refits that vary one ingredient at a time, or demonstrate that the AME version and charge-radius expression have negligible effect on δB_negl^rms.
[Abstract, Secs. V, VI C, VI E] The abstract states that the neglect of the new ingredients leads to errors “of the order of 0.8 MeV or higher for the three major classes” of CEDFs. For the DDME and NLME classes, the paper gives δB_negl^rms = 0.77 and 0.84 MeV (Fig. 9(a,b)), though with the attribution caveat above. For the PC class, however, Sec. VI E explicitly states that “at present it is impossible to accurately quantify the δB_negl^rms values,” and Sec. VI C explains that the PC-Z fit is biased by the exclusion of actinides and superheavy nuclei from the correction function because PC functionals do not converge at NF = 40 (Fig. 2). The PC estimate “larger than 1.0 MeV” from Fig. 9(c) is therefore not an accurate quantification and should not be used to support the abstract’s “three major classes” claim. The wording of the abstract and conclusions should be revised to restrict the quantitative 0.8 MeV statement to the DDME and NLME classes, or the authors should provide a reliable PC error estimate that accounts for the biased fitting region.
[Sec. V, Supplemental Sec. III] The infinite-basis corrections ΔBF∞(Z,N) are defined through the functional being fitted (Eq. (8)) and are updated iteratively in the ABOA rounds. The validation of the extrapolation procedure is performed against NF = 40 results for a “testing set of nuclei scattered more or less equally across experimentally known nuclear landscape,” with claimed global accuracy better than 15 and 10 keV for DD-MEZ and NL5(Z), respectively. These numbers, however, apply only to the selected test nuclei; the procedure is then applied to all 882 nuclei without an explicit chart-wide uncertainty estimate. Because the central error budget for the Y functionals (δB_negl^rms ≈ 0.8 MeV) is much larger than this validation accuracy, this is not the main limitation, but the paper should report how the extrapolation uncertainty propagates into the 28 keV (DD-MEZ) and 23 keV (NL5(Z)) estimates for the Z functionals, and should state more carefully that the 15/10 keV values are validation-set accuracies rather than global uncertainties.
[Sec. VI E] The same methodological issue that affects δB_negl^rms for binding energies also affects the reported global calculation errors for charge radii and separation energies. The values δ(rch)_negl^rms = 0.010 fm (DD-MEY) and δ(S2n)_negl^rms = 0.387 MeV (DD-MEY) are obtained from the Y–Z differences in the same uncontrolled comparison. Unless the authors provide an ablation separating the contributions of the three protocol changes, these quantities should be described as model-sensitivity measures rather than as well-defined “global calculation errors,” or the analysis should be extended to control the other variables.

minor comments (7)

[Title, Sec. I] The manuscript text contains “d ensity” in the title and running header; this should be corrected to “density.”
[Sec. VI E, Eq. (10)] The use of “±” to combine ΔB_rms and δB_negl^rms is not standard; please specify whether the stated uncertainty is one sigma, a quadrature sum, or the rms of the difference itself.
[Table III] The table classifies existing functionals as atomic or nuclear, but the new Z functionals are not listed; considering they are the main subject of the paper, they should be included or referenced.
[Sec. IV] The conclusion that the isotopic dependence of Bel is negligible is based on only three chains (Pb, Fm, Og); a sentence on why these are representative would be useful.
[Fig. 5] The color scales for the two panels are different (max 0.30 vs 1.0 MeV), which makes visual comparison of the magnitude of bosonic corrections between DD-MEZ and NL5(Z) difficult; a common scale would improve clarity.
[Sec. VI E, footnote 4] This footnote contains a substantial quantitative result (the additional 0.199 MeV contribution for PC-PK1) that is relevant to the main text; consider moving it into the main body.
[Sec. VII, first bullet] “Eliminate numerical uncertainties” is too strong; the text in Sec. VI E states residual errors of ~25–30 keV for the Z functionals. Rephrase to “substantially reduce.”

Circularity Check

1 steps flagged · score 6.0 of 10

The headline 0.8 MeV error estimate is a defined Y-vs-Z functional difference relabeled as the error from neglected basis/Bel terms; the underlying correction procedure itself is not circular.

self definitional [Sec. VI E, Eq. (10) and Fig. 9]
"δB_negl^rms is the global calculation error due to the truncation of the basis and neglected terms (such as total electron binding energy in the conversion from experimental atomic to nuclear binding energies)... Fig. 9(a) allows to define δB_negl^rms = 0.77 MeV for the DD-MEY functional using the DD-MEZ results as a benchmark."

The claimed global error is not derived from a direct estimate of the neglected terms for the Y functional (e.g., from the same Y parameters evaluated in both truncated and corrected protocols). Instead, Eq. (10) plus Fig. 9 define δB_negl^rms as the rms difference between two separately fitted functionals, B(Y)-B(Z). The Z fit differs from Y not only by the basis truncation and total-electron-binding corrections, but also by the AME evaluation (2016 vs 2020; 853 vs 882 nuclei), the anchor set, and the charge-radius expression (full Eq. (1) for Z). The paper asserts the AME difference 'does not play a principal role' without an ablation or sensitivity analysis.

full rationale

The infinite-basis correction procedure is not circular per se: it is a fixed-point iteration with a stated convergence criterion and it is benchmarked against NF=40 calculations for selected nuclei (better than 15 and 10 keV for DD-MEZ and NL5(Z)). The total electron binding energies from Ref. [67] are independent atomic-physics calculations, not fit to CDFT data, so the self-citation there is not load-bearing. The circular element is localized to Sec. VI E: the quantity called 'global calculation error due to truncation and neglected terms' is operationalized as rms[B(Y)-B(Z)], a difference between two independently refitted functionals that also differ in AME version, anchor nuclei, and charge-radius expression. The paper labels this difference as the error caused specifically by the newly included corrections, without ablating the other protocol changes. The abstract's '0.8 MeV or higher for the three major classes' also overstates support for the PC class, since Sec. VI E explicitly says the PC δB_negl^rms cannot be accurately quantified and the PC fit is biased by excluding actinides and superheavy nuclei from the correction function; this is an internal-consistency issue rather than a circularity. Overall, the central numerical claim partially reduces to a defined model comparison, justifying a partial circularity score, but the paper contains substantial independent numerical content and external benchmarks.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claims rest on fitted EDF parameters, two external pairing scalings, and the atomic binding energy tables of the same group. No new physical entities are introduced; the audit surface is concentrated in the extrapolation and error-attribution assumptions.

free parameters (4)

DD-MEZ meson-nucleon coupling parameters (m_sigma, g_sigma, g_omega, g_rho, b_sigma, c_sigma, c_omega, a_rho) = m_sigma=558.606 MeV, g_sigma=10.602, g_omega=12.881, g_rho=3.515, b_sigma=2.668, c_sigma=4.070, c_omega=4.352…
Fitted via ABOA to the binding energies and charge radii of the 12 anchor nuclei plus the 882-nucleus correction function; these values are the output of the paper's central fitting exercise.
NL5(Z) parameters (m_sigma, g_sigma, g_omega, g_rho, g2, g3) = m_sigma=515.823 MeV, g_sigma=10.359, g_omega=12.921, g_rho=4.382, g2=-9.787 fm^-1, g3=-26.395
Fitted via ABOA to the same anchor data; the density-dependence parameters g2 and g3 shift substantially relative to NL5(Y).
PC-Z point-coupling parameters (alpha, beta, gamma, delta) = See Table IX of the paper (values are correlated; see text)
Fitted via ABOA; the paper notes gamma_S/gamma_V and delta_S/delta_V are parametrically correlated with a substantial range of permissible values, so these parameter values are not tightly constrained.
Pairing strength scaling f_pi and f_nu = f_pi=1.877(N+Z)^-0.1072, f_nu=1.208exp(-0.674|N-Z|/(N+Z))
Empirical scalings from Ref. [34] used without refitting; the central binding energy results depend on pairing strength through open-shell nuclei.

assumptions (6)

domain assumption The ABOA correction function, built from 882 even-even experimental binding energies, accurately represents the global performance of the trial functional.
Sec. II and Sec. V use this correction function to define pseudodata; its accuracy for the new functionals is assumed from the earlier ABOA validation in Ref. [22].
domain assumption Total electron binding energies of Ref. [67] are accurate for all experimentally known isotopes, and their isotopic variation can be neglected.
Sec. IV shows the variation is below 1 keV for chains with data, but the absolute values themselves come from calculations by the same group and are used as exact inputs.
domain assumption The basis extrapolation procedure of Sec. VI of Ref. [20] gives infinite fermionic basis corrections accurate to 10-30 keV for all nuclei where it is used.
Sec. V and Supplemental Sec. III rely on this procedure; it is benchmarked only on selected nuclei, and for the PC class it does not converge even at NF=40.
domain assumption Mean-field RHB calculations with separable Gogny pairing are an adequate framework for the global binding energy fits.
Sec. II states the framework; the paper acknowledges beyond mean field effects are neglected and can vary by around 1 MeV between nuclei, especially in light nuclei.
domain assumption The charge radius expression Eq. (1), including neutron and spin-orbit terms, is valid for the anchor nuclei.
Sec. II uses the full expression for anchors but only the first three terms globally; the omitted neutron term still visibly affects differential radii in long isotopic chains.
domain assumption Differences between the Y and Z functionals are caused only by the new protocol ingredients, so they quantify the global calculation error of the Y-type fits.
Sec. VI E compares DD-MEY vs DD-MEZ and NL5(Y) vs NL5(Z) to extract delta_B_negl_rms ~0.8 MeV; this requires that parameter fits converge to the same solution apart from the protocol changes, which is assumed rather than proven.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Further steps towards next generation of covariant energy density functionals." pith.science (2026). https://pith.science/paper/C2ZRYR3F

@misc{pith2026250717082,
  author       = {Pith},
  title        = {Pith review of: Further steps towards next generation of covariant energy density functionals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/C2ZRYR3F}},
  note         = {Machine review of arXiv:2507.17082}
}

read the original abstract

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.

Figures

Figures reproduced from arXiv: 2507.17082 by the authors.

**Figure 2.** FIG. 2. (panel (a)). The convergence of calculated binding e [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 4.** FIG. 4. Infinite basis corrections to nuclear binding energi [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

Figures from the paper (8 more)

**Figure 3.** Figure 3: FIG. 3. Global maps of infinite basis corrections ∆ [PITH_FULL_IMAGE:figures/full_fig_p007_3.png]

**Figure 5.** Figure 5: FIG. 5. Global maps of infinite basis corrections ∆ [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: FIG. 6. The differences [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: and Table VIII. The NL5(Z) and NL5(Y) functionals perform comparably: there is only small improvement in global description of physical observables of interest on the transition from NL5(Y) to NL5(Z). 0 0 0 0 0 "! " 0 [PITH_FULL_IMAGE:figures/full_fig_p01…

**Figure 8.** Figure 8: FIG. 8. The same as Fig. 7 but for the PC-Z functional. Only [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

**Figure 9.** Figure 9: FIG. 9. The differences between nuclear binding energies cal [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

**Figure 1.** Figure 1: FIG. 1. The illustration of the iterative procedure for def [PITH_FULL_IMAGE:figures/full_fig_p018_1.png]

**Figure 2.** Figure 2: FIG. 2. The difference [in MeV] of infinite basis corrections [PITH_FULL_IMAGE:figures/full_fig_p019_2.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Isotope shift for total electron binding energy of atoms
physics.atom-ph 2025-07 conditional novelty 6.0 of 10

A systematic relativistic Hartree-Fock calculation produces tabulated field and mass isotope shift coefficients for total electron binding energy of atoms and ions up to Z=120, with a simple power-law interpolation ac...

Reference graph

Works this paper leans on

98 extracted references · 63 canonical work pages · cited by 1 Pith paper

[1]

Mittig, A

W. Mittig, A. L´ epine-Szily, and N. A. Orr, Annu. Rev. Nucl. Sci. 47, 27 (2003)

2003
[2]

Erler, N

J. Erler, N. Birge, M. Kortelainen, W. Nazarewicz, E. Olsen, A. M. Perhac, and M. Stoitsov, Nature 486, 509 (2012)

2012
[3]

S. E. Agbemava, A. V. Afanasjev, D. Ray, and P. Ring, Phys. Rev. C 89, 054320 (2014)

2014
[4]

Dilling, K

J. Dilling, K. Blaum, M. Brodeur, and S. Eliseev, Annu. Rev. Nucl. Sci. 68, 45 (2018)

2018
[5]

for the deﬁnition of ∆ BF ∞(Z, N) in global calculation since it is substantially less numerically and memory de- manding. At the same time, this procedure reproduces fully convergent NF = 40 results obtained with the DD- MEZ and NL5(Z) CEDFs for a testing set of nuclei scat- tered more or less equally across experimentally known nuclear landscape with gl...
[6]

J. J. Cowan, C. Sneden, J. E. Lawler, A. Aprahamian, M. Wiescher, K. Langanke, G. Mart ´ ınez-Pinedo, and F.-K. Thielemann, Rev. Mod. Phys. 93, 015002 (2021)

2021
[7]

Chamel and P

N. Chamel and P. Haensel, Living Rev. Relativity 11, 10 (2008)

2008
[8]

R. Lau, M. Beard, S. S. Gupta, A. V. Afanasjev, E. F. Brown, A. Deibel, L. R. Gasques, G. W. Hitt, W. R. Hix, 5 In this paper, the Dirac W oods-Saxon basis is used and the nu- merical errors in the calculations of binding energies are s ubstan- tially reduced as compared with those of the global calculat ions presented in Refs. [80, 82, 90] which also emp...

2018

Show all 98 references

[9]

Bender, P.-H

M. Bender, P.-H. Heenen, and P.-G. Reinhard, Rev. Mod. Phys. 75, 121 (2003)

2003
[10]

Arnould, S

M. Arnould, S. Goriely, and K. Takahashi, Phys. Rep. 450, 97 (2007)

2007
[11]

Tondeur, S

F. Tondeur, S. Goriely, J. M. Pearson, and M. Onsi, Phys. Rev. C 62, 024308 (2000)

2000
[12]

Samyn, S

M. Samyn, S. Goriely, P.-H. Heenen, J. M. Pearson, and F. Tondeur, Nucl. Phys. A 700, 142 (2002)

2002
[13]

Goriely, N

S. Goriely, N. Chamel, and J. M. Pearson, Phys. Rev. C 88, 061302 (2013)

2013
[14]

Baldo, L

M. Baldo, L. M. Robledo, P. Schuck, and X. Vi˜ nas, Phys. Rev. C 87, 064305 (2013)

2013
[15]

Vretenar, A

D. Vretenar, A. V. Afanasjev, G. A. Lalazissis, and P. Ring, Phys. Rep. 409, 101 (2005)

2005
[16]

Kortelainen, T

M. Kortelainen, T. Lesinski, J. Mor´ e, W. Nazarewicz, J. Sarich, N. Schunck, M. V. Stoitsov, and S. Wild, Phys. Rev. C 82, 024313 (2010)

2010
[17]

Kortelainen, J

M. Kortelainen, J. McDonnell, W. Nazarewicz, P.-G. Reinhard, J. Sarich, N. Schunck, M. V. Stoitsov, and S. M. Wild, Phys. Rev. C 85, 024304 (2012)

2012
[18]

Kortelainen, J

M. Kortelainen, J. McDonnell, W. Nazarewicz, E. Olsen, P.-G. Reinhard, J. Sarich, N. Schunck, S. M. Wild, D. Davesne, J. Erler, and A. Pastore, Phys. Rev. C 89, 054314 (2014)

2014
[20]

Note that to our knowl- edge this is the ﬁrst time when all terms of Eq

for further discussion). Note that to our knowl- edge this is the ﬁrst time when all terms of Eq. (1) are used in the ﬁtting protocol of CEDFs: early ﬁts carried out by diﬀerent groups are restricted to the ﬁrst two terms of this equation since they dominate Eq. (1) 1. In the ...

1904
[21]

M¨ oller, A

P. M¨ oller, A. J. Sierk, T. Ichikawa, and H. Sagawa, At. Data and Nucl. Data Tables 109, 1 (2016)

2016
[22]

Taninah and A

A. Taninah and A. V. Afanasjev, Phys. Rev. C 107, L041301 (2023)

2023
[23]

Taninah, S

A. Taninah, S. E. Agbemava, A. V. Afanasjev, and P. Ring, Phys. Lett. B 800, 135065 (2020)

2020
[24]

C. J. Horowitz and J. Piekarewicz, Phys. Rev. C 86, 045503 (2012)

2012
[25]

Taninah, B

A. Taninah, B. Osei, A. V. Afanasjev, U. C. Perera, and S. Teeti, Phys. Rev. C 109, 024321 (2024)

2024
[26]

Pe˜ na-Arteaga, S

D. Pe˜ na-Arteaga, S. Goriely, and N. Chamel, Eur. Phys. J. A 52, 320 (2016). 15

2016
[27]

Naito, T

T. Naito, T. Oishi, H. Sagawa, and Z. Wang, Phys. Rev. C 107, 054307 (2022)

2022
[28]

M. Wang, W. J. Huang, F. G. Kondev, G. Audi, and S. Naimi, Chin. Phys. C45, 030003 (2021)

2021
[29]

Angeli and K

I. Angeli and K. P. Marinova, At. Data Nucl. Data Tables 99, 69 (2013)

2013
[30]

Kurasawa and T

H. Kurasawa and T. Suzuki, Prog. Th. Exp. Phys. 2019, 113D01 (2019)

2019
[31]

Reinhard and W

P.-G. Reinhard and W. Nazarewicz, Phys. Rev. C 103, 054310 (2021)

2021
[32]

B¨ urvenich, D

T. B¨ urvenich, D. G. Madland, J. A. Maruhn, and P.-G. Reinhard, Phys. Rev. C 65, 044308 (2002)

2002
[33]

Y. Tian, Z. Y. Ma, and P. Ring, Phys. Lett. B 676, 44 (2009)

2009
[34]

Teeti and A

S. Teeti and A. V. Afanasjev, Phys. Rev. C 103, 034310 (2021)

2021
[35]

Boguta and R

J. Boguta and R. Bodmer, Nucl. Phys. A292, 413 (1977)

1977
[36]

Typel and H

S. Typel and H. H. Wolter, Nucl. Phys. A656, 331 (1999)

1999
[37]

Saˆ ad, J

B. Saˆ ad, J. Mult. Eng. Sc. Tech 3, 5012 (2016)

2016
[38]

Lunney, J

D. Lunney, J. M. Pearson, and C. Thibault, Rev. Mod. Phys. 75, 1021 (2003)

2003
[39]

Rufa, P.-G

M. Rufa, P.-G. Reinhard, J. A. Maruhn, W. Greiner, and M. R. Strayer, Phys. Rev. C 38, 390 (1988)

1988
[40]

Full convergence is reached at N ′ F when ∆ B(N ′ F ) = ∆B(N ′ F + 2) = 0

− B(NF ) as a function of NF for the 170Gd, 240Pu and 290Lv nuclei. Full convergence is reached at N ′ F when ∆ B(N ′ F ) = ∆B(N ′ F + 2) = 0. the consequence of the fact that the expansion in har- monic oscillator basis states convergences very slowly for zero-range forces (s...
[41]

Bender, K

M. Bender, K. Rutz, P.-G. Reinhard, and J. A. Maruhn, Eur. Phys. J. A 8, 59 (2000)

2000
[42]

Hilaire, J.-F

S. Hilaire, J.-F. Berger, M. Girod, W. Satula, and P. Schuck, Phys. Lett. B 531, 61 (2002)

2002
[43]

Roca-Maza, X

X. Roca-Maza, X. Vi˜ nas, M. Centelles, P. Ring, and P. Schuck, Phys. Rev. C 84, 054309 (2011)

2011
[44]

W. Long, J. Meng, N. V. Giai, and S.-G. Zhou, Phys. Rev. C 69, 034319 (2004)

2004
[45]

G. A. Lalazissis, J. K¨ onig, and P. Ring, Phys. Rev. C 55, 540 (1997)

1997
[46]

G. A. Lalazissis, S. Karatzikos, R. Fossion, D. P. Arteaga, A. V. Afanasjev, and P. Ring, Phys. Lett. B671, 36 (2009)

2009
[47]

Nikˇ si´ c, D

T. Nikˇ si´ c, D. Vretenar, P. Finelli, and P. Ring, Phys. Rev. C 66, 024306 (2002)

2002
[48]

B. A. Nikolaus, T. Hoch, and D. G. Madland, Phys. Rev. C 46, 1757 (1992)

1992
[49]

Kumar, S

B. Kumar, S. K. Singh, B. K. Agrawal, and S. K. Patra, Nucl. Phys. A 966, 197 (2017)

2017
[50]

P. W. Zhao, Z. P. Li, J. M. Yao, and J. Meng, Phys. Rev. C 82, 054319 (2010)

2010
[51]

B. Wei, Q. Zhao, Z.-H. Wang, J. Geng, B.-Y. Sun, Y.-F. Niu, and W.-H. Long, Chin. Phys. C 44, 074107 (2020)

2020
[52]

G. A. Lalazissis, T. Nikˇ si´ c, D. Vretenar, and P. Ring, Phys. Rev. C 71, 024312 (2005)

2005
[53]

Beiner, H

M. Beiner, H. Flocard, N. van Giai, and P. Quentin, Nucl. Phys. A 238, 29 (1975)

1975
[54]

Kl¨ upfel, P.-G

P. Kl¨ upfel, P.-G. Reinhard, T. J. B¨ urvenich, and J. A. Maruhn, Phys. Rev. C 79, 034310 (2009)

2009
[55]

B. K. Agrawal, A. Sulaksono, and P.-G. Reinhard, Nucl. Phys. A 882, 1 (2012)

2012
[56]

Sharma, Phys

M. Sharma, Phys. Lett. B 666, 140 (2008)

2008
[57]

Z. X. Liu, Y. H. Lam, N. Lu, and P. Ring, Phys. Lett. B 842, 137946 (2023)

2023
[58]

Gogny, in: G

D. Gogny, in: G. Ripka, M. Porneuf (Eds.), Nuclear Self- Consistent Fields, Proc. Internat. Conf. held at the Cen- ter for Theoretical Physics, Trieste, Italy, 1975, North- Holland, Amsterdam , 333 (1975)

1975
[59]

J. F. Berger, M. Girod, and D. Gogny, Nucl. Phys. A428, 23c (1984)

1984
[60]

Chabanat, P

E. Chabanat, P. Bonche, P. Haensel, J. Meyer, and R. Schaeﬀer, Nucl. Phys. A 635, 231 (1998)

1998
[61]

Bartel, P

J. Bartel, P. Quentin, M. Brack, C. Guet, and H. B. H ˚ akansson, Nucl. Phys. A635, 231 (1998)

1998
[62]

Navarro P´ erez, N

R. Navarro P´ erez, N. Schunck, A. Dyhdalo, R. J. Furn- stahl, and S. K. Bogner, Phys. Rev. C 97, 054304 (2018)

2018
[63]

M. Liu, N. Wang, Y. Deng, and X. Wu, Phys. Rev. C 84, 014333 (2011)

2011
[64]

N. Wang, M. Liu, X. Wu, and J. Meng, Phys. Lett. B 734, 215 (2014)

2014
[65]

M¨ oller, J

P. M¨ oller, J. R. Nix, W. D. Myers, and W. J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995)

1995
[66]

N. Wang, M. Liu, and X. Wu, Phys. Rev. C 81, 044322 (2010)

2010
[67]

Total electron binding energies are diﬀerent for diﬀer- ent isotopes due to the diﬀerence in nuclear charge ra- dius (ﬁeld shift) and nuclear mass (mass shift)

are carried out in the present paper to cover this gap in our knowledge. Total electron binding energies are diﬀerent for diﬀer- ent isotopes due to the diﬀerence in nuclear charge ra- dius (ﬁeld shift) and nuclear mass (mass shift). It is well known that for heavy atoms ﬁeld ...
[68]

N. Wang, Z. Liang, M. Liu, and X. Wu, Phys. Rev. C 82, 044304 (2010)

2010
[69]

V. V. Flambaum and J. S. M. Ginges, Phys. Rev. A 73, 052115 (2005)

2005
[70]

Huang, M

K.-N. Huang, M. Aoyagi, M. H. Chen, B. Crasemann, and H. Mark, At. Data and Nucl. Data Tables 18, 243 (1976)

1976
[71]

G. C. Rodrigues, P. Indelicato, J. P. Santos, P. Patt´ e, and F. Parente, Atom. Data Nuc. Data Tables 86, 117 (2004)

2004
[72]

V. A. Dzuba, V. V. Flambaum, and A. V. Afanasjev, Phys. Rev. A 110, 052810 (2024)

2024
[73]

V. A. Dzuba, V. V. Flambaum, and M. S. Safronova, Phys. Rev. A 73, 022112 (2006)

2006
[74]

I. I. Sobelman, Atomic Spectra and Radiative Transitions (Springer-Verlag Heidelberg New York, 1979)

1979
[75]

V. A. Dzuba, J. C. Berengut, C. Harabati, and V. V. Flambaum, Phys. Rev. A 95, 012503 (2017)

2017
[76]

B. G. C. Lackenby, V. A. Dzuba, and V. V. Flambaum, Phys. Rev. A 98, 022518 (2018)

2018
[77]

B. G. C. Lackenby, V. A. Dzuba, and V. V. Flambaum, Phys. Rev. A 99, 042509 (2019)

2019
[78]

B. G. C. Lackenby, V. A. Dzuba, and V. V. Flambaum, Phys. Rev. A 101, 012514 (2020)

2020
[79]

Goriely, M

S. Goriely, M. Samyn, P.-H. Heenen, J. M. Pearson, and F. Tondeur, Phys. Rev. C 66, 024326 (2002)

2002
[80]

Taninah, S

A. Taninah, S. E. Agbemava, and A. V. Afanasjev, Phys. Rev. C 102, 054330 (2020)

2020
[81]

S. E. Agbemava, A. V. Afanasjev, T. Nakatsukasa, and P. Ring, Phys. Rev. C 92, 054310 (2015)

2015
[82]

S. A. Coon, M. I. Avetian, M. K. G. Kruse, U. van Kolck, P. Maris, and J. P. Vary, Phys. Rev. C 86, 054002 (2012)

2012
[83]

M. Wang, G. Audi, F. G. Kondev, W. Huang, S. Naimi, and X. Xu, Chin. Phys. C 41, 030003 (2017)

2017
[84]

Dutra, O

M. Dutra, O. Lourenco, S. S. Avancini, B. V. Carlson, A. Delﬁno, D. P. Menezes, C. Providencia, S. Typel, and J. R. Stone, Phys. Rev. C 90, 055203 (2014)

2014
[85]

Y. L. Yang, Y. K. Wang, P. W. Zhao, and Z. P. Li, Phys. Rev. C 104, 054312 (2021)

2021
[86]

Y. Fu, H. Mei, J. Xiang, Z. P. Li, J. M. Yao, and J. Meng, Phys. Rev. C 87, 054305 (2013)

2013
[87]

K. Q. Lu, Z. X. Li, Z. P. Li, J. M. Yao, and J. Meng, Phys. Rev. C 91, 027304 (2015)

2015
[88]

Dutra, O

M. Dutra, O. Lourenco, J. S. S. Martins, A. Delﬁno, J. R. Stone, and P. D. Stevenson, Phys. Rev. C 85, 035201 (2012). 16

2012
[89]

Reinhard and B

P.-G. Reinhard and B. K. Agrawal, Int. Jour. Mod. Phys. E20, 1379 (2011)

2011
[90]

Goriely, N

S. Goriely, N. Chamel, and J. M. Pearson, Phys. Rev. C 82, 035804 (2010)

2010
[91]

Gonzalez-Boquera, M

C. Gonzalez-Boquera, M. Centelles, X. Vinas, and L. M. Robledo, Phys. Lett. 779, 195 (2018)

2018
[92]

G. A. Lalazissis, S. Raman, and P. Ring, At. Data Nucl. Data Table 71, 1 (1999)

1999
[93]

L. Geng, H. Toki, and J. Meng, Prog. Theor. Phys. 113, 785 (2005)

2005
[94]

S. E. Agbemava, A. V. Afanasjev, and A. Taninah, Phys. Rev. C 99, 014318 (2019). . 17 Supplemental material I. OVER VIEW Supplemental material provides additional information to the manuscript. Field isotopic shifts to total electron binding energies of the atoms of superheavy...

2019
[95]

Q. S. Zhang, Z. M. Niu, Z. P. Li, J. M. Yao, and J. Meng, Frontiers of Physics 9, 529 (2014)

2014
[96]

Goriely, S

S. Goriely, S. Hilaire, M. Girod, and S. P´ eru, Phys. Rev. Lett. 102, 242501 (2009)

2009
[97]

Hilaire and M

S. Hilaire and M. Girod, Eur. Phys. J. 33, 237 (2007)

2007
[98]

Zhang, M.-K

K. Zhang, M.-K. Cheoun, Y.-B. Choi, P. S. Chong, J. Dong, Z. Dong, X. Du, L. Geng, E. Ha, X.-T. He, C. Heo, M. C. Ho, E. J. In, S. Kim, Y. Kim, C.-H. Lee, J. Lee, H. Li, Z. Li, T. Luo, J. Meng, M.-H. Munb, Z. Niu, C. Pan, P. Papakonstantinou, X. Shang, C. Shen, G. Shen, W. Sun...

2022
[2023]

[22] which allowed global ﬁts of CEDFs at a reasonable computational cost (see Ref

It is only the advent of the anchor based optimiza- tion approach (further ABOA) in Ref. [22] which allowed global ﬁts of CEDFs at a reasonable computational cost (see Ref. [20]). In this approach, the optimization of the parameters of EDFs is carried out for a selected set of...

2025 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Mittig, A

W. Mittig, A. L´ epine-Szily, and N. A. Orr, Annu. Rev. Nucl. Sci. 47, 27 (2003)

2003

[2] [2]

Erler, N

J. Erler, N. Birge, M. Kortelainen, W. Nazarewicz, E. Olsen, A. M. Perhac, and M. Stoitsov, Nature 486, 509 (2012)

2012

[3] [3]

S. E. Agbemava, A. V. Afanasjev, D. Ray, and P. Ring, Phys. Rev. C 89, 054320 (2014)

2014

[4] [4]

Dilling, K

J. Dilling, K. Blaum, M. Brodeur, and S. Eliseev, Annu. Rev. Nucl. Sci. 68, 45 (2018)

2018

[5] [5]

for the deﬁnition of ∆ BF ∞(Z, N) in global calculation since it is substantially less numerically and memory de- manding. At the same time, this procedure reproduces fully convergent NF = 40 results obtained with the DD- MEZ and NL5(Z) CEDFs for a testing set of nuclei scat- tered more or less equally across experimentally known nuclear landscape with gl...

[6] [6]

J. J. Cowan, C. Sneden, J. E. Lawler, A. Aprahamian, M. Wiescher, K. Langanke, G. Mart ´ ınez-Pinedo, and F.-K. Thielemann, Rev. Mod. Phys. 93, 015002 (2021)

2021

[7] [7]

Chamel and P

N. Chamel and P. Haensel, Living Rev. Relativity 11, 10 (2008)

2008

[8] [8]

R. Lau, M. Beard, S. S. Gupta, A. V. Afanasjev, E. F. Brown, A. Deibel, L. R. Gasques, G. W. Hitt, W. R. Hix, 5 In this paper, the Dirac W oods-Saxon basis is used and the nu- merical errors in the calculations of binding energies are s ubstan- tially reduced as compared with those of the global calculat ions presented in Refs. [80, 82, 90] which also emp...

2018