Bayesian Inference of the Symmetry Energy and the Neutron Skin in $^{48}$Ca and $^{208}$Pb from CREX and PREX-2
Bibliographic record
Abstract
Using the recent model-independent determination of the charge-weak form factor difference $ΔF_{\rm CW}$ in $^{48}$Ca and $^{208}$Pb by the CREX and PREX-2 collaborations together with some well-determined properties of doubly magic nuclei, we perform Bayesian inference of the symmetry energy $E_{\rm sym}(ρ)$ and the neutron skin thickness $Δr_{\rm np}$ of $^{48}$Ca and $^{208}$Pb within the Skyrme energy density functional (EDF). We find the inferred $E_{\rm sym}(ρ)$ and $Δr_{\rm np}$ separately from CREX and PREX-2 are compatible with each other at $90\%$ C.L., although they are inconsistent at $68.3\%$ C.L. with CREX (PREX-2) favoring a very soft (stiff) $E_{\rm sym}(ρ)$ and rather small (large) $Δr_{\rm np}$. By combining the CREX and PREX-2 data, we obtain a soft symmetry energy around saturation density $ρ_0$ and thinner $Δr_{\rm np}$ of $^{48}$Ca and $^{208}$Pb, which are found to be closer to the corresponding results from CREX alone, implying the PREX-2 is less effective to constrain the $E_{\rm sym}(ρ)$ and $Δr_{\rm np}$ due to its lower precision of $ΔF_{\rm CW}$. Furthermore, we find the Skyrme EDF results inferred by combining the CREX and PREX-2 data nicely agree with the measured dipole polarizabilities $α_D$ in $^{48}$Ca and $^{208}$Pb as well as the neutron matter equation of state from microscopic calculations. The implications of the inferred soft $E_{\rm sym}(ρ)$ around $ρ_0$ are discussed.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".