Experimental Nuclear Structure Data Overview

• Experimental nuclear structure data are quantitative observables detailing properties like binding energies, charge radii, and decay modes.
• They are systematically compiled with precise uncertainties using state-of-the-art methods such as Penning traps, electron scattering, and gamma spectroscopy.
• Unified databases and toolkits enable large-scale comparisons and benchmarking between experimental results and theoretical nuclear models.

Experimental nuclear structure data encompass quantitative observables that characterize the basic properties of nuclei, including binding energies, charge radii, neutron-skin thicknesses, incompressibilities, single-particle levels (including hypernuclei), electromagnetic response functions, and decay properties such as β-delayed neutron emission. The systematic measurement, compilation, and dissemination of these variables underpin the global experimental and theoretical program in nuclear structure, meta-analyses of nuclear matter, and applications from astrophysics to reactor science. Recent developments include comprehensive toolkits for data access and unified online databases, facilitating large-scale comparison, benchmarking, and theoretical constraint across isotopic and modal domains (Margueron et al., 25 Jun 2025).

1. Core Classes of Experimental Nuclear Structure Data

Experimental nuclear structure data are organized into several primary observable categories, reflecting underlying nuclear degrees of freedom and operational measurement approaches:

• Nuclear Masses (Ground-State Binding Energies): Tabulated in the Atomic Mass Evaluation (AME), coverage includes ≈2550 nuclides for $Z=1$–$118$, with uncertainties ranging down to $\sim10^{-4}$ MeV for stable nuclei. These are the foundation for evaluating separation energies and trends in nuclear binding.
• Charge Radii: Compiled primarily through muonic atom spectroscopy, electron scattering, and isotope shift measurements; the Angeli–Marinova compilation (2013) is the reference for $\sim$800 isotopes. Uncertainties typically fall in the $0.005$–$0.02$ fm range.
• Neutron-Skin Thickness $(\Delta R_{np})$: Directly probed via hadronic, leptonic, and parity-violating scattering experiments, e.g., antiprotonic atoms, PVES, and hadron scattering. In $^{48}$Ca and $^{208}$Pb, multiple independent measurements yield $\Delta R_{np}$ to a typical precision of $0.02$–$0.06$ fm.
• Isoscalar Giant Monopole Resonance (ISGMR) Centroids: The centroid energies of the ISGMR (compression mode) are inferred from inelastic $\alpha$, $^{16}$O, or heavy-ion scattering, constraining the nuclear incompressibility modulus. Uncertainties for extracted $E_{GMR}$ are $\sim0.1$–$0.3$ MeV.
• Hypernuclear Spectra: Single- and double-$\Lambda$ as well as $\Xi^-$ hypernuclear levels are derived from emulsion, spectrometer, and $\gamma$-ray experiments; uncertainties in $B_\Lambda$, $B_\Xi$ range $0.1$–$0.3$ MeV.
• Electromagnetic Transition Strengths and Deformations: $\gamma$-ray spectroscopy elucidates excitation spectra, reduced transition probabilities $B(E2)$, and mass and charge deformation parameters.
• Beta-Decay and Beta-Delayed Neutron Emission: Databases provide $T_{1/2}$ and probability $P_{xn}$ (branching ratios for $x$-neutron emission) for $\sim$300 neutron-rich precursors, with evaluated group parameters and aggregate delayed neutron yields for applications.
• Photon Strength Functions: Photonuclear, neutron capture, and Oslo-method data quantify dipole $E1$, $M1$ photon strength functions, crucial for reaction network calculations and astrophysical rates (Goriely et al., 2019).

Each class of data possesses a specific experimental uncertainty profile, original source standards, and standardized numerical formats enabling direct comparison and code-level integration (e.g. numpy arrays, pandas DataFrames) (Margueron et al., 25 Jun 2025).

2. Reference Datasets, Uncertainties, and Computational Access

Systematic compilations have standardized raw and evaluated observables, with precision and methodology tailored to each class:

Observable	Reference Compilation / Source	Typical Uncertainty
Binding Energy	AME 2020, W. J. Huang et al.	0.0001–0.1 MeV
Charge Radius	Angeli–Marinova 2013	0.005–0.02 fm
$\Delta R_{np}$	Lombardi 2016 / Schupp 2024	0.02–0.06 fm
ISGMR Centroid	Garg et al. 2018, Li et al. 2010	0.1–0.3 MeV
$B_\Lambda$	Gal–Hungerford–Millener 2016, Ahn 2013, Nakazawa 2015	0.1–0.3 MeV
$T_{1/2}, P_{xn}$	IAEA Reference Database for β-delayed neutron emission	1–10% (P₁ₙ), up to 80% for rare branches
Photon Strength	IAEA PSF Database, EXFOR, Oslo, NRF	5–40% (method– and $E_\gamma$–dependent)

Specialized toolkits such as nucleardatapy (nuda) provide programmatic access, allowing users to retrieve, filter, and process data directly within Python (e.g., selection of specific $A$, $Z$, propagating uncertainties), with each dataset linked to its precise source reference and documented format (Margueron et al., 25 Jun 2025).

3. Key Definitions and Structural Formulas

Experimental nuclear structure data rest on rigorous operational definitions:

• Neutron-Skin Thickness: $\Delta R_{np} = R_n - R_p$
• Isospin Asymmetry: $\delta = \frac{\rho_n - \rho_p}{\rho_n + \rho_p}$
• Separation Energies: $S_{2n}(Z,N) = BE(Z,N) - BE(Z,N-2)$ $S_{2p}(Z,N) = BE(Z,N) - BE(Z-2,N)$
• Hypernuclear Bond Energy: $$\Delta B_{\Lambda\Lambda} = B_{\Lambda\Lambda}(^{A}_{\Lambda\Lambda}Z) - 2\,B_{\Lambda}(^{A-1}_{\Lambda}Z)$$

For photon strength functions, the standard relation is:

$$f_{XL}(E_\gamma) = \frac{\sigma_{XL}(E_\gamma)}{g_J (\pi\hbar c)^2 E_\gamma^{2L-1}}$$

and transmission coefficients:

$$T_{XL}(E_\gamma) = 2\pi\,E_\gamma^{2L+1} f_{XL}(E_\gamma)$$

Delayed neutron data employ group representation:

$\nu_d = \sum_{i} Y_i P_{n,i}$

where $Y_i$ is the cumulative fission yield and $P_{n,i}$ the emission probability.

4. Representative Results and Systematic Trends

Standardized meta-analyses and large-scale comparisons reveal key trends across isotopic chains and observable classes:

Isotope	BE (MeV)	$R_{ch}$ (fm)	$\Delta R_{np}$ (fm)	$E_{GMR}$ (MeV)	$B_\Lambda$ (MeV)
$^{48}$Ca	416.0(0.01)	3.477(0.011)	0.12(0.03)	18.1(0.2)	9.0(0.2)
$^{208}$Pb	1636.4(0.002)	5.501(0.009)	0.15(0.02)	13.5(0.1)	26.3(0.1)

Trends:

• $BE/A$ saturates at 8–9 MeV for heavy nuclei.
• $R_{ch}$ scales as $A^{1/3}$ with minor corrections from isospin asymmetry.
• $\Delta R_{np}$ increases monotonically with neutron excess $\delta$.
• $E_{GMR}$ decreases with rising $A$ (indicative of softer incompressibility in heavier nuclei).
• $B_\Lambda$ rises with $A$ and saturates for heavy hypernuclei.

These patterns are directly and systematically accessible for all experimentally surveyed nuclides within unified toolkits and can be plotted or statistically compared across the nuclear chart.

5. Experimental Methods and Uncertainty Characterization

Measurement protocols and uncertainty quantification are modality-specific:

• Masses: High-precision Penning traps, storage rings, and time-of-flight spectrometry feed AME tables; dominant uncertainties arise from calibration standards and systematic drift, typically $<10$ keV for stable or near-stable isotopes.
• Charge Radii: Muonic-atom and isotope-shift methods; uncertainties are dominated by atomic physics corrections and statistical errors in electron scattering.
• Neutron Skins: Combined analyses across hadronic, electromagnetic, and antiprotonic probes; model dependence (e.g., reaction models for hadronic scattering) is a primary uncertainty contributor.
• ISGMR: Multipole decomposition in (α,α′) or (O,O′) inelastic scattering; background subtraction and continuum fitting are main sources of uncertainty.
• Hypernuclear Energies: Precise $\gamma$-ray or missing-mass spectroscopy; model discrimination between spin–orbit partners limited by available resolution.
• Photon Strength Functions: NRF, Oslo, $(n,\gamma)$, and proton capture each produce characteristic systematics; summarized uncertainties range 5% (NRF) to >40% (DRC in nuclei with few resonances).
• Beta-Delayed Neutron Emission: Ensemble-averaged values harness multiple independent methods (neutron counting, ion recoil detection, time-of-flight), with careful cross-normalization to standards and propagation of both statistical and systematics; recommended values tabulated with explicit $\pm\sigma$ and, for group parameters, covariance matrices.

Each dataset in nucleardatapy or the IAEA databases includes integrated source attribution and experimental error tracking to allow robust uncertainty quantification (Dimitriou et al., 2021).

6. Applications, Visualization, and Meta-Analysis

The centralization and standardization of nuclear structure data enable:

• Comprehensive Meta-Analyses: Direct comparison between experimental datasets and predictions from ab initio, density-functional, and meta-model frameworks; e.g., benchmarking pressure at $2\rho_{sat}$ as constrained by nuclear physics and astrophysical data (Margueron et al., 25 Jun 2025).
• Theory–Experiment Confrontation: Key experimental observables (mass trends, $\Delta R_{np}$, ISGMR centroids, $B(E2)$ strengths) are directly comparable to theoretical outputs, supporting parameter optimization and validation.
• Visualization: Collected data can be displayed in multi-panel figures (e.g., BE vs. $A$, $R_{ch}$ vs. $A^{1/3}$, $\Delta R_{np}$ vs. $\delta$, $E_{GMR}$ vs. $A$, $B_\Lambda$ vs. $A$), revealing shell effects and systematic structure.
• Astrophysical Constraints: $P_{xn}$, $T_{1/2}$, and photon strength functions inform r-process nucleosynthesis and neutron-star EOS modeling, with meta-analysis tools linking laboratory observables to cosmic conditions.

Public toolchains, by maintaining original reference citations, full uncertainty propagation, and cross-referring experimental methodologies, support transparent and reproducible large-scale nuclear structure analyses, including user-driven updates and community extensions (Margueron et al., 25 Jun 2025, Goriely et al., 2019, Dimitriou et al., 2021).

7. Outlook and Future Directions

The continued consolidation and augmentation of experimental nuclear structure data are essential for advancing nuclear science, particularly:

• Expansion to Drip-Line and Hypernuclear Studies: As facilities probe increasingly exotic isotopes and multi-strange systems, systematic incorporation of new measurements (e.g., charge radii from laser spectroscopy, direct $\Delta R_{np}$ from parity-violating electron scattering, high-resolution hypernuclear levels) is necessary.
• Integration with Theoretical and Astrophysical Observations: Unified datasets enable cross-fertilization, such as combining gravitational-wave measurements of neutron-star mergers with laboratory constraints on symmetry energy and incompressibility.
• Community-Driven Tools: Frameworks like nucleardatapy are developed as continuously updated, open platforms, supporting direct data contributions, workflow automation, and novel meta-analytic methodologies.
• Advanced Uncertainty Quantification: Ongoing efforts focus on quantifying and reducing experimental and model-dependent uncertainties, with systematic error propagation into downstream applications.

The structure and accessibility of contemporary nuclear data resources establish a foundation for predictive, cross-disciplinary nuclear science and for the rigorous comparison of theory and experiment in the quest for a unified description of atomic nuclei.