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DOE OSTI2025

Quantifying uncertainty in machine learning for nuclear binding energy

Techniques from artificial intelligence and machine learning are increasingly employed in nuclear theory; however, the uncertainties that arise from the complex parameter manifold encoded by the neural networks are often overlooked. Epistemic uncertainties arising from training the same network multiple times for an ensemble of initial weight sets offer a first insight into the confidence of machine learning predictions, but they often come with a high computational cost. Instead, we apply a single-model uncertainty quantification method called Δ-UQ that gives epistemic uncertainties with one-time training. Here, we demonstrate our approach on a two-feature model of nuclear binding energies per nucleon with proton and neutron number pairs as inputs. We show that Δ-UQ can produce reliable and self-consistent epistemic uncertainty estimates and can be used to assess the degree of confidence in predictions made with deep neural networks.

Huang, Mengyao [Lawrence Livermore National Labora↗

DOE OSTI2025

Criticality analysis of nuclear binding energy neural networks

Machine learning methods, in particular deep learning methods such as artificial neural networks (ANNs) with many layers, have become widespread and useful tools in nuclear physics. However, these ANNs are typically treated as ‘black boxes’, with their architecture (width, depth, and weight/bias initialization) and the training algorithm and parameters chosen empirically by optimizing learning based on limited exploration. We test a non-empirical approach to understanding and optimizing nuclear physics ANNs by adapting a criticality analysis based on renormalization group flows in terms of the hyperparameters for weight/bias initialization, training rates, and the ratio of depth to width. This treatment utilizes the statistical properties of neural network initialization to find a generating functional for network outputs at any layer, allowing for a path integral formulation of the ANN outputs as a Euclidean statistical field theory. We use a prototypical example to test the applicability of this approach: a simple ANN for nuclear binding energies. We find that with training using a stochastic gradient descent optimizer, the predicted criticality behavior is realized, and optimal performance is found with critical tuning. However, the use of an adaptive learning algorithm leads to somewhat superior results without concern for tuning and thus obscures the analysis. Nevertheless, the criticality analysis offers a way to look within the black box of ANNs, which is a first step towards potential improvements in network performance beyond using adaptive optimizers.

artificial neural network↗

DOE OSTI2025

Identification of Prompt Proton Emission in $N = Z - 1$ 61 Ga: Isospin Symmetry at the Limit of Nuclear Binding

Excited states in the proton drip line nucleus 61 Ga were populated via the fusion-evaporation reaction 24 Mg ⁢( 40 Ca, 𝑝⁢2⁢𝑛)⁢ 61 Ga. The experimental setup at Argonne National Laboratory comprised a novel combination of the Gammasphere array with two CD-shaped double-sided Si-strip detectors inside the Microball CsI(Tl) charged-particle detection array, as well as the Neutron-Shell liquid scintillators and the Fragment Mass Analyzer. Owing to the setup’s unprecedented in-beam proton spectroscopy and tracking capabilities, a coincidence between a 957.6(5)-keV 𝛾 ray and a 1.876(24)-MeV proton line was observed, which identifies the quasibound proton 𝜋⁢𝑔 9/2 single-particle state in 61 Ga at 𝐸 𝑥 = 2150⁢(34) keV. This probes isospin symmetry at the limit of nuclear binding by providing a unique challenge for the shell-model interpretation of mirror nuclei beyond doubly magic 56 Ni .

Hrabar, Yuliia [Lund Univ. (Sweden)] (ORCID:000000↗

DOE OSTI2025

Enhanced Nuclear Binding near the Proton Drip Line Opens Possible Bypass of the 64 Ge Rapid Proton Capture Process Waiting Point

Abstract We performed astrophysics model calculations with updated nuclear data to identify a possible bypass of the 64 Ge waiting point, a defining feature of the rapid proton capture (rp) process that powers type I X-ray bursts on accreting neutron stars. We find that the rp-process flow through the 64 Ge bypass could be up to 36% for astrophysically relevant conditions. Our results call for new studies of 65 Se, including the nuclear mass, β -delayed proton emission branching, and nuclear structure as it pertains to the 64 As( p , γ ) reaction rate at X-ray burst temperatures.

Nuclear astrophysics↗

DOE OSTI2025

Discovery of new isotopes in the fragmentation of 82 Se and insights into their production

The production cross sections of neutron-rich nuclei for elements just above 60 Ca were measured at the Facility for Rare Isotope Beams (FRIB). Four previously unobserved isotopes ( 63 Sc, 65,66 Ti, and 68 V) were produced, separated, and identified for the first time using the Advanced Rare Isotope Separator (ARIS). One event was found to be consistent with 61 Ca . The new isotopes were created through the interaction of an 82 Se beam with a carbon target at an energy of 228 MeV/𝑢 and a primary beam current of 1.07 p⁢µ⁢A. The event-by-event particle identification of the mass number (𝐴), atomic number (𝑍), and ionic charge state (𝑞) for the reaction products was achieved by combining measurements of energy loss, time of flight, magnetic rigidity, and total kinetic energy. This successful search for new isotopes, conducted at the beginning of FRIB's third year of operation, highlights the facility's discovery potential, which will continue to grow as the beam current increases. The production cross sections were analyzed in the context of the newly developed Δ⁢𝐵⁢𝐸 systematics that provides trends in neutron-rich regions and increased sensitivity to nuclear binding, an important nuclear structure observable. Furthermore, the new systematics addresses gaps in 𝑄 𝑔 -based methods commonly used to interpret the production cross sections of light neutron-rich elements, and provides an efficient empirical approach to describe cross-section trends across isotopic chains. Good agreement with the measured data was obtained when the Δ⁢𝐵⁢𝐸 systematics and abrasion-ablation calculations were performed using the Hartree-Fock-Bogoliubov (HFB-22) mass table.

59 ≤ A ≤ 89↗

DOE OSTI2023

Constraints on Nuclear Symmetry Energy Parameters

A review is made of constraints on the nuclear symmetry energy parameters arising from nuclear binding energy measurements, theoretical chiral effective field predictions of neutron matter properties, the unitary gas conjecture, and measurements of neutron skin thicknesses and dipole polarizabilities. While most studies have been confined to the parameters 𝑆 𝑉 and L, the important roles played by, and constraints on 𝐾 sym , or, equivalently, the neutron matter incompressibility 𝐾 𝑁 , are discussed. Strong correlations among 𝑆 𝑉 ,𝐿, and 𝐾 𝑁 are found from both nuclear binding energies and neutron matter theory. However, these correlations somewhat differ in the two cases, and those from neutron matter theory have smaller uncertainties. To 68% confidence, it is found from neutron matter theory that 𝑆 𝑉 = 32.0 ± 1.1 MeV, 𝐿 = 51.9 ± 7.9 MeV and 𝐾 𝑁 = 152.2 ± 38.1 MeV. Theoretical predictions for neutron skin thickness and dipole polarizability measurements of the neutron-rich nuclei 48 Ca, 120 Sn, and 208 Pb are compared to recent experimental measurements, most notably the CREX and PREX neutron skin experiments from Jefferson Laboratory. By themselves, PREX I+II measurements of 208 Pb and CREX measurement of 48 Ca suggest 𝐿 = 121 ± 47 MeV and 𝐿 = −5 ± 40 MeV, respectively, to 68% confidence. However, we show that nuclear interactions optimally satisfying both measurements imply 𝐿 = 53 ± 13 MeV, nearly the range suggested by either nuclear mass measurements or neutron matter theory, and is also consistent with nuclear dipole polarizability measurements. This small parameter range implies 𝑅 1.4 = 11.6 ± 1.0 km and Λ 1.4 = 228$^{+148}_{−90}$, which are consistent with NICER X-ray and LIGO/Virgo gravitational wave observations of neutron stars.

neutron skins↗

NASA NTRS2002

A calmodulin-binding/CGCG box DNA-binding protein family involved in multiple signaling pathways in plants

We reported earlier that the tobacco early ethylene-responsive gene NtER1 encodes a calmodulin-binding protein (Yang, T., and Poovaiah, B. W. (2000) J. Biol. Chem. 275, 38467-38473). Here we demonstrate that there is one NtER1 homolog as well as five related genes in Arabidopsis. These six genes are rapidly and differentially induced by environmental signals such as temperature extremes, UVB, salt, and wounding; hormones such as ethylene and abscisic acid; and signal molecules such as methyl jasmonate, H(2)O(2), and salicylic acid. Hence, they were designated as AtSR1-6 (Arabidopsis thaliana signal-responsive genes). Ca(2+)/calmodulin binds to all AtSRs, and their calmodulin-binding regions are located on a conserved basic amphiphilic alpha-helical motif in the C terminus. AtSR1 targets the nucleus and specifically recognizes a novel 6-bp CGCG box (A/C/G)CGCG(G/T/C). The multiple CGCG cis-elements are found in promoters of genes such as those involved in ethylene signaling, abscisic acid signaling, and light signal perception. The DNA-binding domain in AtSR1 is located on the N-terminal 146 bp where all AtSR1-related proteins share high similarity but have no similarity to other known DNA-binding proteins. The calmodulin-binding nuclear proteins isolated from wounded leaves exhibit specific CGCG box DNA binding activities. These results suggest that the AtSR gene family encodes a family of calmodulin-binding/DNA-binding proteins involved in multiple signal transduction pathways in plants.

Non-NASA Center↗

DOE OSTI2025

Multiscale Physics of Atomic Nuclei from First Principles

Atomic nuclei exhibit multiple energy scales ranging from hundreds of MeV in binding energies to fractions of an MeV for low-lying collective excitations. As the limits of nuclear binding are approached near the neutron and proton drip lines, traditional shell structure starts to melt with an onset of deformation and an emergence of coexisting shapes. It is a long-standing challenge to describe this multiscale physics starting from nuclear forces with roots in quantum chromodynamics. Here, we achieve this within a unified and nonperturbative quantum many-body framework that captures both short- and long-range correlations starting from modern nucleon-nucleon and three-nucleon forces from chiral effective field theory. The short-range (dynamic) correlations which account for the bulk of the binding energy are included within a symmetry-breaking framework, while long-range (static) correlations (and fine details about the collective structure) are included by employing symmetry projection techniques. Our calculations accurately reproduce—within theoretical error bars—available experimental data for low-lying collective states and the electromagnetic quadrupole transitions in 20−30 Ne. In addition, we reveal coexisting spherical and deformed shapes in 30 Ne, which indicates the breakdown of the magic neutron number 𝑁 = 20 as the key nucleus 28 O is approached, and we predict that the drip line nuclei 32,34 Ne are strongly deformed and collective. By developing reduced-order models for symmetry-projected states, we perform a global sensitivity analysis and find that the subleading singlet 𝑆-wave contact and a pion-nucleon coupling strongly impact nuclear deformation in chiral effective field theory. The techniques developed in this work clarify how microscopic nuclear forces generate the multiscale physics of nuclei spanning collective phenomena as well as short-range correlations and allow one to capture emergent and dynamical phenomena in finite fermion systems such as atom clusters, molecules, and atomic nuclei.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

Global Framework for Emulation of Nuclear Calculations

We introduce a hierarchical framework that combines ab initio many-body calculations with a Bayesian neural network, developing emulators capable of accurately predicting nuclear properties across isotopic chains simultaneously and being applicable to different regions of the nuclear chart. We benchmark our developments using the oxygen isotopic chain, achieving accurate results for ground-state energies and nuclear charge radii, while providing robust uncertainty quantification. Our framework enables global sensitivity analysis of nuclear binding energies and charge radii with respect to the low-energy constants that describe the nuclear force.

FOS: Computer and information sciences↗

DOE OSTI2025

Discovering nuclear models from symbolic machine learning

Numerous phenomenological nuclear models have been proposed to describe specific observables within different regions of the nuclear chart. However, developing a unified model that describes the complex behavior of all nuclei remains an open challenge. Here, we explore whether symbolic Machine Learning (ML) can rediscover traditional nuclear physics models or identify alternatives with improved simplicity, fidelity, and predictive power. To address this challenge, we developed a Multi-objective Iterated Symbolic Regression approach that handles symbolic regressions over multiple target observables, accounts for experimental uncertainties and is robust against high-dimensional problems. As a proof of principle, we applied this method to describe the nuclear binding energies and charge radii of light and medium mass nuclei. Our approach identified simple analytical relationships based on the number of protons and neutrons, providing interpretable models with precision comparable to state-of-the-art nuclear models. Additionally, we integrated this ML-discovered model with an existing complementary model to estimate the limits of nuclear stability. These results highlight the potential of symbolic ML to develop accurate nuclear models and guide our description of complex many-body problems.

Nuclear structure↗

DOE OSTI2026

Computational schemes for the Magnus expansion of the in-medium similarity renormalization group

The in-medium similarity renormalization group (IMSRG) is a popular many-body method used for computations of nuclei. It solves the many-body Schrödinger equation through a continuous unitary transformation of the many-body Hamiltonian. The IMSRG transformation is typically truncated at the normal-ordered two-body level, the IMSRG(2), but recently several approaches have been developed to capture the effects of normal-ordered three-body operators, the IMSRG(3). In particular, a factorized approximation to the IMSRG(3) proposes to capture the leading effects of three-body operators at the same computational cost as the IMSRG(2) approximation. This approach often employs an approximate scheme for solving the IMSRG equations, the so-called hunter-gatherer scheme. In this work, I study the uncertainty associated with this scheme. I find that the hunter-gatherer scheme differs by up to 7MeV for ground-state energies and 0.5MeV for excitation energies from standard IMSRG(2) approaches. These differences are in some cases comparable to the expected size of IMSRG(3) corrections.

39 ≤ A ≤ 58↗

NASA NTRS1975

Momentum distributions of isotopes produced by fragmentation of relativistic C-12 and O-16 projectiles

The fragment momentum distributions in the projectile rest frame are, typically, Gaussian shaped, narrow, consistent with isotropy, depend on fragment and projectile, and have no significant correlation with target mass or beam energy. The nuclear temperature is inferred from the momentum distributions of the fragments and is approximately equal to the projectile nuclear binding energy, indicative of small energy transfer between target and fragment.

Greiner, D. E.↗

NASA NTRS1999

Chemoprevention of Radiation Induced Rat Mammary Neoplasms

Radiations encountered in space include protons and heavy ions such as iron as well as their secondaries. The relative biological effect (RBE) of these ions is not known, particularly at the doses and dose-rates expected for planetary missions. Neutrons, are not particularly relevant to space travel, but have been found experimentally to have an increase in their RBE with decreasing dose. If a similar trend of increasing RBE with decreasing dose is present for heavy ions and protons during irradiation in space, the small doses received during space travel could potentially have substantial carcinogenic risk. Clearly more investigation of the effects of heavy ions and protons is needed before accurate risk assessment for prolonged travel in space can be done. One means to mitigate the increased risk of cancer due to radiation exposure in space is by developing effective countermeasures that can reduce the incidence of tumor development. Tamoxifen has recently been shown to be an effective chemopreventive agent in both animal models and humans for the prevention of mammary tumors. Tamoxifen is a unique drug, with a highly specific mechanism of action affecting a specific radiation-sensitive population of epithelial cells in the mammary gland. In human studies, the annual incidence of a primary tumor in the contralateral breast of women with previous breast cancer is about 8 per 1000, making them an exceedingly high-risk group for the development of breast cancer. In this high risk group, treated with tamoxifen, daily, for 2 years, the incidence of a new primary tumor in the contralateral breast was approximately one third of that noted in the non-tamoxifen treatment group. Tamoxifen antagonizes the action of estrogen by competing for the nuclear receptor complex thereby altering the association of the receptor complex and nuclear binding sites. Its effects in reducing the development of breast cancer could be accomplished by controlling clinically undetectable microcancers, arresting preneoplastic lesions, or correcting abnormal environments which predispose to high risk of malignant transformation.

Huso, David L.↗

NASA NTRS2000

A mutation in the Arabidopsis HYL1 gene encoding a dsRNA binding protein affects responses to abscisic acid, auxin, and cytokinin

Both physiological and genetic evidence indicate interconnections among plant responses to different hormones. We describe a pleiotropic recessive Arabidopsis transposon insertion mutation, designated hyponastic leaves (hyl1), that alters the plant's responses to several hormones. The mutant is characterized by shorter stature, delayed flowering, leaf hyponasty, reduced fertility, decreased rate of root growth, and an altered root gravitropic response. It also exhibits less sensitivity to auxin and cytokinin and hypersensitivity to abscisic acid (ABA). The auxin transport inhibitor 2,3,5-triiodobenzoic acid normalizes the mutant phenotype somewhat, whereas another auxin transport inhibitor, N-(1-naph-thyl)phthalamic acid, exacerbates the phenotype. The gene, designated HYL1, encodes a 419-amino acid protein that contains two double-stranded RNA (dsRNA) binding motifs, a nuclear localization motif, and a C-terminal repeat structure suggestive of a protein-protein interaction domain. We present evidence that the HYL1 gene is ABA-regulated and encodes a nuclear dsRNA binding protein. We hypothesize that the HYL1 protein is a regulatory protein functioning at the transcriptional or post-transcriptional level.

NASA Discipline Plant Biology↗

DOE OSTI2025

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 ~3 up to ~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.

Binding energy & masses↗

DOE OSTI2025

Exploring isospin symmetry breaking in exotic nuclei: High-precision mass measurement of 23 Si and shell-model calculations of 𝑇 = 5/2 nuclei

Here, we present a high-precision mass measurement of the proton-rich nucleus 23 Si, performed with the LEBIT Penning trap at the Facility for Rare Isotope Beams (FRIB) utilizing the time-of-flight ion cyclotron resonance (TOF-ICR) technique. We determined a mass excess of 23362.9(5.8) keV, which agrees with a recent storage-ring measurement from the experimental Cooler-Storage Ring (CSRe) in Lanzhou but has a factor of 20 improved precision 23 Si is hence the nucleus with the most precisely known mass among all nuclei with an isospin projection of 𝑇 𝑧 = −5/2. We performed shell-model calculations with the USDC and USDCm Hamiltonians to study binding energy differences and Thomas-Ehrmann shifts in mirror systems with an isospin up to 𝑇 = 5/2. Our experimental result and other recently reported masses of neutron-deficient sd-shell nuclei agree well with the theoretical predictions, demonstrating that isospin symmetry breaking in sd-shell nuclei—even at high isospin values—is well described by modern shell-model calculations.

20 ≤ A ≤ 38↗

DOE OSTI2025

Further steps toward the 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. Infinite basis corrections to binding energies in the fermionic and bosonic sectors of the covariant density functional theory are taken into account in the fitting protocol within the covariant density functional theory. In addition, total electron binding energies are used in the conversion of atomic binding energies into nuclear ones. Their dependence on neutron excess is investigated across the nuclear chart within the atomic approach. Furthermore, these factors were disregarded in the previous generation of covariant energy density functionals, but their omission 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.

Binding energy & masses↗

NASA NTRS1996

Identification of the cAMP response element that controls transcriptional activation of the insulin-like growth factor-I gene by prostaglandin E2 in osteoblasts

Insulin-like growth factor-I (IGF-I), a multifunctional growth factor, plays a key role in skeletal growth and can enhance bone cell replication and differentiation. We previously showed that prostaglandin E2 (PGE2) and other agents that increase cAMP activated IGF-I gene transcription in primary rat osteoblast cultures through promoter 1 (P1), the major IGF-I promoter, and found that transcriptional induction was mediated by protein kinase A. We now have identified a short segment of P1 that is essential for full hormonal regulation and have characterized inducible DNA-protein interactions involving this site. Transient transfections of IGF-I P1 reporter genes into primary rat osteoblasts showed that the 328-base pair untranslated region of exon 1 was required for a full 5.3-fold response to PGE2; mutation in a previously footprinted site, HS3D (base pairs +193 to +215), reduced induction by 65%. PGE2 stimulated nuclear protein binding to HS3D. Binding, as determined by gel mobility shift assay, was not seen in nuclear extracts from untreated osteoblast cultures, was detected within 2 h of PGE2 treatment, and was maximal by 4 h. This DNA-protein interaction was not observed in cytoplasmic extracts from PGE2-treated cultures, indicating nuclear localization of the protein kinase A-activated factor(s). Activation of this factor was not blocked by cycloheximide (Chx), and Chx did not impair stimulation of IGF-I gene expression by PGE2. In contrast, binding to a consensus cAMP response element (CRE; 5'-TGACGTCA-3') from the rat somatostatin gene was not modulated by PGE2 or Chx. Competition gel mobility shift analysis using mutated DNA probes identified 5'-CGCAATCG-3' as the minimal sequence needed for inducible binding. All modified IGF-I P1 promoterreporter genes with mutations within this CRE sequence also showed a diminished functional response to PGE2. These results identify the CRE within the 5'-untranslated region of IGF-I exon 1 that is required for hormonal activation of IGF-I gene transcription by cAMP in osteoblasts.

NASA Discipline Musculoskeletal↗