Accurate neutron-induced $(n,p)$ reaction cross sections are essential for applications in nuclear energy, radionuclide production, materials studies, and nuclear astrophysics. However, experimental data remain sparse for many isotopes, and evaluated nuclear data libraries can show systematic deviations from available measurements. We develop a Bayesian neural network (BNN) residual learning model, denoted \texttt{BNN-R5}, to improve $(n,p)$ reaction cross-section predictions. The model uses five physically motivated nuclear descriptors and does not employ experimental or evaluated cross-section values as input features. Rather than predicting the cross sections directly, \texttt{BNN-R5} learns the log-space residual between the evaluated TENDL-2023 data and experimental measurements, thereby providing a data-driven correction to the evaluated library. The model is trained using stochastic variational inference, which provides predictive mean values together with Bayesian uncertainty estimates. Across a broad range of target nuclei, the corrected cross sections generally show improved agreement with experimental data and outperform the original TENDL-2023 evaluations. Feature-importance analysis using SHapley Additive exPlanations (SHAP) identifies the pairing term $δ$ as the most influential descriptor, followed by the excitation-energy variable $\ln(ΔE)$ and the neutron number $N$, while the proton number $Z$ has the smallest overall influence. These results demonstrate that Bayesian residual learning provides a robust and interpretable framework for improving evaluated nuclear data and predicting reaction cross sections in data-sparse regions of the nuclear chart.
We develop for the first time a microscopic global nucleon-nucleus optical potential with quantified uncertainties suitable for analyzing nuclear reaction experiments at next-generation rare-isotope beam facilities. Within the improved local density approximation and without any adjustable parameters, we begin by computing proton-nucleus and neutron-nucleus optical potentials from a set of five nuclear forces from chiral effective field theory for 1800 target nuclei in the mass range 12 $\leq$ A $\leq$ 242 for energies between 0 MeV $<$ E $\lesssim$ 150 MeV. We then parameterize a global optic…
We develop an effective field theory (EFT) for nuclear vibrations. The key ingredients - quadrupole degrees of freedom, rotational invariance, and a breakdown scale around the three-phonon level - are taken from data. The EFT is developed for spectra and electromagnetic moments and transitions. We employ tools from Bayesian statistics for the quantification of theoretical uncertainties. The EFT consistently describes spectra and electromagnetic transitions for $^{62}$Ni, $^{98,100}$Ru, $^{106,108}$Pd, $^{110,112,114}$Cd, and $^{118,120,122}$Te within the theoretical uncertainties. This suggest…
Bayesian calibration of a regional optical potential and uncertainty-quantified predictions for compound nucleus reactions
University of Surrey（萨里大学）；Facility for Rare Isotope Beams, Michigan State University（密歇根州立大学稀有同位素束设施）；Department of Physics and Astronomy, Michigan State University（密歇根州立大学物理与天文学系）；AWE Nuclear Security Technologies（阿韦核安全技术有限公司）
Context. Monte Carlo methods can be used to evaluate the uncertainty of a reaction rate that arises from many uncertain nuclear inputs. However, until now no attempt has been made to find the effect of correlated energy uncertainties in input resonance parameters. Aims. To investigate the impact of correlated energy uncertainties on reaction rates. Methods. Using a combination of numerical and Monte Carlo variation of resonance energies, the effect of correlations are investigated. Five reactions are considered: two fictional, illustrative cases and three reactions whose rates are of current i…
Experimental and theoretical results of the $P_{\mathrm{CN}}$ fusion probability of reactants in the entrance channel and the $W_{\mathrm{sur}}$ survival probability against fission at deexcitation of the compound nucleus formed in heavy-ion collisions are discussed. The theoretical results for a set of nuclear reactions leading to formation of compound nuclei (CNs) with the charge number $Z=102\text{--}122$ reveal a strong sensitivity of $P_{\mathrm{CN}}$ to the characteristics of colliding nuclei in the entrance channel, dynamics of the reaction mechanism, and excitation energy of the system…
We have quantified the statistical uncertainties of the low-energy coupling-constants (LECs) of an optimized nucleon-nucleon (NN) interaction from chiral effective field theory ($χ$EFT) at next-to-next-to-leading order (NNLO). In addition, we have propagated the impact of the uncertainties of the LECs to two-nucleon scattering phase shifts, effective range parameters, and deuteron observables.
Theoretical predictions need quantified uncertainties for a meaningful comparison to experimental results. This is an idea which presently permeates the field of theoretical nuclear physics. In light of the recent progress in estimating theoretical uncertainties in ab initio nuclear physics, we here present and compare methods for evaluating the statistical part of the uncertainties. A special focus is put on the (for the field) novel method of Lagrange multipliers (LM). Uncertainties from the fit of the nuclear interaction to experimental data are propagated to a few observables in light-mass…
Uncertainty quantification has become increasingly more prominent in nuclear physics over the past several years. In few-body reaction theory, there are four main sources that contribute to the uncertainties in the calculated observables: the effective potentials, approximations made to the few-body problem, structure functions, and degrees of freedom left out of the model space. In this work, we illustrate some of the features that can be obtained when modern statistical tools are applied in the context of nuclear reactions. This work consists of a summary of the progress that has been made i…
Until recently, uncertainty quantification in low energy nuclear theory was typically performed using frequentist approaches. However in the last few years, the field has shifted toward Bayesian statistics for evaluating confidence intervals. Although there are statistical arguments to prefer the Bayesian approach, no direct comparison is available. In this work, we compare, directly and systematically, the frequentist and Bayesian approaches to quantifying uncertainties in direct nuclear reactions. Starting from identical initial assumptions, we determine confidence intervals associated with …
Transfer reactions provide information about the single-particle nature of nuclear levels. In particular, the differential cross sections from these measurements are sensitive to the angular momentum of the transferred particle and the spectroscopic factor of the populated level. However, the process of extracting these properties is subject to uncertainties, both from experimental and theoretical sources. By integrating the distorted wave Born approximation into a Bayesian model, we propagate these uncertainties through to the spectroscopic factors and orbital angular momentum values. We use …
Neutron star crust and outer core equation of state from chiral effective field theory with quantified uncertainties
Technische Universität Darmstadt（达姆施塔特工业大学）；ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH（极端物质研究所 (EMMI), 重离子研究中心）；Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）
本文基于 chiral 有效场论，利用贝叶斯框架研究不对称核物质的能量密度展开，并构建中子星地壳和外核的方程 of state，考虑了 EFT 截断的不确定性。
Uncertainty quantified three-body model applied to the two-neutron halo $^{22}$C
Facility for Rare Isotope Beams, Michigan State University（密歇根州立大学稀有同位束设施）；Université Paris-Saclay, CNRS/IN2P3, IJCLab（巴黎萨克雷大学，法国国家科学研究中心/法国国家核子与粒子物理研究所，IJCLab）；Department of Physics and Astronomy, Michigan State University（密歇根州立大学物理与天文学系）
Context. Monte Carlo methods have enabled nuclear reaction rates from uncertain inputs to be presented in a statistically meaningful manner. However, these uncertainties are currently computed assuming no correlations between the physical quantities that enter those calculations. This is not always an appropriate assumption. Astrophysically important reactions are often dominated by resonances, whose properties are usually normalized to a well-known reference resonance. This insight provides a basis from which to develop a flexible framework for including correlations in Monte Carlo reaction r…
Being able to rigorously quantify the uncertainties in reaction models is crucial to moving this field forward. Even though Bayesian methods are becoming increasingly popular in nuclear theory, they are yet to be implemented and applied in reaction theory problems. The purpose of this work is to investigate, using Bayesian methods, the uncertainties in the optical potentials generated from fits to elastic scattering data and the subsequent uncertainties in the transfer predictions. We also study the differences in two reaction models where the parameters are constrained in a similar manner, as…
\noindent{\bf Background:} Deuteron-induced nuclear reactions are an essential tool for probing the structure of nuclei as well as astrophysical information such as $(n,γ)$ cross sections. The deuteron-nucleus system is typically described within a Faddeev three-body model consisting of a neutron ($n$), a proton ($p$), and the target nucleus ($A$) interacting through pairwise phenomenological potentials. While Faddeev techniques enable the exact description of the three-body dynamics, their predictive power is limited in part by the omission of irreducible neutron-proton-nucleus three-body for…
Background: Recent high-precision measurements of alpha-induced reaction data below the Coulomb barrier have pointed out questions of the alpha-particle optical-model potential (OMP) which are yet open within various mass ranges. Purpose: The applicability of a previous optical potential and eventual uncertainties and/or systematic errors of the OMP assessment at low energies can be further considered on this basis. Method: Nuclear model parameters based on the analysis of recent independent data, particularly gamma-ray strength functions, have been involved within statistical model calculatio…
Background: The ($α$,n) and ($α$,$γ$) reactions on $^{17,18}$O have significant impact on the neutron balance in the astrophysical $s$-process. In this scenario stellar reaction rates are required for relatively low temperatures below $T_9 \lesssim 1$. Purpose: The uncertainties of the $^{17,18}$O($α$,n)$^{20,21}$Ne reactions are investigated. Statistical model calculations are performed to study the applicability of this model for relatively light nuclei in extension to a recent review for the $20 \le A \le 50$ mass range. Method: The available experimental data for the $^{17,18}$O($α$,n)$^{2…
Sensitivities of nuclear reaction rates to a variation of nuclear properties are studied. Target nuclei range from proton- to neutron-dripline for 10<=Z<=83. Reactions considered are nucleon- and alpha-induced reactions mediated by the strong interaction. The contribution of reactions proceeding on the target ground state to the total stellar rate is also given. General dependences on various input quantities are discussed. Additionally, sensitivities of laboratory cross sections of nucleon-, alpha-, and gamma-induced reactions are shown, allowing to estimate the impact of cross section measur…
We analyze in details the standard Primordial Nucleosynthesis scenario. In particular we discuss the key theoretical issues which are involved in a detailed prediction of light nuclide abundances, as the weak reaction rates, neutrino decoupling and nuclear rate modeling. We also perform a new analysis of available data on the main nuclear processes entering the nucleosynthesis reaction network, with particular stress on their uncertainties as well as on their role in determining the corresponding uncertainties on light nuclide theoretical estimates. The current status of theoretical versus exp…
The main s-process taking place in low mass stars produces about half of the elements heavier than iron. It is therefore very important to determine the importance and impact of nuclear physics uncertainties on this process. We have performed extensive nuclear reaction network calculations using individual and temperature-dependent uncertainties for reactions involving elements heavier than iron, within a Monte Carlo framework. Using this technique, we determined the uncertainty in the main s-process abundance predictions due to nuclear uncertainties link to weak interactions and neutron captu…
In a recent work, the cross section measurement of the 64Zn(p,alpha)61Cu reaction was used to prove that the standard alpha-nucleus optical potentials used in astrophysical network calculation fail to reproduce the experimental data at energies relevant for heavy element nucleosynthesis. In the present paper the analysis of the obtained experimental data is continued by comparing the results with the predictions using different parameters. It is shown that the recently suggested modification of the standard optical potential leads to a better description of the data.
Massive stars are crucial to galactic chemical evolution for elements heavier than iron. Their contribution at early times in the evolution of the Universe, however, is unclear due to poorly constrained nuclear reaction rates. The competing $^{17}$O($α,γ$)$^{21}$Ne and $^{17}$O($α,n$)$^{20}$Ne reactions strongly impact weak s-process yields from rotating massive stars at low metallicities. Abundant $^{16}$O absorbs neutrons, removing flux from the s-process, and producing $^{17}$O. The $^{17}$O($α,n$)$^{20}$Ne reaction releases neutrons, allowing continued s-process nucleosynthesis, if the $^{…
It has been suggested that a $ν$p process can occur when hot, dense, and proton-rich matter is expanding within a strong flux of anti-neutrinos. In such an environment, proton-rich nuclides can be produced in sequences of proton captures and (n,p) reactions, where the free neutrons are created in situ by $\overlineν_\mathrm{e}+\mathrm{p} \rightarrow \mathrm{n}+\mathrm{e}^+$ reactions. The detailed hydrodynamic evolution determines where the nucleosynthesis path turns off from N = Z line and how far up the nuclear chart it runs. In this work, the uncertainties on the final isotopic abundances s…
Background: Charge-exchange reactions are a powerful tool for exploring nuclear structure and nuclear astrophysics, however, a robust charge-exchange reaction theory with quantified uncertainties is essential to extracting reliable physics. Purpose: The goal of this work is to determine the uncertainties due to optical potentials used in the theory for charge-exchange reactions to isobaric analogue states. Method: We implement a two-body reaction model to study (p,n) charge-exchange transitions and perform a Bayesian analysis. We study the (p,n) reaction to the isobaric analog states of $^{14}…
We investigated the impact of uncertainties in neutron-capture and weak reactions (on heavy elements) on the s-process nucleosynthesis in low-mass stars using a Monte-Carlo based approach. We performed extensive nuclear reaction network calculations that include newly evaluated temperature-dependent upper and lower limits for the individual reaction rates. Our sophisticated approach is able to evaluate the reactions that impact more significantly the final abundances. We found that beta-decay rate uncertainties affect typically nuclides near s-process branchings, whereas most of the uncertaint…
We present a Monte Carlo calculation of the astrophysical rate of the 15O(alpha,gamma)19Ne reaction based on an evaluation of published experimental data. By considering the likelihood distributions of individual resonance parameters derived from measurements, estimates of upper and lower limits on the reaction rate at the 99.73% confidence level are derived in addition to the recommended, median value. These three reaction rates are used as input for three separate calculations of Type I x-ray bursts using spherically symmetric, hydrodynamic simulations of an accreting neutron star. In this w…
We explore properties of core-collapse supernova progenitors with respect to the composite uncertainties in the thermonuclear reaction rates by coupling the reaction rate probability density functions provided by the STARLIB reaction rate library with $\texttt{MESA}$ stellar models. We evolve 1000 15 $M_{\odot}$ models from the pre main-sequence to core O-depletion at solar and subsolar metallicities for a total of 2000 Monte Carlo stellar models. For each stellar model, we independently and simultaneously sample 665 thermonuclear reaction rates and use them in a $\texttt{MESA}$ in situ reacti…
In this work, we study the uncertainty of nuclear model parameters for neutron induced ^{56}Fe reactions in fast neutron region by using the Total Monte Carlo method. We perform a large number of TALYS runs and compare the calculated results with the experimental data of the cross sections to obtain the uncertainties of the model parameters. Based on the derived uncertainties another 1000 TALYS runs have been performed to create random cross section files. For comparison with the experimental data we calculate a weighted χ^2 value for each random file as well as the ENDF/B-VII.1, JEFF3.1, JEND…
Uncertainties in the production of iron-group nuclides in core-collapse supernovae from Monte Carlo variations of reaction rates
Kogakuin University（工学院大学）；The University of Tokyo（东京大学）；RIKEN Pioneering Research Institute (PRI)（理化学研究所先导研究本部）；National Astronomical Observatory of Japan (NAOJ)（日本国立天文台）；North Carolina State University（北卡罗来纳州立大学）；University of Basel（巴塞尔大学）；University of Hertfordshire（赫特福德大学）
Uncertainties in nucleosynthesis models originating from uncertainties in astrophysical reaction rates were estimated in a Monte Carlo variation procedure. Thousands of rates were simultaneously varied within individual, temperature-dependent errors to calculate their combined effect on final abundances. After a presentation of the method, results from application to three different nucleosynthesis processes are shown: the $γ$-process and the s-process in massive stars, and the main s-process in AGB stars (preliminary results). Thermal excitation of nuclei in the stellar plasma and the combine…
Optical-model potentials (OMPs) continue to play a key role in nuclear reaction calculations. However, the uncertainty of phenomenological OMPs in widespread use -- inherent to any parametric model trained on data -- has not been fully characterized, and its impact on downstream users of OMPs remains unclear. Here we assign well-calibrated uncertainties for two representative global OMPs, those of Koning-Delaroche and Chapel Hill '89, using Markov-Chain Monte Carlo for parameter inference. By comparing the canonical versions of these OMPs against the experimental data originally used to constr…
The propagation of uncertainties in reaction cross sections and rates of neutron-, proton-, and $α$-induced reactions into the final isotopic abundances obtained in nucleosynthesis models is an important issue in studies of nucleosynthesis and Galactic Chemical Evolution. We developed a Monte Carlo method to allow large-scale postprocessing studies of the impact of nuclear uncertainties on nucleosynthesis. Temperature-dependent rate uncertainties combining realistic experimental and theoretical uncertainties are used. The importance of contributions of cross sections of reactions on excited st…
Context. Direct observation of gamma-ray emission from the decay of $^{18}$F ejected in classical nova outbursts remains a major focus of the nuclear astrophysics community. However, modeling the abundance of ejected $^{18}$F, and thus the predicted detectability distance of a gamma-ray signal near 511 keV emitted from these transient thermonuclear episodes, is hampered by significant uncertainties in our knowledge of the key $^{18}$F(p,$α$) reaction rate. Aims. We analyze uncertainties in the most recent nuclear physics experimental results employed to calculate the $^{18}$F(p,$α$) reaction r…
Neutrino-driven ejecta in core collapse supernovae (CCSNe) offer an interesting astrophysical scenario where lighter heavy elements between Sr and Ag can be synthesized. Previous studies emphasized the important role that ($α,n$) reactions play in the production of these elements, particularly in neutron-rich and alpha-rich environments. In this paper, we have investigated the sensitivity of elemental abundances to specific ($α,n$) reaction-rate uncertainties under different astrophysical conditions. Following a Monte Carlo nucleosynthesis study with over 36 representative astrophysical wind c…
The chart of the nuclides is limited by particle drip lines beyond which nuclear stability to proton or neutron emission is lost. Predicting the range of particle-bound isotopes poses an appreciable challenge for nuclear theory as it involves extreme extrapolations of nuclear masses beyond the regions where experimental information is available. Still, quantified extrapolations are crucial for a variety of applications, including the modeling of stellar nucleosynthesis. We use microscopic nuclear mass models and Bayesian methodology to provide quantified predictions of proton and neutron separ…
The $νp$ process appears in proton-rich, hot matter which is expanding in a neutrino wind and may be realised in explosive environments such as core-collapse supernovae or in outflows from accretion disks. The impact of uncertainties in nuclear reaction cross sections on the finally produced abundances has been studied by applying Monte Carlo variation of all astrophysical reaction rates in a large reaction network. As the detailed astrophysical conditions of the $νp$ process still are unknown, a parameter study was performed, with 23 trajectories covering a large range of entropies and $Y_\ma…
The $s$-process in massive stars produces the weak component of the $s$-process (nuclei up to $A \sim 90$), in amounts that match solar abundances. For heavier isotopes, such as barium, production through neutron capture is significantly enhanced in very metal-poor stars with fast rotation. However, detailed theoretical predictions for the resulting final $s$-process abundances have important uncertainties caused both by the underlying uncertainties in the nuclear physics (principally neutron capture reaction and $β$-decay rates) as well as by the stellar evolution modeling. In this work, we i…
Recent work has studied the uncertainty in predictions for A(d,p)B reactions using the distorted-wave Born approximation (DWBA), coming from the parameterization of the effective dA interactions [Lovell et al., Phys. Rev. C 95, 024611]. There are different levels of sophistication in theories for one-nucleon transfer reactions, including the adiabatic wave approximation (ADWA) which takes deuteron breakup into account to all orders. In this work, we quantify the uncertainties associated with the ADWA method that come from the parameterization of the NA interactions, and compare ADWA with DWBA.…
Charged-current neutrino-nucleus cross sections for 54,56Fe and 58,60Ni are calculated and compared using frameworks based on relativistic and Skyrme energy density functionals, and the shell model. The current theoretical uncertainties in modeling neutrino-nucleus cross sections are assessed in relation to the predicted Gamow-Teller transition strength and available data, multipole decomposition of the cross sections, and cross sections averaged over the Michel flux and Fermi-Dirac distribution. Employing different microscopic approaches and models, the DAR neutrino-56Fe cross section and its…
The extent of nucleosynthesis in models of type I X-ray bursts and the associated impact on the energy released in these explosive events are sensitive to nuclear masses and reaction rates around the $^{64}$Ge waiting point. Using the well known mass of $^{64}$Ge, the recently measured $^{65}$As mass, and large-scale shell model calculations, we have determined new thermonuclear rates of the $^{64}$Ge($p$,$γ$)$^{65}$As and $^{65}$As($p$,$γ$)$^{66}$Se reactions with reliable uncertainties. The new reaction rates differ significantly from previously published rates. Using the new data we analyze…
Proton-rich nuclei, the so-called p-nuclei, are made in photodisintegration processes in outer shells of massive stars in the course of the final supernova explosion. Nuclear uncertainties in the production of these nuclei have been quantified in a Monte Carlo procedure. Bespoke temperature-dependent uncertainties were assigned to different types of reactions involving nuclei from Fe to Bi and all rates were varied randomly within the uncertainties. The resulting total production uncertainties of the p-nuclei are below a factor of two, with few exceptions. Key reactions dominating the final un…
Within the asymptotic theory proposed by authors R. Yarmukhamedov and K.I. Tursunmakhatov [Phys. Rev. C (submitted 2019)] for the peripheral sub- and above-barrier transfer $A$($x$, $y$)$B$ reaction in the three-body ($A$, $a$ and $y$) model ($ x$= $y$ + $a$ and $B$= $A$ + $a$, and $ a$ is a transferred particle), the analysis of the experimental angular distributions of the differential cross sections is performed for the peripheral proton and triton transfer ${\rm{^9Be(^{10}B,\,^9Be)^{10}B}}$, ${\rm{^{16}O(^3He}},\,d{\rm{)^{17}F}}$ and ${\rm{^{19}F(}}p,\,α{\rm{)^{16}O}}$ reactions at above-a…
Carbon-enhanced metal-poor (CEMP) r/s-stars show surface-abundance distributions characteristic of the so-called intermediate neutron capture process (i-process) of nucleosynthesis. We previously showed that the ingestion of protons in the convective helium-burning region of a low-mass low-metallicity star can explain the surface abundance distribution observed in CEMP r/s stars relatively well. Such an i-process requires detailed reaction network calculations involving hundreds of nuclei for which reaction rates have not yet been determined experimentally. We investigate the nuclear physics u…
We investigated the impact of uncertainties in neutron-capture and weak reactions (on heavy elements) on the s-process nucleosynthesis in low-mass stars and massive stars using a Monte-Carlo based approach. We performed extensive nuclear reaction network calculations that include newly evaluated temperature-dependent upper and lower limits for the individual reaction rates. We found beta-decay rate uncertainties affect only a few nuclei near s-process branchings, whereas most of the uncertainty in the final abundances is caused by uncertainties in the neutron capture rates. We suggest a list o…
The overall uncertainties in predicting heavy element synthesis cross sections are examined in terms of the uncertainties associated with the calculations of capture cross sections, fusion probabilities and survival probabilities. Attention is focussed on hot fusion reactions. The predicted heavy element formation cross sections are uncertain to at least one order of magnitude.
The study of d+d reactions is of major interest since their reaction rates affect the predicted abundances of D, 3He, and 7Li. In particular, recent measurements of primordial D/H ratios call for reduced uncertainties in the theoretical abundances predicted by big bang nucleosynthesis (BBN). Different authors have studied reactions involved in BBN by incorporating new experimental data and a careful treatment of systematic and probabilistic uncertainties. To analyze the experimental data, Coc et al. (2015) used results of ab initio models for the theoretical calculation of the energy dependenc…
