Quantifying uncertainties and correlations in the nuclear-matter equation of state
C. Drischler, J. A. Melendez, R. J. Furnstahl, D. R. Phillips
备注：
23 pages, 21 figures, 4 tables, supplemental material; close to the published version; minor corrections and additional table summarizing the main results; Jupyter notebooks for reproducing the results and figures can be found at https://buqeye.github.io/software/
We perform statistically rigorous uncertainty quantification (UQ) for chiral effective field theory ($χ$EFT) applied to infinite nuclear matter up to twice nuclear saturation density. The equation of state (EOS) is based on high-order many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the $χ$EFT expansion. From these calculations our newly developed Bayesian machine-learning approach extracts the size and smoothness properties of the correlated EFT truncation error. We then propose a novel extension that uses multitask machine learning to reveal correlations between the EOS at different proton fractions. The inferred in-medium $χ$EFT breakdown scale in pure neutron matter and symmetric nuclear matter is consistent with that from free-space nucleon-nucleon scattering. These significant advances allow us to provide posterior distributions for the nuclear saturation point and propagate theoretical uncertainties to derived quantities: the pressure and incompressibility of symmetric nuclear matter, the nuclear symmetry energy, and its derivative. Our results, which are validated by statistical diagnostics, demonstrate that an understanding of truncation-error correlations between different densities and different observables is crucial for reliable UQ. The methods developed here are publicly available as annotated Jupyter notebooks.
We propose a numerical definition for baryon stopping in relativistic heavy ion collisions that is obtainable from final hadron rapidity distributions as well as from bremsstrahlung measurements. Thus a new channel of communication is opened between the two methods.
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…
We present a simple method for determining the (correlated) uncertainties of the light element abundances expected from big bang nucleosynthesis, which avoids the need for lengthy Monte Carlo simulations. Our approach helps to clarify the role of the different nuclear reactions contributing to a particular elemental abundance and makes it easy to implement energy-independent changes in the measured reaction rates. As an application, we demonstrate how this method simplifies the statistical estimation of the nucleon-to-photon ratio through comparison of the standard BBN predictions with the obs…
Probabilistic machine learning techniques can learn both complex relations between input features and output quantities of interest as well as take into account stochasticity or uncertainty within a data set. In this initial work, we explore the use of one such probabilistic network, the Mixture Density Network (MDN), to reproduce fission yields and their uncertainties. We study mass yields for the spontaneous fission of $^{252}$Cf, exploring the number of training samples needed for converged predictions, how different levels of uncertainty propagate from the training set to the MDN predictio…
The coupled-channels density-matrix technique for nuclear reaction dynamics, which is based on the Liouville-von Neumann equation with Lindblad dissipative terms, is developed with the inclusion of full angular momentum couplings. It allows a quantitative study of the role and importance of quantum decoherence in nuclear scattering. Formulae of asymptotic observables that can reveal effects of quantum decoherence are given. A method for extracting energy-resolved scattering information from the time-dependent density matrix is introduced. As an example, model calculations are carried out for t…
With the increasing sensitivity of gravitational-wave detectors, we expect to observe multiple binary neutron-star systems through gravitational waves in the near future. The combined analysis of these gravitational-wave signals offers the possibility to constrain the neutron-star radius and the equation of state of dense nuclear matter with unprecedented accuracy. However, it is crucial to ensure that uncertainties inherent in the gravitational-wave models will not lead to systematic biases when information from multiple detections are combined. To quantify waveform systematics, we perform an…
The influence of the uncertainties of the equation of state empirical parameters on the neutron stars crust-core phase transition is explored within a meta-modeling approach, in which the energy per particle is expanded as a Taylor series in density and asymmetry around the saturation point. The phase transition point is estimated from the intersection of the spinodal instability region for dynamical fluctuations with the chemical equilibrium curve. Special attention is paid to the inclusion of high-order parameters of the Taylor series and their influence on the transition point. An uncorrela…
We describe the Bayesian Analysis of Nuclear Dynamics (BAND) framework, a cyberinfrastructure that we are developing which will unify the treatment of nuclear models, experimental data, and associated uncertainties. We overview the statistical principles and nuclear-physics contexts underlying the BAND toolset, with an emphasis on Bayesian methodology's ability to leverage insight from multiple models. In order to facilitate understanding of these tools we provide a simple and accessible example of the BAND framework's application. Four case studies are presented to highlight how elements of t…
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…
The evaluation of short range contributions to neutrinoless double beta decay has been challenged due to critics of the ansatz of the nuclear matrix element calculations. We comment on the critics and uncertainties of these calculations and the effect on the derived limits.
Propagating Uncertainties from Nuclear Physics to Gamma-rays in Core Collapse Supernovae
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Michigan State University（密歇根州立大学）；North Carolina State University（北卡罗来纳州立大学）；Triangle Universities Nuclear Laboratory（三角大学核实验室）；Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena（耶拿弗里德里希·席勒大学理论物理研究所）；Universitat de Valencia（瓦伦西亚大学）；University of Victoria（维多利亚大学）；Arizona State University（亚利桑那州立大学）；School of Physics, Engineering and Technology, University of York（约克大学物理、工程与技术学院）；Louisiana State University（路易斯安那州立大学）；Technische Universität Darmstadt（达姆施塔特工业大学）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（德国重离子研究中心）；Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）
A compressible liquid-drop model (CLDM) is used to correlate uncertainties associated with the properties of the neutron star (NS) crust with theoretical estimates of the uncertainties associated with the equation of state (EOS) of homogeneous neutron and nuclear matter. For the latter, we employ recent calculations based on Hamiltonians constructed using Chiral Effective Field theory. Fits to experimental nuclear masses are employed to constrain the CLDM further, and we find that they disfavor some of the Chiral Hamiltonians. The CLDM allows us to study the complex interplay between bulk, sur…
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…
We analyze experimental data of nuclear structure-function ratios F_2^A/F_2^{A'} and Drell-Yan cross section ratios for obtaining optimum parton distribution functions (PDFs) in nuclei. Then, uncertainties of the nuclear PDFs are estimated by the Hessian method. Valence-quark distributions are determined by the F_2 data at large x; however, the small-x part is not obvious from the data. On the other hand, the antiquark distributions are determined well at x~0.01 from the F_2 data and at x~0.1 by the Drell-Yan data; however, the large-x behavior is not clear. Gluon distributions cannot be fixed…
What is the origin of nuclear clustering and how does it emerge from the nuclear interaction? While there is ample experimental evidence for this phenomenon, its theoretical characterization directly from nucleons as degrees of freedom remains a challenge, making it difficult to improve nuclear forces using clustering observables. In this work, a simple ratio of energies based on effective scale arguments is proposed to assess the quality of nuclear forces on alpha clustering (${ {}^{4}\text{He} }$) in bound and narrow ground-state nuclei. The proposed clustering ratio is parameter-free and co…
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…
Despite great theoretical efforts the NN interaction can only be determined with a finite precision, implying an error upper bound for nuclear masses. We analyze for the first time the problem of estimating the systematic errors related to the form of the potential and their impact on nuclear binding. To this end we exploit the concept of coarse grained interactions to typical nuclear wavelengths. Our estimate gives an error of 0.1-0.4 MeV for the binding energy per particle and paves the way for ab initio calculations tailored to such a precision.
Theoretical estimates for the half life of neutrinoless double beta decay in candidate nuclei are affected by both particle and nuclear physics uncertainties, which may complicate the interpretation of decay signals or limits. We study such uncertainties and their degeneracies in the following context: three nuclei of great interest for large-scale experiments (76-Ge, 130-Te, 136-Xe), two representative particle physics mechanisms (light and heavy Majorana neutrino exchange), and a large set of nuclear matrix elements (NME), computed within the quasiparticle random phase approximation (QRPA). …
The energy levels of light hypernuclei are experimentally accessible observables that contain valuable information about the interaction between hyperons and nucleons. In this work we study strangeness $S = -1$ systems $^{3,4}_Λ$H and $^{4,5}_Λ$He using the ab initio no-core shell model (NCSM) with realistic interactions obtained from chiral effective field theory ($χ$EFT). In particular, we quantify the finite precision of theoretical predictions that can be attributed to nuclear physics uncertainties. We study both the convergence of the solution of the many-body problem (method uncertainty)…
The hypertriton bound state is relevant for inference of knowledge about the hyperon-nucleon (YN) interaction. In this work we compute the binding energy of the hypertriton using the ab initio hypernuclear no-core shell model (NCSM) with realistic interactions derived from chiral effective field theory. In particular, we employ a large family of nucleon-nucleon interactions with the aim to quantify the theoretical precision of predicted hypernuclear observables arising from nuclear-physics uncertainties. The three-body calculations are performed in a relative Jacobi-coordinate harmonic oscilla…
Nuclear astrophysics and californium fission neutron spectrum averaged cross sections and their uncertainties for ENDF materials have been calculated. Absolute values were deduced with Maxwellian and Mannhart spectra, while uncertainties are based on ENDF/B-VII.1, JEFF-3.1.2, JENDL-4.0 and Low-Fidelity covariances. These quantities are compared with available data, independent benchmarks, EXFOR library, and analyzed for a wide range of cases. Recommendations for neutron cross section covariances are given and implications are discussed.
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…
Ab initio calculations in Nuclear physics for atomic nuclei require a specific knowledge of the interactions among their constituents, protons and neutrons. In particular, NN interactions can be constrained down to scale resolutions of $Δr \sim 0.6 {\rm fm}$ from the study of phase shifts below the pion production threshold. However, this allows for ambiguities and uncertainties which have an impact on finite nuclei, nuclear- and neutron-matter properties. On the other hand the nuclear many body problem is intrinsically difficult and the computational cost increases with numerical precision an…
Background: Modern ab initio theory combined with high-quality nucleon-nucleon (NN) and three-nucleon (3N) interactions from chiral effective field theory (EFT) can provide a predictive description of low-energy light-nuclei reactions relevant for astrophysics and fusion-energy applications. However, the high cost of computations has so far impeded a complete analysis of the uncertainty budget of such calculations. Purpose: Starting from NN potentials up to fifth order (N4LO) combined with leading-order 3N forces, we study how the order-by-order convergence of the chiral expansion and confiden…
\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…
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)，GSI 重离子研究中心有限公司）；National Center for Computational Sciences, Oak Ridge National Laboratory（国家计算科学中心，橡树岭国家实验室）；Physics Division, Oak Ridge National Laboratory（物理部，橡树岭国家实验室）；Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）
There is an increasing interest in quantifying the predictive power in nuclear structure calculations. We discuss how both experimental and systematic errors at the NN-level can be used to estimate the theoretical uncertainties by rather simple means and without solving the full nuclear many body problem. We emphasize the role of effective interactions defined by coarse graining the NN potential to length scales of the order of the minimal de Broglie wavelength probed between nucleons in nuclei. We find an a priori error of \DeltaB/A \sim 0.1 - 0.4MeV for the binding energy per particle throug…
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…
I construct a model of the inner crust of neutron stars using interactions from chiral effective field theory (EFT) in order to calculate its equation of state (EOS), shear properties, and the spectrum of crustal shear modes. I systematically study uncertainties associated with the nuclear physics input, the crust composition, and neutron entrainment, and estimate their impact on crustal shear properties and the shear-mode spectrum. I find that the uncertainties originate mainly in two sources: The neutron-matter EOS and neutron entrainment. I compare the spectrum of crustal shear modes to obs…
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…
Nuclear parton distribution functions (NPDFs) are determined by global analyses of experimental data on structure-function ratios F_2^A/F_2^{A'} and Drell-Yan cross-section ratios σ_{DY}^A/σ_{DY}^{A'}. The analyses are done in the leading order (LO) and next-to-leading order (NLO) of running coupling constant α_s. Uncertainties of the NPDFs are estimated in both LO and NLO for finding possible NLO improvement. Valence-quark distributions are well determined, and antiquark distributions are also determined at x<0.1. However, the antiquark distributions have large uncertainties at x>0.2. Gluon m…
High precision measurements of the parity-violating asymmetry in polarized electron scattering from nuclei can be used to extract information on nuclear and nucleon structure or to determine Standard Model couplings and higher-order radiative corrections. To this end, low uncertainties are also required in the effects that inevitably arise from modeling the underlying nuclear structure. An experimental precision of a few tenths of a percent may be attainable for the asymmetry if the appropriate kinematic range is chosen, as will be discussed here for the case of $^{12}$C. And given this, the d…
We evaluate the uncertainties due to nuclear effects in global fits of proton parton distribution functions (PDFs) that utilise deep-inelastic scattering and Drell-Yan data on deuterium targets. To do this we use an iterative procedure to determine proton and deuteron PDFs simultaneously, each including the uncertainties in the other. We apply this procedure to determine the nuclear uncertainties in the SLAC, BCDMS, NMC and DYE866/NuSea fixed target deuteron data included in the NNPDF3.1 global fit. We show that the effect of the nuclear uncertainty on the proton PDFs is small, and that the in…
According to the Hugenholtz-Van Hove theorem, the nuclear symmetry energy $S(ρ)$ and its slope $L(ρ)$ at arbitrary densities can be decomposed in terms of the density and momentum dependence of the single-nucleon potentials in isospin-asymmetric nuclear matter which are potentially accessible to experiment. We quantify the correlations between several well-known isovector observables and $L(ρ)$ to locate the density range in which each isovector observable is most sensitive to the density dependence of the $S(ρ)$. We then study the correlation coefficients between those isovector observables a…
Reliable predictions of nuclear properties are needed as much to answer fundamental science questions as in applications such as reactor physics or data evaluation. Nuclear density functional theory is currently the only microscopic, global approach to nuclear structure that is applicable throughout the nuclear chart. In the past few years, a lot of effort has been devoted to setting up a general methodology to assess theoretical uncertainties in nuclear DFT calculations. In this paper, we summarize some of the recent progress in this direction. Most of the new material discussed here will be …
The nuclear modification factor R_{AA} measured in Pb+Pb collisions at the Large Hadron Collider (LHC) suggests that the jet-medium coupling in a Quark-Gluon Plasma at LHC energies is reduced as compared to energies reached at the Relativistic Heavy Ion Collider (RHIC). We estimate the reduction factor using a simple generic energy-loss model and find that the jet-medium coupling at the LHC is approximately 10% smaller than at RHIC. Moreover, we examine different jet-energy loss prescriptions with $dE/dx\sim E^a$ and show that the measured momentum dependence of the nuclear modification factor…
To shed light on the deuteron radius puzzle we analyze the theoretical uncertainties of the nuclear structure corrections to the Lamb shift in muonic deuterium. We find that the discrepancy between the calculated two-photon exchange correction and the corresponding experimentally inferred value by Pohl et al. [1] remain. The present result is consistent with our previous estimate, although the discrepancy is reduced from 2.6 $σ$ to 2 $σ$. The error analysis includes statistic as well as systematic uncertainties stemming from the use of nucleon-nucleon interactions derived from chiral effective…
Employing four different parametrization of the pairing plus multipolar type of effective two-body interaction and three different parametrizations of Jastrow-type of short range correlations, the uncertainties in the nuclear transition matrix elements $M_{N}^{(0ν)}$ due to the exchange of heavy Majorana neutrino for the $0^{+}\rightarrow 0^{+}$ transition of neutrinoless double beta decay of $^{94}$Zr, $^{96}$Zr, $^{98}$Mo, $^{100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd isotopes in the PHFB model are estimated to be around 25%. Excluding the nuclear transition matrix elemen…
Quantifying uncertainty in physics-based predictions of rare-isotope production cross sections via Bayesian-inspired model averaging across nuclear mass tables
Facility for Rare Isotope Beams, Michigan State University（稀有同位素束流设施，密歇根州立大学）
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 charge radius of the deuteron (D), was recently determined to three times the precision compared with previous measurements using the measured Lamb shift in muonic deuterium (muD). However, the muD value is 5.6 $σ$ smaller than the world averaged CODATA-2014 value [1]. To shed light on this discrepancy we analyze the uncertainties of the nuclear structure calculations of the Lamb shift in muD and conclude that nuclear theory uncertainty is not likely to be the source of the discrepancy.
Neutrino oscillation experiments use heavy nuclear targets to achieve sufficient interaction rates. Nuclear effects are introduced in the experimental environment by the use of these targets and need to be quantified as they add to the systematic errors. In the low energy region(around 1 GeV) multinucleon events are also present along with Quasi Elastic(QE) and Delta interactions. Therefore if these multinucleon events are not incorporated in the data set properly, we end up with an inaccurate reconstruction of neutrino energy. In our work, we have illustrated the importance of incorporation o…
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…
Bayesian approach for many-body uncertainties in nuclear structure: Many-body perturbation theory for finite nuclei
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)，GSI 重离子研究中心有限公司）；Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）
The European Lead-Cooled Training Reactor (ELECTRA) has been proposed as a training reactor for fast systems within the Swedish nuclear program. It is a low-power fast reactor cooled by pure liquid lead. In this work, we propagate the uncertainties in Pu-239 transport data to uncertainties in the fuel inventory of ELECTRA during the reactor life using the Total Monte Carlo approach (TMC). Within the TENDL project the nuclear models input parameters were randomized within their uncertainties and 740 Pu-239 nuclear data libraries were generated. These libraries are used as inputs to reactor code…
Parameters of the nuclear density functional theory (DFT) models are usually adjusted to experimental data. As a result they carry certain theoretical error, which, as a consequence, carries out to the predicted quantities. In this work we address the propagation of theoretical error, within the nuclear DFT models, from the model parameters to the predicted observables. In particularly, the focus is set on the Skyrme energy density functional models.
Nucleosynthesis beyond Fe poses additional challenges not encountered when studying astrophysical processes involving light nuclei. Generally higher temperatures and nuclear level densities lead to stronger contributions of transitions on excited target states. This may prevent cross section measurements to determine stellar reaction rates and theory contributions remain important. Furthermore, measurements often are not feasible in the astrophysically relevant energy range. Sensitivity analysis allows not only to determine the contributing nuclear properties but also is a handy tool for exper…
In this article we obtain a new set of nuclear parton distribution functions (nuclear PDFs) at next-to-leading order and next-to-next-to-leading order accuracy in perturbative QCD. The common nuclear deep-inelastic scattering (DIS) data analyzed in our study are complemented by the available charged-current neutrino DIS data with nuclear targets and data from Drell-Yan cross-section measurements for several nuclear targets. In addition, the most recent DIS data from the Jefferson Lab CLAS and Hall C experiments are also added to our data sample. For these specific datasets, we consider the imp…
We critically examine uncertainties in parton distribution functions (PDFs) at large x arising from nuclear effects in deuterium F2 structure function data. Within a global PDF analysis, we assess the impact on the PDFs from uncertainties in the deuteron wave function at short distances and nucleon off-shell effects, the use of relativistic kinematics, as well as the use of less a restrictive parametrization of the d/u ratio. We find that in particular the d-quark and gluon PDFs vary significantly with the choice of nuclear model. We highlight the impact of these uncertainties on the determina…
