arXiv subjects

Kai Hebeler

Publications and source records attributed to Kai Hebeler.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Monte Carlo Calculations of Light Nuclei with Fully Propagated Theoretical Uncertainties

We report on the first quantum Monte Carlo calculations of helium isotopes with fully propagated theoretical uncertainties from the interaction to the many-body observables. To achieve this, we build emulators for solutions to the Faddeev equations for the binding energy and Gamow-Teller matrix element of $^3\text{H}$, as well as for auxiliary-field diffusion Monte Carlo calculations of the $^4\text{He}$ charge radius, employing local two- and three-body interactions up to next-to-next-to-leading order in chiral effective field theory. We use these emulators to determine the posterior distributions for all low-energy couplings that appear in the interaction up to this order using Bayesian inference while accounting for theoretical uncertainties. We then build emulators for auxiliary-field diffusion Monte Carlo for helium isotopes and propagate the full posterior distributions to these systems. Our approach serves as a framework for $\textit{ab initio}$ studies of atomic nuclei with consistently treated and correlated theoretical uncertainties.

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arXiv2026

Equation of state and neutron star properties with new mass-radius constraints from PSR~J1614--2230, PSR~J2124--3358, and 47~Tuc~X7

We study the impact of new mass-radius information from PSR J1614-2230, PSR J2124-3358, and 47 Tuc X7 in a combined equation of state inference based on chiral effective field theory constraints at nuclear densities and using different high-density extensions, including perturbative QCD constraints. The largest impact stems from the heavy-mass PSR J1614-2230 star, which shifts heavy neutron stars to smaller radii by around 0.4 km. Moreover, the combined astrophysical NICER, LIGO/Virgo, and X-ray information drives the radius posterior to a more data-driven distribution, which is less sensitive to the high-density extension. For the equation of state, the new mass-radius information significantly tightens the pressure and speed-of-sound posterior distributions, especially around three times saturation density. Finally, we make predictions for the poorly constrained masses of PSR J2124-3358 and 47 Tuc X7 based on the combined equation of state analysis and the other astrophysical sources.

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arXiv2026

Hartree-Fock emulators for nuclei: Application to charge radii of $^{48,52}$Ca

Understanding the emergence of complex structures of nuclei from chiral effective field theory (EFT) is a central challenge. The large number of low-energy couplings (LECs) in the EFT expansion and the significant cost of $\textit{ab initio}$ many-body calculations render large-scale sensitivity studies of many-body observables computationally prohibitive, necessitating the use of emulators as low-cost surrogates. In this work, we study a Hartree-Fock emulator based on eigenvector continuation to investigate trends in nuclear charge radii of neutron-rich calcium isotopes. We systematically vary the five LECs entering the leading three-nucleon (3N) interactions, and demonstrate the precision of the emulator through cross-validation over a wide parameter space. Our findings indicate that large charge radius increase from $^{48}$Ca to $^{52}$Ca is likely not explained by variations of the leading 3N couplings. This suggests that other effects, such as sensitivities to chiral two-nucleon interactions or neglected many-body effects, e.g., associated with nuclear collectivity, play an important role.

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arXiv2026

Astrophysics equation of state inference with Bayesian chiral effective field theory uncertainties

We investigate Bayesian chiral effective field theory ($χ$EFT) uncertainties, which assign a statistical interpretation to equation of state (EOS) distributions near nuclear saturation density, n$_0$, as well as constraints from perturbative quantum chromodynamics (pQCD) to Bayesian EOS inference from LIGO/Virgo, NICER and pulsar mass observations. The tails of the $χ$EFT uncertainties allow for broader pressure ranges in our priors, but large parts of these are excluded by the astrophysical observations, so that the EOS and the resulting mass-radius posteriors are still very consistent with our earlier work. Within our broad prior ranges, we observe a clear stiffening of the EOS at $n \gtrsim 3 n_0$. Moreover, the impact of the pQCD constraints on the posterior EOS and mass-radius range is negligible due to the astrophysics constraints. Exploiting the strong correlation between pure neutron matter and matter in beta equilibrium, we infer the symmetry energy slope parameter $L$ from astrophysics. For the $68\%$ credible interval, we obtain $L=42.6-52$ MeV and $L=44.2-56.7$ MeV using piecewise-polytrope and speed-of-sound high-density extensions, respectively. The $L$ posterior is mainly driven by the combination of GW170817 LIGO/Virgo and PSR J0740+6620, PSR J0437-4715, and PSR J0614-3329 NICER observations.

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arXiv2026

Exploring quark mass dependent three-nucleon forces in medium-mass nuclei

Recently, new quark mass dependent three-nucleon (3N) forces have been identified, whose contributions in nuclear matter exceed expectations of Weinberg power-counting arguments. In this work, we investigate the impact of the most dominant new interaction term, characterized by the coupling $F_2$, in ab initio calculations of medium-mass nuclei. For this, we combine the new $F_2$ interaction with established 3N interactions up to next-to-next-to-leading order (N$^2$LO) and next-to-next-to-next-to-leading order (N$^3$LO) in chiral effective field theory. We explore two fit strategies for the low-energy couplings. The first is based only on few-body observables, while the second also incorporates information from $^{16}$O. Generally, we find that the $F_2$ interaction has a significant impact on energies and radii, however mainly due to changes in the short-range couplings. Overall, we do not find systematic improvements in the reproduction of medium-mass nuclei when the additional $F_2$ interaction is included.

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arXiv2026

Equation-of-state-informed pulse profile modeling

NICER has enabled mass-radius inferences for pulsars using pulse profile modeling (PPM), providing constraints on the equation of state (EOS) of cold, dense matter. To date, PPM and EOS inference have been carried out as two separate steps, with the former using EOS-agnostic priors. This approach has several drawbacks. Ideally, one would perform a fully hierarchical Bayesian inference where the pulse profile and EOS model parameters are jointly fit, but implementing such a framework is complex and computationally demanding. Here, we present an intermediate solution introducing an EOS-informed prior on mass-radius into the existing PPM pipeline using normalizing flows. By focusing on the parameter space consistent with certain EOSs, this approach both tightens constraints on neutron star parameters while reducing computational costs and requiring minimal additional implementation effort. We test this approach on two pulsars, PSR J0740+6620 and PSR J0437-4715, and with two EOS model families: a model based on the speed of sound inside the neutron star interior (CS) and a piecewise-polytropic (PP) model. Both EOS models implement constraints from chiral effective field theory calculations of dense matter. For both pulsar datasets, the inferred radius credible intervals are narrower than in the EOS-agnostic case, with CS favoring smaller radii and PP favoring larger radii. For PSR J0437-4715, the EOS-informed priors reveal a new, more extreme geometric mode that is statistically favored but physically questionable. Including the PPM posteriors in the subsequent EOS inference further tightens the mass-radius posteriors through the chiral effective field theory constraints. However, there is also a sensitivity to the high-density extensions, where the PP (CS) model produces a shift towards larger (smaller) radii and corresponding stiffening (softening) of the pressure-energy density relation.

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arXiv2026

Bayesian approach for many-body uncertainties in nuclear structure: Many-body perturbation theory for finite nuclei

A comprehensive assessment of theoretical uncertainties defines an important frontier in nuclear structure research. Ideally, theory predictions include uncertainty estimates that take into account truncation effects from both the interactions and the many-body expansion. While the uncertainties from the expansion of the interactions within effective field theories have been studied systematically using Bayesian methods, many-body truncations are usually addressed by expert assessment. In this work we use a Bayesian framework to study many-body uncertainties within many-body perturbation theory applied to finite nuclei. Our framework is applied to a broad range of nuclei across the nuclear chart calculated from two- and three-nucleon interactions based on chiral effective field theory. These developments represent a step towards a more complete and systematic quantification of uncertainties in \emph{ab initio} calculations of nuclei.

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arXiv2025

Equation of state and Fermi liquid properties of dense matter based on chiral effective field theory interactions

We present results for the equation of state of symmetric nuclear matter and pure neutron matter obtained in many-body-perturbation theory (MBPT) up to third order, based on various chiral two- and three-nucleon interactions used in ab initio calculations of nuclei. We extract equation of state properties, such as the incompressibility and the symmetry energy, and discuss estimates of the theoretical uncertainties due to neglected higher-order contributions in the MBPT expansion as well as the chiral effective field theory expansion. In addition, we discuss the Fermi liquid approach to nuclear matter. We calculate all two- and three-nucleon contributions to the quasiparticle interaction up to second order in MBPT and present results for the Landau parameters, effective mass, and speed of sound for pure neutron matter.

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arXiv2025

Dense Matter in Neutron Stars with eXTP

In this White Paper, we present the potential of the enhanced X-ray Timing and Polarimetry (eXTP) mission to constrain the equation of state of dense matter in neutron stars, exploring regimes not directly accessible to terrestrial experiments. By observing a diverse population of neutron stars - including isolated objects, X-ray bursters, and accreting systems - eXTP's unique combination of timing, spectroscopy, and polarimetry enables high-precision measurements of compactness, spin, surface temperature, polarimetric signals, and timing irregularity. These multifaceted observations, combined with advances in theoretical modeling, pave the way toward a comprehensive description of the properties and phases of dense matter from the crust to the core of neutron stars. Under development by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Sciences, the eXTP mission is planned to be launched in early 2030.

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arXiv2024

Constraining the dense matter equation of state with new NICER mass-radius measurements and new chiral effective field theory inputs

Pulse profile modeling of X-ray data from NICER is now enabling precision inference of neutron star mass and radius. Combined with nuclear physics constraints from chiral effective field theory ($χ$EFT), and masses and tidal deformabilities inferred from gravitational wave detections of binary neutron star mergers, this has lead to a steady improvement in our understanding of the dense matter equation of state (EOS). Here we consider the impact of several new results: the radius measurement for the 1.42$\,M_\odot$ pulsar PSR J0437$-$4715 presented by Choudhury et al. (2024), updates to the masses and radii of PSR J0740$+$6620 and PSR J0030$+$0451, and new $χ$EFT results for neutron star matter up to 1.5 times nuclear saturation density. Using two different high-density EOS extensions -- a piecewise-polytropic (PP) model and a model based on the speed of sound in a neutron star (CS) -- we find the radius of a 1.4$\,M_\odot$ (2.0$\,M_\odot$) neutron star to be constrained to the 95% credible ranges $12.28^{+0.50}_{-0.76}\,$km ($12.33^{+0.70}_{-1.34}\,$km) for the PP model and $12.01^{+0.56}_{-0.75}\,$km ($11.55^{+0.94}_{-1.09}\,$km) for the CS model. The maximum neutron star mass is predicted to be $2.15^{+0.14}_{-0.16}\,$$M_\odot$ and $2.08^{+0.28}_{-0.16}\,$$M_\odot$ for the PP and CS model, respectively. We explore the sensitivity of our results to different orders and different densities up to which $χ$EFT is used, and show how the astrophysical observations provide constraints for the pressure at intermediate densities. Moreover, we investigate the difference $R_{2.0} - R_{1.4}$ of the radius of 2$\,M_\odot$ and 1.4$\,M_\odot$ neutron stars within our EOS inference.

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arXiv2024

Eigenvector continuation for the pairing Hamiltonian

The development of emulators for the evaluation of many-body observables has gained increasing attention over the last years. In particular the framework of eigenvector continuation (EC) has been identified as a powerful tool when the Hamiltonian admits for a parametric dependence. By training the emulator on a set of training data the many-body solution for arbitrary parameter values can be robustly predicted in many cases. Furthermore, it can be used to resum perturbative expansions that otherwise diverge. In this work, we apply EC to the pairing Hamiltonian and show that EC-resummed perturbation theory is in qualitative agreement with the exact solution and that EC-based emulators robustly predict the ground-state energy once the training data are chosen appropriately. In particular the phase transition from the normal to the superfluid regime is quantitatively predicted using a very low number of training points.

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arXiv2023

Constraints on strong phase transitions in neutron stars

We study current bounds on strong first-order phase transitions (PTs) along the equation of state (EOS) of dense strongly interacting matter in neutron stars, under the simplifying assumption that on either side of the PT the EOS can be approximated by a simple polytropic form. We construct a large ensemble of possible EOSs of this form, anchor them to chiral effective field theory calculations at nuclear density and perturbative QCD at high densities, and subject them to astrophysical constraints from high-mass pulsars and gravitational-wave observations. Within this setup, we find that a PT permits neutron-star solutions with larger radii, but only if the transition begins below twice nuclear saturation density. We also identify a large parameter space of allowed PTs currently unexplored by numerical-relativity studies. Additionally, we locate a small region of parameter space allowing twin-star solutions, though we find them to only marginally pass the current astrophysical constraints. Finally, we find that sizeable cores of high-density matter beyond the PT may be located in the centers of some stable neutron stars, primarily those with larger masses.

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arXiv2022

Excited states from eigenvector continuation: the anharmonic oscillator

Eigenvector continuation (EC) has recently attracted a lot attention in nuclear structure and reactions as a variational resummation tool for many-body expansions. While previous applications focused on ground-state energies, excited states can be accessed on equal footing. This work is dedicated to a detailed understanding of the emergence of excited states from the eigenvector continuation approach. For numerical applications the one-dimensional quartic anharmonic oscillator is investigated, which represents a strongly non-perturbative quantum system where the use of standard perturbation techniques break down. We discuss how different choices for the construction of the EC manifold affect the quality of the EC resummation and investigate in detail the results from EC for excited states compared to results from a full diagonalization as a function of the basis-space size.

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arXiv2022

Neutron-deuteron scattering cross-sections with chiral $NN$ interactions using wave-packet continuum discretization

In this work we present a framework that allows to solve the Faddeev equations for three-nucleon scattering using the wave-packet continuum-discretization method. We perform systematic benchmarks using results in the literature and study in detail the convergence of this method with respect to the number of wave packets. We compute several different elastic neutron-deuteron scattering cross-section observables for a variety of energies using chiral nucleon-nucleon interactions. For the interaction $\text{N2LO}_{\text{opt}}$ we find good agreement with data for nucleon scattering-energies $E_\text{Lab} \leq 70$ MeV and a slightly larger maximum of the neutron analyzing power $A_y(n)$ at $E_\text{Lab} = 10$ MeV and 21 MeV compared with other interactions. This work represents a first step towards a systematic inclusion of three-nucleon scattering observables in the construction of next-generation nuclear interactions.

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arXiv2021

Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter

Recent advances in nuclear structure theory have significantly enlarged the accessible part of the nuclear landscape via ab initio many-body calculations. These developments open new ways for microscopic studies of light, medium-mass and heavy nuclei as well as nuclear matter and represent an important step toward a systematic and comprehensive understanding of atomic nuclei across the nuclear chart. While remarkable agreement has been found between different many-body methods for a given nuclear Hamiltonian, the comparison with experiment and the understanding of theoretical uncertainties are still important open questions. The observed discrepancies to experiment indicate deficiencies in presently used nuclear interactions and operators. Chiral effective field theory (EFT) allows to systematically derive contributions to nucleon-nucleon (NN), three-nucleon (3N) and higher-body interactions including estimates of theoretical uncertainties. While the treatment of NN interactions in many-body calculations is well established, the calculation of 3N interactions and their incorporation in ab initio frameworks is still a frontier. This work reviews in detail recent and current developments on the derivation and implementation of improved 3N interactions and provides a comprehensive introduction to fundamental methods for their practical calculation and representation. We further give an overview of novel and established methods that facilitate the inclusion and treatment of 3N interactions in ab initio nuclear structure frameworks and present a selection of the latest calculations of atomic nuclei as well as nuclear matter based on state-of-the-art nuclear NN and 3N interactions derived within chiral EFT. Finally, we discuss ongoing efforts, open questions and future directions.

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arXiv2019

Improved many-body expansions from eigenvector continuation

Quantum many-body theory has witnessed tremendous progress in various fields, ranging from atomic and solid-state physics to quantum chemistry and nuclear structure. Due to the inherent computational burden linked to the ab initio treatment of microscopic fermionic systems, it is desirable to obtain accurate results through low-order perturbation theory. In atomic nuclei however, effects such as strong short-range repulsion between nucleons can spoil the convergence of the expansion and make the reliability of perturbation theory unclear. Mathematicians have devised an extensive machinery to overcome the problem of divergent expansions by making use of so-called resummation methods. In large-scale many-body applications such schemes are often of limited use since no a priori analytical knowledge of the expansion is available. We present here eigenvector continuation as an alternative resummation tool that is both efficient and reliable because it is based on robust and simple mathematical principles.

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arXiv2019

Family of Chiral Two- plus Three-Nucleon Interactions for Accurate Nuclear Structure Studies

We present a family of nucleon-nucleon (NN) plus three-nucleon (3N) interactions up to N3LO in the chiral expansion that provides an accurate ab initio description of ground-state energies and charge radii up to the medium-mass regime with quantified theory uncertainties. Starting from the NN interactions proposed by Entem, Machleidt and Nosyk, we construct 3N interactions with consistent chiral order, non-local regulator, and cutoff value and explore the dependence of nuclear observables over a range of mass numbers on the 3N low-energy constants. By fixing these constants using the 3-H and 16-O ground-state energies, we obtain interactions that robustly reproduce experimental energies and radii for large range from p-shell nuclei to the nickel isotopic chain and resolve many of the deficiencies of previous interactions. Based on the order-by-order convergence and the cutoff dependence of nuclear observables, we assess the uncertainties due the interaction, which yield a significant contribution to the total theory uncertainty.

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arXiv2018

Dense matter with eXTP

In this White Paper we present the potential of the Enhanced X-ray Timing and Polarimetry (eXTP) mission for determining the nature of dense matter; neutron star cores host an extreme density regime which cannot be replicated in a terrestrial laboratory. The tightest statistical constraints on the dense matter equation of state will come from pulse profile modelling of accretion-powered pulsars, burst oscillation sources, and rotation-powered pulsars. Additional constraints will derive from spin measurements, burst spectra, and properties of the accretion flows in the vicinity of the neutron star. Under development by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Science, the eXTP mission is expected to be launched in the mid 2020s.

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