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The in-medium similarity renormalization group (IMSRG) is a powerful and flexible many-body method to compute the structure of nuclei starting from nuclear forces. Recent developments have extended the IMSRG from its standard truncation at the normal-ordered two-body level, the IMSRG(2), to a precision approximation including normal-ordered three-body operators, the IMSRG(3)-$N^7$. This improvement provides a more precise solution to the many-body problem and makes it possible to quantify many-body uncertainties in IMSRG calculations. We explore the structure of $^{44,48,52}$Ca using the IMSRG(3)-$N^7$, focusing on understanding existing discrepancies of the IMSRG(2) to experimental results. We find a significantly better description of the first $2^+$ excitation energy of $^{48}Ca$, improving the description of the shell closure at $N=28$. At the same time, we find that the IMSRG(3)-$N^7$ corrections to charge radii do not resolve the systematic underprediction of the puzzling large charge radius difference between $^{52}$Ca and $^{48}$Ca. We present estimates of many-body uncertainties of IMSRG(2) calculations applicable also to other systems based on the size extensivity of the method., Comment: 15 pages, 8 figures, 1 table

Neutron matter is an important many-body system that provides valuable constraints for the equation of state (EOS) of neutron stars. Neutron-matter calculations employing chiral effective field theory (EFT) interactions have been extensively used for this purpose. Among the various many-body methods, quantum Monte Carlo (QMC) methods stand out due to their nonperturbative nature and the achievable precision. However, QMC methods require local interactions as input, which leads to the appearance of stronger regulator artifacts as compared to non-local interactions. To circumvent this, we employ large-cutoff interactions derived within chiral EFT (400 MeV $\leq \Lambda_c \leq$ 700 MeV) for studies of pure neutron matter. These interactions have been adjusted to nucleon-nucleon scattering phase shifts, the triton binding energy, as well as the triton beta-decay half life. We find that regulator artifacts significantly decrease with increasing cutoff, leading to a significant reduction of uncertainties in the neutron-matter EOS. We discuss implications for the symmetry energy and demonstrate how our new calculations lead to a reduction in the theoretical uncertainty of predicted neutron-star radii by up to 30% for low-mass stars., Comment: 7 pages, 3 figures

Neutron stars contain neutron-rich matter with around 5% protons at nuclear saturation density. In this Letter, we consider equilibrium between bulk phases of matter based on asymmetric nuclear matter calculations using chiral effective field theory interactions rather than, as has been done in the past, by interpolation between the properties of symmetric nuclear matter and pure neutron matter. Neutron drip (coexistence of nuclear matter with pure neutrons) is well established, but from earlier work it is unclear whether proton drip (equilibrium between two phases, both of which contain protons and neutrons) is possible. We find that proton drip is a robust prediction of any physically reasonable equation of state, but that it occurs over a limited region of densities and proton fractions. An analytical model based on expanding the energy in powers of the proton density, rather than the neutron excess, is able to account for these features of the phase diagram., Comment: 6 pages, 4 figures, published version

Neutron-rich nuclei provide important insights to nuclear forces and to the nuclear equation of state. Advances in ab initio methods combined with new opportunities with rare isotope beams enable unique explorations of their properties based on nuclear forces applicable over the entire nuclear chart. In this Letter, we develop novel chiral low-resolution interactions that accurately describe bulk properties from $^{16}$O to $^{208}$Pb. With these, we investigate density distributions and neutron skins of neutron-rich nuclei. Our results show that neutron skins are narrowly predicted over all nuclei with interesting sensitivities for the most extreme, experimentally unexplored cases., Comment: 8 pages, 7 figures including supplemental material

We investigate the effects of two-body currents on magnetic dipole moments of medium-mass and heavy nuclei using the valence-space in-medium similarity renormalization group with chiral effective field theory interactions and currents. Focusing on near doubly magic nuclei from oxygen to bismuth, we have found that the leading two-body currents globally improve the agreement with experimental magnetic moments. Moreover, our results show the importance of multi-shell effects for $^{41}$Ca, which suggest that the $Z=N=20$ gap in $^{40}$Ca is not as robust as in $^{48}$Ca. The increasing contribution of two-body currents in heavier systems is explained by the operator structure of the center-of-mass dependent Sachs term., Comment: 6 pages, 4 figures, supplemental material included

Many-body approaches for atomic nuclei generally rely on a basis expansion of the nuclear states, interactions, and current operators. In this work, we derive the representation of the magnetic dipole operator in plane-wave and harmonic-oscillator basis states, as needed for Faddeev calculations of few-body systems or many-body calculations within, e.g., the no-core shell model, the in-medium renormalization group, coupled-cluster theory, or the nuclear shell model. We focus in particular on the next-to-leading-order two-body contributions derived from chiral effective field theory. We provide detailed benchmarks and also comparisons with quantum Monte Carlo results for three-body systems. The derived operator matrix elements represent the basic input for studying magnetic properties of atomic nuclei based on chiral effective field theory., Comment: 17 pages, 7 figures

Ab initio calculations for nuclei and nuclear matter are limited by the computational requirements of processing large data objects. In this work, we develop low-rank singular value decompositions for chiral three-nucleon interactions, which dominate these limitations. In order to handle the large dimensions in representing three-body operators, we use randomized decomposition techniques. We study in detail the sensitivity of different three-nucleon topologies to low-rank matrix factorizations. The developed low-rank three-nucleon interactions are benchmarked in Faddeev calculations of the triton and ab initio calculations of medium-mass nuclei. Exploiting low-rank properties of nuclear interactions will be particularly important for the extension of ab initio studies to heavier and deformed systems, where storage requirements will exceed the computational capacities of the most advanced high-performance-computing facilities., Comment: 7 pages, 4 figures

Three-nucleon (3N) interactions are key for an accurate solution of the nuclear many-body problem. However, fully taking into account 3N forces constitutes a computational challenge and hence approximate treatments are commonly employed. The method of normal ordering has proven to be a powerful tool that allows to systematically include 3N interactions in an efficient way, but traditional normal-ordering frameworks require the representation of 3N interactions in a large single-particle basis, typically necessitating a truncation of 3N matrix elements. While this truncation has only a minor impact for light and medium-mass nuclei, its effects become sizable for heavier systems and hence limit the scope of \textit{ab initio} calculations. In this work, we present a novel normal-ordering framework that allows to circumvent this limitation by performing the normal ordering directly in a Jacobi basis. We discuss in detail the new framework, benchmark it against established results, and present calculations for ground-state energies and charge radii of heavy nuclei, such as $^{132}$Sn and $^{208}$Pb., Comment: 13 pages, 9 figures, 2 tables, published version

We present a comprehensive investigation of few-nucleon systems as well as light and medium-mass nuclei up to $A=48$ using the current Low Energy Nuclear Physics International Collaboration two-nucleon interactions in combination with the third-order (N$^2$LO) three-nucleon forces. To address the systematic overbinding of nuclei starting from $A \sim 10$ found in our earlier study utilizing the N$^2$LO two- and three-nucleon forces, we take into account higher-order corrections to the two-nucleon potentials up through fifth order in chiral effective field theory. The resulting Hamiltonian can be completely determined using the $A=3$ binding energies and selected nucleon-deuteron cross sections as input. It is then shown to predict other nucleon-deuteron scattering observables and spectra of light $p$-shell nuclei, for which a detailed correlated truncation error analysis is performed, in agreement with experimental data. Moreover, the predicted ground state energies of nuclei in the oxygen isotopic chain from $^{14}$O to $^{26}$O as well as $^{40}$Ca and $^{48}$Ca show a remarkably good agreement with experimental values, given that the Hamiltonian is fixed completely from the $A \leq 3$ data, once the fourth-order (N$^3$LO) corrections to the two-nucleon interactions are taken into account. On the other hand, the charge radii are found to be underpredicted by $\sim 10\%$ for the oxygen isotopes and by almost $20\%$ for $^{40}$Ca and $^{48}$Ca., Comment: 20 pages, 14 figures, 8 tables

It was recently observed that chiral two-body interactions can be efficiently represented using matrix factorization techniques such as the singular value decomposition. However, the exploitation of these low-rank structures in a few- or many-body framework is nontrivial and requires reformulations that explicitly utilize the decomposition format. In this work, we present a general least-square approach that is applicable to different few- and many-body frameworks and allows for an efficient reduction to a low number of singular values in the least-square iteration. We verify the feasibility of the least-square approach by solving the Lippmann-Schwinger equation in factorized form. The resulting low-rank approximations of the $T$ matrix are found to fully capture scattering observables. Potential applications of the least-square approach to other frameworks with the goal of employing tensor factorization techniques are discussed., Comment: 8 pages, 4 figures, 1 table, version accepted at Phys. Rev. C

We calculate the equation of state of asymmetric nuclear matter at finite temperature based on chiral effective field theory interactions to next-to-next-to-next-to-leading order. Our results assess the theoretical uncertainties from the many-body calculation and the chiral expansion. Using a Gaussian process emulator for the free energy, we derive the thermodynamic properties of matter through consistent derivatives and use the Gaussian process to access arbitrary proton fraction and temperature. This enables a first nonparametric calculation of the equation of state in beta equilibrium, and of the speed of sound and the symmetry energy at finite temperature. Moreover, our results show that the thermal part of the pressure decreases with increasing densities., Comment: 7 pages, 5 figures, minor updates and improvements, published version

Ab initio nuclear many-body frameworks require extensive computational resources, especially when targeting heavier nuclei. Importance-truncation (IT) techniques allow to significantly reduce the dimensionality of the problem by neglecting unimportant contributions to the solution of the many-body problem. In this work, we apply IT methods to the nonperturbative in-medium similarity renormalization group (IMSRG) approach and investigate the induced errors for ground-state energies in different mass regimes based on different nuclear Hamiltonians. We study various importance measures, which define the IT selection, and identify two measures that perform best, resulting in only small errors to the full IMSRG(2) calculations even for sizable compression ratios. The neglected contributions are accounted for in a perturbative way and serve as an estimate of the IT-induced error. Overall we find that the IT-IMSRG(2) performs well across all systems considered, while the largest compression ratios for a given error can be achieved when using soft Hamiltonians and for large single-particle bases., Comment: 14 pages, 9 figures, published version

In recent years our understanding of the dense matter equation of state (EOS) of neutron stars has significantly improved by analyzing multimessenger data from radio/X-ray pulsars, gravitational wave events, and from nuclear physics constraints. Here we study the additional impact on the EOS from the jointly estimated mass and radius of PSR J0740+6620, presented in Riley et al. (2021) by analyzing a combined dataset from X-ray telescopes NICER and XMM-Newton. We employ two different high-density EOS parameterizations: a piecewise-polytropic (PP) model and a model based on the speed of sound in a neutron star (CS). At nuclear densities these are connected to microscopic calculations of neutron matter based on chiral effective field theory interactions. In addition to the new NICER data for this heavy neutron star, we separately study constraints from the radio timing mass measurement of PSR J0740+6620, the gravitational wave events of binary neutron stars GW190425 and GW170817, and for the latter the associated kilonova AT2017gfo. By combining all these, and the NICER mass-radius estimate of PSR J0030+0451 we find the radius of a 1.4 solar mass neutron star to be constrained to the 95% credible ranges 12.33^{+0.76}_{-0.81} km (PP model) and 12.18^{+0.56}_{-0.79} km (CS model). In addition, we explore different chiral effective field theory calculations and show that the new NICER results provide tight constraints for the pressure of neutron star matter at around twice saturation density, which shows the power of these observations to constrain dense matter interactions at intermediate densities., Comment: 17 pages, 8 figures; accepted for publication in the Astrophysical Journal Letters

The extension of ab initio quantum many-body theory to higher accuracy and larger systems is intrinsically limited by the handling of large data objects in form of wave-function expansions and/or many-body operators. In this work we present matrix factorization techniques as a systematically improvable and robust tool to significantly reduce the computational cost in many-body applications at the price of introducing a moderate decomposition error. We demonstrate the power of this approach for the nuclear two-body systems, for many-body perturbation theory calculations of symmetric nuclear matter, and for non-perturbative in-medium similarity renormalization group simulations of finite nuclei. Establishing low-rank expansions of chiral nuclear interactions offers possibilities to reformulate many-body methods in ways that take advantage of tensor factorization strategies., Comment: 7 pages, 5 figures, published in Phys. Lett. B

We propose a novel storage scheme for three-nucleon (3N) interaction matrix elements relevant for the normal-ordered two-body approximation used extensively in ab initio calculations of atomic nuclei. This scheme reduces the required memory by approximately two orders of magnitude, which allows the generation of 3N interaction matrix elements with the standard truncation of $E_{\rm 3max}=28$, well beyond the previous limit of 18. We demonstrate that this is sufficient to obtain the ground-state energy of $^{132}$Sn converged to within a few MeV with respect to the $E_{\rm 3max}$ truncation.In addition, we study the asymptotic convergence behavior and perform extrapolations to the un-truncated limit. Finally, we investigate the impact of truncations made when evolving free-space 3N interactions with the similarity renormalization group. We find that the contribution of blocks with angular momentum $J_{\rm rel}>9/2$ to the ground-state energy is dominated by a basis-truncation artifact which vanishes in the large-space limit, so these computationally expensive components can be neglected. For the two sets of nuclear interactions employed in this work, the resulting binding energy of $^{132}$Sn agrees with the experimental value within theoretical uncertainties. This work enables converged ab initio calculations of heavy nuclei., Comment: 16 pages, 11 figures. Appendix is added. Published version

Over the past decade the in-medium similarity renormalization group (IMSRG) approach has proven to be a powerful and versatile ab initio many-body method for studying medium-mass nuclei. So far, the IMSRG was limited to the approximation in which only up to two-body operators are incorporated in the renormalization group flow, referred to as the IMSRG(2). In this work, we extend the IMSRG(2) approach to fully include three-body operators yielding the IMSRG(3) approximation. We use a perturbative scaling analysis to estimate the importance of individual terms in this approximation and introduce truncations that aim to approximate the IMSRG(3) at a lower computational cost. The IMSRG(3) is systematically benchmarked for different nuclear Hamiltonians for ${}^{4}\text{He}$ and ${}^{16}\text{O}$ in small model spaces. The IMSRG(3) systematically improves over the IMSRG(2) relative to exact results. Approximate IMSRG(3) truncations constructed based on computational cost are able to reproduce much of the systematic improvement offered by the full IMSRG(3). We also find that the approximate IMSRG(3) truncations behave consistently with expectations from our perturbative analysis, indicating that this strategy may also be used to systematically approximate the IMSRG(3)., Comment: 23 pages, 10 figures, published version

We present a systematic investigation of few-nucleon systems and light nuclei using the current LENPIC interactions comprising semilocal momentum-space regularized two- and three-nucleon forces up to third chiral order (N$^2$LO). Following our earlier study utilizing the coordinate-space regularized interactions, the two low-energy constants entering the three-body force are determined from the triton binding energy and the differential cross section minimum in elastic nucleon-deuteron scattering. Predictions are made for selected observables in elastic nucleon-deuteron scattering and in the deuteron breakup reactions, for properties of the $A=3$ and $A=4$ nuclei, and for spectra of $p$-shell nuclei up to $A = 16$. A comprehensive error analysis is performed including an estimation of correlated truncation uncertainties for nuclear spectra. The obtained predictions are generally found to agree with experimental data within errors. Similar to the coordinate-space regularized chiral interactions at the same order, a systematic overbinding of heavier nuclei is observed, which sets in for $A \sim 10$ and increases with $A$., Comment: 21 pages, 13 figures, 5 tables, added reference

We study the equation of state of neutron matter at finite temperature based on two- and three-nucleon interactions derived within chiral effective field theory to next-to-next-to-next-to-leading order. The free energy, pressure, entropy, and internal energy are calculated using many-body perturbation theory including terms up to third order around the self-consistent Hartree-Fock solution. We include contributions from three-nucleon interactions without employing the normal-ordering approximation and provide theoretical uncertainty estimates based on an order-by-order analysis in the chiral expansion. Our results demonstrate that thermal effects can be captured remarkably well via a thermal index and a density-dependent effective mass. The presented framework provides the basis for studying the dense matter equation of state at general temperatures and proton fractions relevant for core-collapse supernovae and neutron star mergers., Comment: 14 pages, 14 figures, minor changes, published version

The nuclear many-body problem for medium-mass systems is commonly addressed using wave-function expansion methods that build upon a second-quantized representation of many-body operators with respect to a chosen computational basis. While various options for the computational basis are available, perturbatively constructed natural orbitals recently have been shown to lead to significant improvement in many-body applications yielding faster model-space convergence and lower sensitivity to basis set parameters in large-scale no-core shell model diagonalizations. This work provides a detailed comparison of single-particle basis sets and a systematic benchmark of natural orbitals in nonperturbative many-body calculations using the in-medium similarity renormalization group approach. As a key outcome we find that the construction of natural orbitals in a large single-particle basis enables for performing the many-body calculation in a reduced space of much lower dimension, thus offering significant computational savings in practice that help extend the reach of ab initio methods towards heavier masses and higher accuracy., Comment: 15 pages, 9 figures, published version

We explore constraints on the equation of state (EOS) of neutron-rich matter based on microscopic calculations up to nuclear densities and observations of neutron stars. In a previous work we showed that predictions based on modern nuclear interactions derived within chiral effective field theory and the observation of two-solar-mass neutron stars result in a robust uncertainty range for neutron star radii and the EOS over a wide range of densities. In this work we extend this study, employing both the piecewise polytrope extension from Hebeler et al. as well as the speed of sound model of Greif et al., and show that moment of inertia measurements of neutron stars can significantly improve the constraints on the EOS and neutron star radii., Comment: 11 pages, 10 figures, published version

A direct measurement of the decay width of the excited $0^+_1$ state of $^6$Li using the relative self-absorption technique is reported. Our value of $\Gamma_{\gamma, 0^+_1 \to 1^+_1} = 8.17(14)_\mathrm{stat.}(11)_\mathrm{syst.} \mathrm{eV}$ provides sufficiently low experimental uncertainties to test modern theories of nuclear forces. The corresponding transition rate is compared to the results of ab initio calculations based on chiral effective field theory that take into account contributions to the magnetic dipole operator beyond leading order. This enables a precision test of the impact of two-body currents that enter at next-to-leading order., Comment: 7 pages, 3 figures

The NICER collaboration recently published a joint estimate of the mass and the radius of PSR J0030+0451, derived via X-ray pulse-profile modeling. Raaijmakers et al. (2019) explored the implications of this measurement for the dense matter equation of state (EOS) using two parameterizations of the high-density EOS: a piecewise-polytropic model, and a model based on the speed of sound in neutron stars. In this work we obtain further constraints on the EOS following this approach, but we also include information about the tidal deformability of neutron stars from the gravitational wave signal of the compact binary merger GW170817. We compare the constraints on the EOS to those set by the recent measurement of a 2.14 solar mass pulsar, included as a likelihood function approximated by a Gaussian, and find a small increase in information gain. To show the flexibility of our method, we also explore the possibility that GW170817 was a neutron star-black hole merger, which yields weaker constraints on the EOS., Comment: 18 pages, 8 figures. Accepted for publication in ApJ Letters

Both the mass and radius of the millisecond pulsar PSR J0030+0451 have been inferred via pulse-profile modeling of X-ray data obtained by NASA's NICER mission. In this Letter we study the implications of the mass-radius inference reported for this source by Riley et al. (2019) for the dense matter equation of state (EOS), in the context of prior information from nuclear physics at low densities. Using a Bayesian framework we infer central densities and EOS properties for two choices of high-density extensions: a piecewise-polytropic model and a model based on assumptions of the speed of sound in dense matter. Around nuclear saturation density these extensions are matched to an EOS uncertainty band obtained from calculations based on chiral effective field theory interactions, which provide a realistic description of atomic nuclei as well as empirical nuclear matter properties within uncertainties. We further constrain EOS expectations with input from the current highest measured pulsar mass; together, these constraints offer a narrow Bayesian prior informed by theory as well as laboratory and astrophysical measurements. The NICER mass-radius likelihood function derived by Riley et al. (2019) using pulse-profile modeling is consistent with the highest-density region of this prior. The present relatively large uncertainties on mass and radius for PSR J0030+0451 offer, however, only a weak posterior information gain over the prior. We explore the sensitivity to the inferred geometry of the heated regions that give rise to the pulsed emission, and find a small increase in posterior gain for an alternative (but less preferred) model. Lastly, we investigate the hypothetical scenario of increasing the NICER exposure time for PSR J0030+0451., Comment: Appears in ApJ Letters Focus Issue on NICER Constraints on the Dense Matter Equation of State, 17 pages, 5 figures

First principles calculations of atomic nuclei based on microscopic nuclear forces derived from chiral effective field theory (EFT) have blossomed in the past years. A key element of such ab initio studies is the understanding and quantification of systematic and statistical errors arising from the omission of higher-order terms in the chiral expansion as well as the model calibration. While there has been significant progress in analyzing theoretical uncertainties for nucleon-nucleon scattering observables, the generalization to multi-nucleon systems has not been feasible yet due to the high computational cost of evaluating observables for a large set of low-energy couplings. In this Letter we show that a new method called eigenvector continuation (EC) can be used for constructing an efficient and accurate emulator for nuclear many-body observables, thereby enabling uncertainty quantification in multi-nucleon systems. We demonstrate the power of EC emulation with a proof-of-principle calculation that lays out all correlations between bulk ground-state observables in the few-nucleon sector. On the basis of ab initio calculations for the ground-state energy and radius in 4He, we demonstrate that EC is more accurate and efficient compared to established methods like Gaussian processes., Comment: 8 pages, 6 figures, Python code and input files provided as ancillary material, published version

We study the equation of state of symmetric nuclear matter at zero temperature over a wide range of densities using two complementary theoretical approaches. At low densities up to twice nuclear saturation density, we compute the energy per particle based on modern nucleon-nucleon and three-nucleon interactions derived within chiral effective field theory. For higher densities we derive for the first time constraints in a Fierz-complete setting directly based on quantum chromodynamics using functional renormalization group techniques. We find remarkable consistency of the results obtained from both approaches as they come together in density and the natural emergence of a maximum in the speed of sound $c_S$ at supranuclear densities with a value beyond the asymptotic $c_S^2 = 1/3$. The presence of a maximum appears tightly connected to the formation of a diquark gap., Comment: 7 pages, 2 figures

We discuss the current status of chiral effective field theory in the three-nucleon sector and present selected results for nucleon-deuteron scattering observables based on semilocal momentum-space-regularized chiral two-nucleon potentials together with consistently regularized three-nucleon forces up to third chiral order. Using a Bayesian model for estimating truncation errors, the obtained results are found to provide a good description of the experimental data. We confirm our earlier findings that a high-precision description of nucleon-deuteron scattering data below pion production threshold will require the theory to be pushed to fifth chiral order. This conclusion is substantiated by an exploratory study of selected short-range contributions to the three-nucleon force at that order, which, as expected, are found to have significant effects on polarization observables at intermediate and high energies. We also outline the challenges that will need to be addressed in order to push the chiral expansion of three-nucleon scattering observables to higher orders., Comment: 14 pages, 12 figures, 1 table; contribution to the EPJA topical issue on "The tower of effective (field) theories and the emergence of nuclear phenomena"

We study ground-state energies and charge radii of closed-shell medium-mass nuclei based on novel chiral nucleon-nucleon (NN) and three-nucleon (3N) interactions, with a focus on exploring the connections between finite nuclei and nuclear matter. To this end, we perform in-medium similarity renormalization group (IM-SRG) calculations based on chiral interactions at next-to-leading order (NLO), N$^2$LO, and N$^3$LO, where the 3N interactions at N$^2$LO and N$^3$LO are fit to the empirical saturation point of nuclear matter and to the triton binding energy. Our results for energies and radii at N$^2$LO and N$^3$LO overlap within uncertainties, and the cutoff variation of the interactions is within the EFT uncertainty band. We find underbound ground-state energies, as expected from the comparison to the empirical saturation point. The radii are systematically too large, but the agreement with experiment is better. We further explore variations of the 3N couplings to test their sensitivity in nuclei. While nuclear matter at saturation density is quite sensitive to the 3N couplings, we find a considerably weaker dependence in medium-mass nuclei. In addition, we explore a consistent momentum-space SRG evolution of these NN and 3N interactions, exhibiting improved many-body convergence. For the SRG-evolved interactions, the sensitivity to the 3N couplings is found to be stronger in medium-mass nuclei., Comment: 10 pages, 11 figures, published version

Understanding the dense matter equation of state at extreme conditions is an important open problem. Astrophysical observations of neutron stars promise to solve this, with NICER poised to make precision measurements of mass and radius for several stars using the waveform modelling technique. What has been less clear, however, is how these mass-radius measurements might translate into equation of state constraints and what are the associated equation of state sensitivities. We use Bayesian inference to explore and contrast the constraints that would result from different choices for the equation of state parametrization; comparing the well-established piecewise polytropic parametrization to one based on physically motivated assumptions for the speed of sound in dense matter. We also compare the constraints resulting from Bayesian inference to those from simple compatibility cuts. We find that the choice of equation of state parametrization and particularly its prior assumptions can have a significant effect on the inferred global mass-radius relation and the equation of state constraints. Our results point to important sensitivities when inferring neutron star and dense matter properties. This applies also to inferences from gravitational wave observations., Comment: to appear in MNRAS

We present a complete calculation of nucleon-deuteron scattering as well as ground and low-lying excited states of light nuclei in the mass range A=3-16 up through next-to-next-to-leading order in chiral effective field theory using semilocal coordinate-space regularized two- and three-nucleon forces. It is shown that both of the low-energy constants entering the three-nucleon force at this order can be reliably determined from the triton binding energy and the differential cross section minimum in elastic nucleon-deuteron scattering. The inclusion of the three-nucleon force is found to improve the agreement with the data for most of the considered observables., Comment: 15 pages, 9 figures, 1 table

We employ a variety of ab initio methods including Faddeev-Yakubovsky equations, No-Core Configuration Interaction Approach, Coupled-Cluster Theory and In-Medium Similarity Renormalization Group to perform a comprehensive analysis of the nucleon-deuteron elastic and breakup reactions and selected properties of light and medium-mass nuclei up to 48Ca using the recently constructed semilocal coordinate-space regularized chiral nucleon-nucleon potentials. We compare the results with those based on selected phenomenological and chiral EFT two-nucleon potentials, discuss the convergence pattern of the chiral expansion and estimate the achievable theoretical accuracy at various chiral orders using the novel approach to quantify truncation errors of the chiral expansion without relying on cutoff variation. We also address the robustness of this method and explore alternative ways to estimate the theoretical uncertainty from the truncation of the chiral expansion., Comment: 34 pages, 15 figures, 11 tables

We present an efficient Monte Carlo framework for perturbative calculations of infinite nuclear matter based on chiral two-, three-, and four-nucleon interactions. The method enables the incorporation of all many-body contributions in a straightforward and transparent way, and makes it possible to extract systematic uncertainty estimates by performing order-by-order calculations in the chiral expansion as well as the many-body expansion. The versatility of this new framework is demonstrated by applying it to chiral low-momentum interactions, exhibiting a very good many-body convergence up to fourth order. Following these benchmarks, we explore new chiral interactions up to next-to-next-to-next-to-leading order (N$^3$LO). Remarkably, simultaneous fits to the triton and to saturation properties can be achieved, while all three-nucleon low-energy couplings remain natural. The theoretical uncertainties of nuclear matter are significantly reduced when going from next-to-next-to-leading order to N$^3$LO., Comment: published version, incl. supplemental material

We perform a comprehensive Weinberg eigenvalue analysis of a representative set of modern nucleon-nucleon interactions derived within chiral effective field theory. Our set contains local, semilocal, and nonlocal potentials, developed by Gezerlis, Tews et al. (2013); Epelbaum, Krebs, and Mei{\ss}ner (2015); and Entem, Machleidt, and Nosyk (2017) as well as Carlsson, Ekstr\"om et al. (2016), respectively. The attractive eigenvalues show a very similar behavior for all investigated interactions, whereas the magnitudes of the repulsive eigenvalues sensitively depend on the details of the regularization scheme of the short- and long-range parts of the interactions. We demonstrate that a direct comparison of numerical cutoff values of different interactions is in general misleading due to the different analytic form of regulators; for example, a cutoff value of $R=0.8$ fm for the semilocal interactions corresponds to about $R=1.2$ fm for the local interactions. Our detailed comparison of Weinberg eigenvalues provides various insights into idiosyncrasies of chiral potentials for different orders and partial waves. This shows that Weinberg eigenvalues could be used as a helpful monitoring scheme when constructing new interactions., Comment: 14 pages, 17 figures, published version

We explore the impact of nuclear matter saturation on the properties and systematics of finite nuclei across the nuclear chart. Using the ab initio in-medium similarity renormalization group (IM-SRG), we study ground-state energies and charge radii of closed-shell nuclei from $^4$He to $^{78}$Ni, based on a set of low-resolution two- and three-nucleon interactions that predict realistic saturation properties. We first investigate in detail the convergence properties of these Hamiltonians with respect to model-space truncations for both two- and three-body interactions. We find one particular interaction that reproduces well the ground-state energies of all closed-shell nuclei studied. As expected from their saturation points relative to this interaction, the other Hamiltonians underbind nuclei, but lead to a remarkably similar systematics of ground-state energies. Extending our calculations to complete isotopic chains in the $sd$ and $pf$ shells with the valence-space IM-SRG, the same interaction reproduces not only experimental ground states but two-neutron-separation energies and first excited $2^+$ states. We also calculate radii with the valence-space IM-SRG for the first time. Since this particular interaction saturates at too high density, charge radii are still too small compared with experiment. Except for this underprediction, the radii systematics is, however, well reproduced. Our results highlight the importance of nuclear matter as a theoretical benchmark for the development of next-generation chiral interactions., Comment: 11 pages, 15 figures, 1 table

We discuss the uncertainties in constraining low-energy constants of chiral effective field theory from $^3$H $\beta$ decay. The half-life is very precisely known, so that the Gamow-Teller matrix element has been used to fit the coupling $c_D$ of the axial-vector current to a short-range two-nucleon pair. Because the same coupling also describes the leading one-pion-exchange three-nucleon force, this in principle provides a very constraining fit, uncorrelated with the $^3$H binding energy fit used to constrain another low-energy coupling in three-nucleon forces. However, so far such $^3$H half-life fits have only been performed at a fixed cutoff value. We show that the cutoff dependence due to the regulators in the axial-vector two-body current can significantly affect the Gamow-Teller matrix elements and consequently also the extracted values for the $c_D$ coupling constant. The degree of the cutoff dependence is correlated with the softness of the employed NN interaction. As a result, present three-nucleon forces based on a fit to $^3$H $\beta$ decay underestimate the uncertainty in $c_D$. We explore a range of $c_D$ values that is compatible within cutoff variation with the experimental $^3$H half-life and estimate the resulting uncertainties for many-body systems by performing calculations of symmetric nuclear matter., Comment: 9 pages, 11 figures, published version, includes Erratum, which corrects Figs. 2-6 due to the incorrect c_D relation between 3N forces and two-body currents used

We present solutions of the BCS gap equation in the channels ${}^1S_0$ and ${}^3P_2-{}^3F_2$ in neutron matter based on nuclear interactions derived within chiral effective field theory (EFT). Our studies are based on a representative set of nonlocal nucleon-nucleon (NN) plus three-nucleon (3N) interactions up to next-to-next-to-next-to-leading order (N$^3$LO) as well as local and semilocal chiral NN interactions up to N$^2$LO and N$^4$LO, respectively. In particular, we investigate for the first time the impact of subleading 3N forces at N$^3$LO on pairing gaps and also derive uncertainty estimates by taking into account results for pairing gaps at different orders in the chiral expansion. Finally, we discuss different methods for obtaining self-consistent solutions of the gap equation. Besides the widely-used quasi-linear method by Khodel et al. we demonstrate that the modified Broyden method is well applicable and exhibits a robust convergence behavior. In contrast to Khodel's method it is based on a direct iteration of the gap equation without imposing an auxiliary potential and is straightforward to implement.

Neutron matter is an ideal laboratory for nuclear interactions derived from chiral effective field theory since all contributions are predicted up to next-to-next-to-next-to-leading order (N$^3$LO) in the chiral expansion. By making use of recent advances in the partial-wave decomposition of three- nucleon (3N) forces, we include for the first time N$^3$LO 3N interactions in many-body perturbation theory (MBPT) up to third order and in self-consistent Green's function theory (SCGF). Using these two complementary many-body frameworks we provide improved predictions for the equation of state of neutron matter at zero temperature and also analyze systematically the many-body convergence for different chiral EFT interactions. Furthermore, we present an extension of the normal-ordering framework to finite temperatures. These developments open the way to improved calculations of neutron-rich matter including estimates of theoretical uncertainties for astrophysical applications., Comment: minor changes, published version

We discuss the role of the three-nucleon isospin T=3/2 amplitude in elastic neutron-deuteron scattering and in the deuteron breakup reaction. The contribution of this amplitude originates from charge-independence breaking of the nucleon-nucleon potential and is driven by the difference between neutron-neutron (proton-proton) and neutron-proton forces. We study the magnitude of that contribution to the elastic scattering and breakup observables, taking the locally regularized chiral N4LO nucleon-nucleon potential supplemented by the chiral N2LO three-nucleon force. For comparison we employ also the Av18 nucleon-nucleon potential combined with the Urbana IX three-nucleon force. We find that the isospin T=3/2 component is important for the breakup reaction and the proper treatment of charge-independence breaking in this case requires the inclusion of the 1S0 state with isospin T=3/2. For neutron-deuteron elastic scattering the T=3/2 contributions are insignificant and charge-independence breaking can be accounted for by using the effective t-matrix generated with the so-called "2/3-1/3" rule., Comment: 24 pages, 8 figures, 3 Tables

Regulator functions applied to two- and three-nucleon forces are a necessary ingredient in many-body calculations based on chiral effective field theory interactions. These interactions have been developed recently with a variety of different cutoff forms, including regulating both the momentum transfer (local) and the relative momentum (nonlocal). While in principle any regulator that suppresses high momentum modes can be employed, in practice artifacts are inevitable in current power counting schemes. Artifacts from particular regulators may cause significant distortions of the physics or may affect many-body convergence rates, so understanding their nature is important. Here we characterize the differences between cutoff effects using uniform matter at Hartree-Fock and second-order in the interaction as a testbed. This provides a clean laboratory to isolate phase-space effects of various regulators on both two- and three-nucleon interactions. We test the normal-ordering approximation for three-nucleon forces in nuclear matter and find that the relative size of the residual 3N contributions is sensitive to the employed regularization scheme., Comment: 29 pages, 27 figures

Despite being a complex many-body system, the atomic nucleus exhibits simple structures for certain "magic" numbers of protons and neutrons. The calcium chain in particular is both unique and puzzling: evidence of doubly-magic features are known in 40,48Ca, and recently suggested in two radioactive isotopes, 52,54Ca. Although many properties of experimentally known Ca isotopes have been successfully described by nuclear theory, it is still a challenge to predict their charge radii evolution. Here we present the first measurements of the charge radii of 49,51,52Ca, obtained from laser spectroscopy experiments at ISOLDE, CERN. The experimental results are complemented by state-of-the-art theoretical calculations. The large and unexpected increase of the size of the neutron-rich calcium isotopes beyond N = 28 challenges the doubly-magic nature of 52Ca and opens new intriguing questions on the evolution of nuclear sizes away from stability, which are of importance for our understanding of neutron-rich atomic nuclei., Comment: Submitted version. See original publication (doi:10.1038/nphys3645) for final version

Renormalization group (RG) methods used to soften Hamiltonians for nuclear many-body calculations change the effective resolution of the interaction. For nucleon knock-out processes, these RG transformations leave cross sections invariant, but initial-state wave functions, interaction currents, and final-state interactions are individually altered. This has implications for the factorization of nuclear structure and reactions. We use deuteron electrodisintegration as a controlled laboratory for studying how structure and reaction components are modified under RG evolution, without the complication of three-body forces or currents. The dependence of these changes on kinematics is explored., Comment: 17 pages, 13 figures, published version

What is the size of the atomic nucleus? This deceivably simple question is difficult to answer. While the electric charge distributions in atomic nuclei were measured accurately already half a century ago, our knowledge of the distribution of neutrons is still deficient. In addition to constraining the size of atomic nuclei, the neutron distribution also impacts the number of nuclei that can exist and the size of neutron stars. We present an ab initio calculation of the neutron distribution of the neutron-rich nucleus $^{48}$Ca. We show that the neutron skin (difference between radii of neutron and proton distributions) is significantly smaller than previously thought. We also make predictions for the electric dipole polarizability and the weak form factor; both quantities are currently targeted by precision measurements. Based on ab initio results for $^{48}$Ca, we provide a constraint on the size of a neutron star.

We review the impact of nuclear forces on matter at neutron-rich extremes. Recent results have shown that neutron-rich nuclei become increasingly sensitive to three-nucleon forces, which are at the forefront of theoretical developments based on effective field theories of quantum chromodynamics. This includes the formation of shell structure, the spectroscopy of exotic nuclei, and the location of the neutron dripline. Nuclear forces also constrain the properties of neutron-rich matter, including the neutron skin, the symmetry energy, and the structure of neutron stars. We first review our understanding of three-nucleon forces and show how chiral effective field theory makes unique predictions for many-body forces. Then, we survey results with three-nucleon forces in neutron-rich oxygen and calcium isotopes and neutron-rich matter, which have been explored with a range of many-body methods. Three-nucleon forces therefore provide an exciting link between theoretical, experimental and observational nuclear physics frontiers., Comment: 28 pages, 13 figures, 1 table

We study ground- and excited-state properties of all sd-shell nuclei with neutron and proton numbers 8 <= N,Z <= 20, based on a set of low-resolution two- and three-nucleon interactions that predict realistic saturation properties of nuclear matter. We focus on estimating the theoretical uncertainties due to variation of the resolution scale, the low-energy couplings, as well as from the many-body method. The experimental two-neutron and two-proton separation energies are reasonably well reproduced, with an uncertainty range of about 5 MeV. The first excited 2+ energies also show overall agreement, with a more narrow uncertainty range of about 500 keV. In most cases, this range is dominated by the uncertainties in the Hamiltonian., Comment: 6 pages, 4 figures

We apply improved nucleon-nucleon potentials up to fifth order in chiral effective field theory, along with a new analysis of the theoretical truncation errors, to study nucleon-deuteron (Nd) scattering and selected low-energy observables in 3H, 4He, and 6Li. Calculations beyond second order differ from experiment well outside the range of quantified uncertainties, providing truly unambiguous evidence for missing three-nucleon forces within the employed framework. The sizes of the required three-nucleon force contributions agree well with expectations based on Weinberg's power counting. We identify the energy range in elastic Nd scattering best suited to study three-nucleon force effects and estimate the achievable accuracy of theoretical predictions for various observables., Comment: 5 pages, 5 figures

We present a novel framework to decompose three-nucleon forces in a momentum space partial-wave basis. The new approach is computationally much more efficient than previous methods and opens the way to ab initio studies of few-nucleon scattering processes, nuclei and nuclear matter based on higher-order chiral 3N forces. We use the new framework to calculate matrix elements of chiral three-nucleon forces at N2LO and N3LO in large basis spaces and carry out benchmark calculations for neutron matter and symmetric nuclear matter. We also study the size of the individual three-nucleon force contributions for $^3$H. For nonlocal regulators, we find that the sub-leading terms, which have been neglected in most calculations so far, provide important contributions. All matrix elements are calculated and stored in a user-friendly way, such that values of low-energy constants as well as the form of regulator functions can be chosen freely., Comment: 10 pages, 4 figures

We solve three-nucleon Faddeev equations with nucleon-nucleon and three-nucleon forces derived consistently in the framework of chiral perturbation theory at next-to-next-to-next-to-leading order in the chiral expansion. In this first investigation we include only matrix elements of the three-nucleon force for partial waves with the total two-nucleon (three-nucleon) angular momenta up to 3 (5/2). Low-energy neutron-deuteron elastic scattering and deuteron breakup reaction are studied. Emphasis is put on Ay puzzle in elastic scattering and cross sections in symmetric-space-star and neutron-neutron quasi-free-scattering breakup configurations, for which large discrepancies between data and theory have been reported., Comment: 22 pages, 7 figures

We study the properties of spin-polarized neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory, including two-, three-, and four-neutron interactions. The energy of spin-polarized neutrons is remarkably close to a non-interacting system at least up to saturation density, where interaction effects provide less than 10% corrections. This shows that the physics of neutron matter is similar to a unitary gas well beyond the scattering-length regime. Implications for energy-density functionals and for a possible ferromagnetic transition in neutron stars are discussed. Our predictions can be tested with lattice QCD, and we present results for varying pion mass., Comment: 5 pages, 4 figures, minor changes, published version

We present details of the derivation of local chiral effective field theory interactions to next-to-next-to-leading order, and show results for nucleon-nucleon phase shifts and deuteron properties for these potentials. We then perform systematic auxiliary-field diffusion Monte Carlo calculations for neutron matter based on the developed local chiral potentials at different orders. This includes studies of the effects of the spectral-function regularization and of the local regulators. For all orders, we compare the quantum Monte Carlo results with perturbative many-body calculations and find excellent agreement for low cutoffs., Comment: 17 pages, 11 figures, published version, LA-UR-14-23894

We discuss neutron matter calculations based on chiral effective field theory interactions and their predictions for the symmetry energy, the neutron skin of 208 Pb, and for the radius of neutron stars., Comment: 7 pages, 8 figures, short review article, to appear in EPJA special issue on symmetry energy

Neutron matter presents a unique system in chiral effective field theory (EFT), because all many-body forces among neutrons are predicted to next-to-next-to-next-to-leading order (N3LO). We discuss perturbative and first Quantum Monte Carlo (QMC) calculations of neutron matter with chiral EFT interactions and their astrophysical impact for the equation of state and neutron stars., Comment: 10 pages, 7 figures, proceedings of the International Conference on Nuclear Theory in the Supercomputing Era 2013, Iowa State University, May 13-17, 2013