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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., Comment: 148 pages, 77 figures, 9 tables, published version

A direct measurement of the decay width of the excited ${0}_{1}^{+}$ state of $^{6}\mathrm{Li}$ using the relative self-absorption technique is reported. Our value of ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\gamma},{0}_{1}^{+}\ensuremath{\rightarrow}{1}_{1}^{+}}=8.17(14{)}_{\mathrm{stat}.}(11{)}_{\mathrm{syst}.}\text{ }\text{ }\mathrm{eV}$ 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.

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)., 23 pages, 10 figures, 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 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., 16 pages, 11 figures. Appendix is added. 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., 17 pages, 8 figures; accepted for publication in the Astrophysical Journal Letters

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., 14 pages, 14 figures, minor changes, 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., 11 pages, 10 figures, published version

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., 18 pages, 8 figures. Accepted for publication in ApJ Letters

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

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., 6 pages, 2 figures

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., 10 pages, 11 figures, published version

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., 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"

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., Comment: Accepted for publication on Sci. China Phys. Mech. Astron. (2019)

We solve three-nucleon (3N) Faddeev equations with nucleon–nucleon (NN) and three-nucleon forces (3NF) derived consistently in the framework of chiral perturbation theory, taking the semilocal coordinate-space regularized chiral N $$^4$$ LO NN potential supplemented by the chiral N $$^2$$ LO 3NF regularized in the same way. Based on these solutions the nucleon–deuteron (Nd) elastic scattering and deuteron breakup reactions are studied. We checked that the elastic Nd scattering cross section can be used as an alternative observable to the doublet neutron–deuteron (nd) scattering length to fix, together with the $$^3$$ H binding energy, the strengths of the contact terms of the N $$^2$$ LO 3NF. We investigated the predicted 3NF effects in 3N continuum reactions putting an emphasis on the $$A_y$$ puzzle in low energy nd elastic scattering and on cross sections in the symmetrical-space-star and quasi-free-scattering breakup configurations. We found that the N $$^2$$ LO 3NF provides effects comparable to those of standard, (semi-)phenomenological $$2\pi $$ -exchange Tucson-Melbourne 3NF.

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., 6 pages, 5 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

This erratum fixes an error in the use of the low-energy constant in the two-body currents. The corrected version of one of the equations and of some of the figures is reported.

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 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., published version, incl. supplemental material

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 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

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 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.

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

We present recent results for 4 He and 6 Li obtained with improved NN interactions derived from chiral effective field theory up to N4 LO. The many-body calculations are performed order-by-order in the chiral expansion. At N3 LO and N4 LO additional renormalization using the Similarity Renormalization Group is adopted to improve numerical convergence of the many-body calculations. We discuss results for the ground state energies, as well as the magnetic moment and the low-lying spectrum of 6 Li.

One of the primary science goals of the next generation of hard x-ray timing instruments is to determine the equation of state of matter at supranuclear densities inside neutron stars by measuring the radius of neutron stars with different masses to accuracies of a few percent. Three main techniques can be used to achieve this goal. The first involves waveform modeling. The flux observed from a hotspot on the neutron star surface offset from the rotational pole will be modulated by the star’s rotation, and this periodic modulation at the spin frequency is called a pulsation. As the photons propagate through the curved spacetime of the star, information about mass and radius is encoded into the shape of the waveform (pulse profile) via special and general-relativistic effects. Using pulsations from known sources (which have hotspots that develop either during thermonuclear bursts or due to channeled accretion) it is possible to obtain tight constraints on mass and radius. The second technique involves characterizing the spin distribution of accreting neutron stars. A large collecting area enables highly sensitive searches for weak or intermittent pulsations (which yield spin) from the many accreting neutron stars whose spin rates are not yet known. The most rapidly rotating stars provide a clean constraint, since the limiting spin rate where the equatorial surface velocity is comparable to the local orbital velocity, at which mass shedding occurs, is a function of mass and radius. However, the overall spin distribution also provides a guide to the torque mechanisms in operation and the moment of inertia, both of which can depend sensitively on dense matter physics. The third technique is to search for quasiperiodic oscillations in x-ray flux associated with global seismic vibrations of magnetars (the most highly magnetized neutron stars), triggered by magnetic explosions. The vibrational frequencies depend on stellar parameters including the dense matter equation of state, and large-area x-ray timing instruments would provide much improved detection capability. An illustration is given of how these complementary x-ray timing techniques can be used to constrain the dense matter equation of state and the results that might be expected from a 10 m2 instrument are discussed. Also discussed are how the results from such a facility would compare to other astronomical investigations of neutron star properties.

What is the size of the atomic nucleus? This deceivably simple question is difficult to answer. Although 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 Ca-48. We show that the neutron skin (difference between the radii of the 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 that are at present targeted by precision measurements. Based on ab initio results for Ca-48, we provide a constraint on the size of a neutron star.

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

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

We perform a systematic study of the odd-even mass staggering generated using a pairing interaction computed at first order in low-momentum interactions. Building on previous work including the (nuclear plus Coulomb) two-nucleon interaction only, we focus here on the first-order contribution from chiral three-nucleon forces. We observe a significant repulsive effect from the three-nucleon interaction. The combined contribution from two- and three-nucleon interactions accounts for approximately 70% of the experimental pairing gaps. This leaves room for higher-order contributions to the pairing kernel and the normal self-energy that need to be computed consistently., 4 pages, 2 figures. Proceedings of the International Niigata 2010 Symposium on Forefronts of Researches in Exotic Nuclear Structures, Tokamachi, Japan, March 1 - March 4, 2010. To be published in Modern Physics Letters A

We study in detail the dependence of the 1S0 superfluid pairing gap on nuclear interactions and on charge-independence breaking at the BCS level. Starting from chiral effective-field theory and conventional nucleon-nucleon (NN) interactions, we use the renormalization group to generate low-momentum interactions V_{low k} with sharp and smooth regulators. The resulting BCS gaps are well constrained by the NN scattering phase shifts, and the cutoff dependence is very weak for sharp or sufficiently narrow smooth regulators with cutoffs Lambda > 1.6 fm^{-1}. It is therefore likely that the effect of three-nucleon interactions on 1S0 superfluidity is small at the BCS level. The charge dependence of nuclear interactions has a 10% effect on the pairing gap., 11 pages, 4 figures, minor changes, to appear in Phys. Lett. B

We study ground- and excited-state properties of all sd-shell nuclei with neutron and proton numbers 8, 6 pages, 4 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.

We calculate the properties of isospin-asymmetric nuclear matter based on chiral nucleon-nucleon (NN) and three-nucleon (3N) interactions. To this end, we develop an improved normal-ordering framework that allows to include general 3N interactions starting from a plane-wave partial-wave-decomposed form. We present results for the energy per particle for general isospin asymmetries based on a set of different Hamiltonians, study their saturation properties, the incompressibility, symmetry energy, and also provide an analytic parametrization for the energy per particle as a function of density and isospin asymmetry., Comment: minor changes, published 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

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., 5 pages, 5 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., 22 pages, 7 figures

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., 7 pages, 8 figures, short review article, to appear in EPJA special issue on symmetry energy

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

The Large Observatory For x-ray Timing (LOFT) was studied within ESA M3 Cosmic Vision framework and participated in the final down-selection for a launch slot in 2022-2024. Thanks to the unprecedented combination of effective area and spectral resolution of its main instrument, LOFT will study the behaviour of matter under extreme conditions, such as the strong gravitational field in the innermost regions of accretion flows close to black holes and neutron stars, and the supra-nuclear densities in the interior of neutron stars. The science payload is based on a Large Area Detector (LAD, 10 m 2 effective area, 2-30 keV, 240 eV spectral resolution, 1 deg collimated field of view) and a WideField Monitor (WFM, 2-50 keV, 4 steradian field of view, 1 arcmin source location accuracy, 300 eV spectral resolution). The WFM is equipped with an on-board system for bright events (e.g. GRB) localization. The trigger time and position of these events are broadcast to the ground within 30 s from discovery. In this paper we present the status of the mission at the end of its Phase A study., Proc. SPIE 9144, Space Telescopes and Instrumentation 2014: Ultraviolet to Gamma Ray, 91442T

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., 17 pages, 11 figures, published version, LA-UR-14-23894

We present the first quantum Monte Carlo (QMC) calculations with chiral effective field theory (EFT) interactions. To achieve this, we remove all sources of nonlocality, which hamper the inclusion in QMC calculations, in nuclear forces to next-to-next-to-leading order. We perform auxiliary-field diffusion Monte Carlo (AFDMC) calculations for the neutron matter energy up to saturation density based on local leading-order, next-to-leading order, and next-to-next-to-leading order nucleon-nucleon interactions. Our results exhibit a systematic order-by-order convergence in chiral EFT and provide nonperturbative benchmarks with theoretical uncertainties. For the softer interactions, perturbative calculations are in excellent agreement with the AFDMC results. This work paves the way for QMC calculations with systematic chiral EFT interactions for nuclei and nuclear matter, for testing the perturbativeness of different orders, and allows for matching to lattice QCD results by varying the pion mass., Comment: 6 pages, 3 figures, 1 table

The neutron-matter equation of state constrains the properties of many physical systems over a wide density range and can be studied systematically using chiral effective field theory (EFT). In chiral EFT, all many-body forces among neutrons are predicted to next-to-next-to-next-to-leading order (N3LO). We present details and additional results of the first complete N3LO calculation of the neutron-matter energy, which includes the subleading three-nucleon as well as the leading four-nucleon forces, and provides theoretical uncertainties. In addition, we discuss the impact of our results for astrophysics: for the supernova equation of state, the symmetry energy and its density derivative, and for the structure of neutron stars. Finally, we give a first estimate for the size of the N3LO many-body contributions to the energy of symmetric nuclear matter, which shows that their inclusion will be important in nuclear structure calculations., published version; 21 pages, 11 figures, 5 tables

Microscopic calculations of neutron matter based on nuclear interactions derived from chiral effective field theory, combined with the recent observation of a 1.97 +- 0.04 M_sun neutron star, constrain the equation of state of neutron-rich matter at sub- and supranuclear densities. We discuss in detail the allowed equations of state and the impact of our results on the structure of neutron stars, the crust-core transition density, and the nuclear symmetry energy. In particular, we show that the predicted range for neutron star radii is robust. For use in astrophysical simulations, we provide detailed numerical tables for a representative set of equations of state consistent with these constraints., 35 pages, 12 figures, NORDITA preprint 2013-22

We present the first results for the neutron matter equation of state (EOS) using nucleon-nucleon and three-nucleon chiral effective field theory interactions that are consistently evolved in the framework of the Similarity Renormalization Group (SRG). The dependence of the EOS on the SRG resolution scale is greatly reduced when induced three-nucleon forces (3NF) are included and the residual variation, which in part is from missing induced four-body interactions, is comparable to estimated many-body perturbation theory truncation errors. The relative growth with decreasing resolution of the 3NF contributions to the energy per neutron is of natural size, but it accelerates at the lowest resolutions where strong renormalization of the long-range 3NF matrix elements is also observed., 6 pages, 5 figures