Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.

The symmetry energy contribution to the nuclear equation of state impacts various phenomena in nuclear astrophysics, nuclear structure, and nuclear reactions. Its determination is a key objective of contemporary nuclear physics, with consequences for the understanding of dense matter within neutron stars. We examine the results of laboratory experiments that have provided initial constraints on the nuclear symmetry energy and on its density dependence at and somewhat below normal nuclear matter density. Even though some of these constraints have been derived from properties of nuclei while others have been derived from the nuclear response to electroweak and hadronic probes, within experimental uncertainties-they are consistent with each other. We also examine the most frequently used theoretical models that predict the symmetry energy and its slope parameter. By comparing existing constraints on the symmetry pressure to theories, we demonstrate how contributions of three-body forces, which are essential ingredients in neutron matter models, can be determined.

We calculate the equation of state of neutron matter with realistic two-and three-nucleon interactions using quantum Monte Carlo techniques, and illustrate that the short-range three-neutron interaction determines the correlation between neutron matter energy at nuclear saturation density and higher densities relevant to neutron stars. Our model also makes an experimentally testable prediction for the correlation between the nuclear symmetry energy and its density dependencedetermined solely by the strength of the short-range terms in the three neutron force. The same force provides a significant constraint on the maximum mass and radius of neutron stars. PACS numbers: 21.65.Cd, 21.65.Ef, 26.60.Kp Since their discovery, neutron stars have remained our sole laboratory to study matter at supra-nuclear density and relatively low temperature. The equation of state (EoS) of matter at these densities is largely unknown but uniquely determines the structure of neutron stars and the relation between their mass (M ) and radius (R). Matter that can support large pressure for a given energy density (typically called a stiff EoS) will favor large neutron star radii for a given mass. Such an EoS also predicts large values for the maximum mass of a neutron star that is stable with respect to gravitational collapse to a black hole. Conversely, a high density phase that predicts a smaller pressure will result in more compact neutron stars and smaller maximum masses.The recent accurate measurement of a large neutron star mass M = 1.97 ± 0.04M solar in the system J1614-2230 provides strong evidence that the high density equation of state is stiff [1]. Interestingly, attempts to infer neutron star radii have favored relatively small values ranging from 9 to 12 km [2][3][4]. Although the radius inference depends on specific model assumptions, these smaller radii imply a soft EoS in the vicinity of nuclear saturation density. Taken together, they indicate that the EoS of dense matter makes a transition from soft to stiff at supra-nuclear density. In this Rapid Communication we show that the three-neutron force (3n) is the key microscopic ingredient that determines the nature of this transition.The importance of three-body forces in nuclear physics is well known, and quantum Monte Carlo (QMC) calculations of light nuclei have clarified its structure and strength. However, in these systems the dominant threebody force acts between two neutrons and proton or between two protons and a neutron. While the force among three neutrons is important in light neutron-rich nuclei, the short distance behavior is not easily accessible [5]. Properties of large neutron-rich nuclei are potentially sensitive to this interaction, especially if the symmetry energy provides a reliable measure of the energy difference between pure neutron matter and symmetric nuclear matter at saturation density. There has been much recent progress in both theory and experiments to measure the symmetry energy and its density dependence, as reviewed in Refs. [6,7]. The s...

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.

The dense matter equation of state (EOS) determines neutron star (NS) structure but can be calculated reliably only up to one to two times the nuclear saturation density, using accurate manybody methods that employ nuclear interactions from chiral effective field theory constrained by scattering data. In this work, we use physically motivated ansatzes for the speed of sound c S at high density to extend microscopic calculations of neutron-rich matter to the highest densities encountered in stable NS cores. We show how existing and expected astrophysical constraints on NS masses and radii from X-ray observations can constrain the speed of sound in the NS core. We confirm earlier expectations that c S is likely to violate the conformal limit of c 2 S ≤ c 2 /3, possibly reaching values closer to the speed of light c at a few times the nuclear saturation density, independent of the nuclear Hamiltonian. If QCD obeys the conformal limit, we conclude that the rapid increase of c S required to accommodate a 2 M NS suggests a form of strongly interacting matter where a description in terms of nucleons will be unwieldy, even between one and two times the nuclear saturation density. For typical NSs with masses in the range 1.2 − 1.4 M , we find radii between 10 and 14 km, and the smallest possible radius of a 1.4 M NS consistent with constraints from nuclear physics and observations is 8.4 km. We also discuss how future observations could constrain the EOS and guide theoretical developments in nuclear physics.