Stefano Gandolfi

Constraints on the symmetry energy and neutron skins from experiments and theory

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.

The maximum mass and radius of neutron stars and the nuclear symmetry energy

We calculate the equation of state of neutron matter with realistic two- and threenucleon interactions using Quantum Monte Carlo techniques, and demonstrate that the short-range three-neutron interaction determines the correlation between neutron matter energy at nuclear saturation density and the higher densities relevant to neutron stars. Our model for the nuclear interactions makes an experimentally testable prediction for the correlation between the neutron matter energy (which in turn is related to the symmetry energy) and its density dependence. This correlation is solely determined by the strength of the short-range 3 neutron force. The same force also provides a stringent constraint on the maximum mass and radius of neutron stars. An experimental measurement of the symmetry energy with an accuracy of < 1 MeV will enable model predictions for neutron star structure that can be tested with current and anticipated constraints on the masses and radii of neutron stars from x-ray observations.

Quantum Monte Carlo methods for nuclear physics

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 equation of state of neutron matter, symmetry energy and neutron star structure

We review the calculation of the equation of state of pure neutron matter using quantum Monte Carlo (QMC) methods. QMC algorithms permit the study of many-body nuclear systems using realistic two- and three-body forces in a non-perturbative framework. We present the results for the equation of state of neutron matter, and focus on the role of three-neutron forces at supranuclear density. We discuss the correlation between the symmetry energy, the neutron star radius and the symmetry energy. We also combine QMC and theoretical models of the three-nucleon interactions, and recent neutron star observations to constrain the value of the symmetry energy and its density dependence.

Local chiral effective field theory interactions and quantum Monte Carlo applications

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.

Chiral Three-Nucleon Interactions in Light Nuclei, Neutron-α Scattering, and Neutron Matter.

We present quantum Monte Carlo calculations of light nuclei, neutron-α scattering, and neutron matter using local two- and three-nucleon (3N) interactions derived from chiral effective field theory up to next-to-next-to-leading order (N(2)LO). The two undetermined 3N low-energy couplings are fit to the (4)He binding energy and, for the first time, to the spin-orbit splitting in the neutron-α P-wave phase shifts. Furthermore, we investigate different choices of local 3N-operator structures and find that chiral interactions at N(2)LO are able to simultaneously reproduce the properties of A=3,4,5 systems and of neutron matter, in contrast to commonly used phenomenological 3N interactions.

Resonantly interacting fermions in a box.

We use two fundamental theoretical frameworks to study the finite-size (shell) properties of the unitary gas in a periodic box: (1) an ab initio quantum Monte Carlo (QMC) calculation for boxes containing 4 to 130 particles provides a precise and complete characterization of the finite-size behavior, and (2) a new density functional theory (DFT) fully encapsulates these effects. The DFT predicts vanishing shell structure for systems comprising more than 50 particles, and allows us to extrapolate the QMC results to the thermodynamic limit, providing the tightest bound to date on the ground-state energy of the unitary gas: ξ(S)≤0.383(1). We also apply the new functional to few-particle harmonically trapped systems, comparing with previous calculations.

Equation of State of Superfluid Neutron Matter and the Calculation of the 1S0 Pairing Gap

We present a quantum Monte Carlo study of the zero-temperature equation of state of neutron matter and the computation of the 1S0 pairing gap in the low-density regime with rho < 0.04 fm(-3). The system is described by a nonrelativistic nuclear Hamiltonian including both two- and three-nucleon interactions of the Argonne and Urbana type. This model interaction provides very accurate results in the calculation of the binding energy of light nuclei. A suppression of the gap with respect to the pure BCS theory is found, but sensibly weaker than in other works that attempt to include polarization effects in an approximate way.

Quantum Monte Carlo calculations of neutron matter with chiral three-body forces

Chiral effective field theory (EFT) enables a systematic description of low-energy hadronic interactions with controlled theoretical uncertainties. For strongly interacting systems, quantum Monte Carlo (QMC) methods provide some of the most accurate solutions, but they require as input local potentials. We have recently constructed local chiral nucleon-nucleon (NN) interactions up to next-to-next-to-leading order (N2LO). Chiral EFT naturally predicts consistent many-body forces. In this paper, we consider the leading chiral three-nucleon (3N) interactions in local form. These are included in auxiliary field diffusion Monte Carlo (AFDMC) simulations. We present results for the equation of state of neutron matter and for the energies and radii of neutron drops. Specifically, we study the regulator dependence at the Hartree-Fock level and in AFDMC and find that present local regulators lead to less repulsion from 3N forces compared to the usual nonlocal regulators.

Neutron Matter from Low to High Density

Neutron matter is an intriguing nuclear system with multiple connections to other areas of physics. Considerable progress has been made over the last two decades in exploring the properties of pure neutron fluids. Here we begin by reviewing work done to explore the behavior of very low density neutron matter, which forms a strongly paired superfluid and is thus similar to cold Fermi atoms, though at energy scales differing by many orders of magnitude. We then increase the density, discussing work that ties the study of neutron matter with the determination of the properties of neutron-rich nuclei and neutron-star crusts. After this, we review the impact neutron matter at even higher densities has on the mass-radius relation of neutron stars, thereby making contact with astrophysical observations.