Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation

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 materia

Microscopic calculations and energy expansions for neutron-rich matter

We investigate asymmetric nuclear matter with two- and three-nucleon interactions based on chiral effective field theory, where three-body forces are fit only to light nuclei. Focusing on neutron-rich matter, we calculate the energy for different proton fractions and include estimates of the theoretical uncertainty. We use our ab-initio results to test the quadratic expansion around symmetric matter with the symmetry energy term, and confirm its validity for highly asymmetric systems. Our calculations are in remarkable agreement with an empirical parametrization for the energy density. These findings are very useful for astrophysical applications and for developing new equations of state.Comment: 15 pages, 9 figures, published versio

Pairing in neutron matter: New uncertainty estimates and three-body forces

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 from chiral two- and three-nucleon calculations up to N3^3LO

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 versio

Effective field theory for dilute Fermi systems at fourth order

We discuss high-order calculations in perturbative effective field theory for fermions at low energy scales. The Fermi-momentum or kFas expansion for the ground-state energy of the dilute Fermi gas is calculated to fourth order, both in cutoff regularization and in dimensional regularization. For the case of spin one-half fermions we find from a Bayesian analysis that the expansion is well converged at this order for |kFas|≲0.5. Furthermore, we show that Padé-Borel resummations can improve the convergence for |kFas|≲1. Our results provide important constraints for nonperturbative calculations of ultracold atoms and dilute neutron matter

Probing chiral interactions up to next-to-next-to-next-to-leading order in medium-mass nuclei

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 versio

BUQEYE Guide to Projection-Based Emulators in Nuclear Physics

The BUQEYE collaboration (Bayesian Uncertainty Quantification: Errors in Your EFT) presents a pedagogical introduction to projection-based, reduced-order emulators for applications in low-energy nuclear physics. The term emulator refers here to a fast surrogate model capable of reliably approximating high-fidelity models. As the general tools employed by these emulators are not yet well-known in the nuclear physics community, we discuss variational and Galerkin projection methods, emphasize the benefits of offline-online decompositions, and explore how these concepts lead to emulators for bound and scattering systems that enable fast & accurate calculations using many different model parameter sets. We also point to future extensions and applications of these emulators for nuclear physics, guided by the mature field of model (order) reduction. All examples discussed here and more are available as interactive, open-source Python code so that practitioners can readily adapt projection-based emulators for their own work.Comment: 31 pages, 10 figures, 1 table; invited contribution to the Research Topic "Uncertainty Quantification in Nuclear Physics" in Frontiers in Physic

Wave function-based emulation for nucleon-nucleon scattering in momentum space

Emulators for low-energy nuclear physics can provide fast & accurate predictions of bound-state and scattering observables for applications that require repeated calculations with different parameters, such as Bayesian uncertainty quantification. In this paper, we extend a scattering emulator based on the Kohn variational principle (KVP) to momentum space (including coupled channels) with arbitrary boundary conditions, which enable the mitigation of spurious singularities known as Kohn anomalies. We test it on a modern chiral nucleon-nucleon (NN) interaction, including emulation of the coupled channels. We provide comparisons between a Lippmann-Schwinger equation emulator and our KVP momentum-space emulator for a representative set of neutron-proton (np) scattering observables, and also introduce a quasi-spline-based approach for the KVP-based emulator. Our findings show that while there are some trade-offs between accuracy and speed, all three emulators perform well. Self-contained Jupyter notebooks that generate the results and figures in this paper are publicly available.Comment: 18 pages, 15 figure