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

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

Constraints on neutron star radii based on chiral effective field theory interactions

We show that microscopic calculations based on chiral effective field theory interactions constrain the properties of neutron-rich matter below nuclear densities to a much higher degree than is reflected in commonly used equations of state. Combined with observed neutron star masses, our results lead to a radius R = 9.7 - 13.9 km for a 1.4 M_{solar} star, where the theoretical range is due, in about equal amounts, to uncertainties in many-body forces and to the extrapolation to high densities.Comment: 4 pages, 4 figures; NORDITA-2010-4

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

Neutron matter at finite temperature based on chiral effective field theory interactions

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

Improved nuclear matter calculations from chiral low-momentum interactions

We present new nuclear matter calculations based on low-momentum interactions derived from chiral effective field theory potentials. The current calculations use an improved treatment of the three-nucleon force contribution that includes a corrected combinatorial factor beyond Hartree-Fock that was omitted in previous nuclear matter calculations. We find realistic saturation properties using parameters fit only to few-body data, but with larger uncertainty estimates from cutoff dependence and the 3NF parametrization than in previous calculations.Comment: 5 pages, 4 figure

Clinical Relevance of Baseline TCP in Transcatheter Aortic Valve Replacement

AIMS: To investigate the influence of baseline thrombocytopenia (TCP) on short-term and long-term outcomes after transcatheter aortic valve replacement (TAVR). METHODS AND RESULTS: A total of 732 consecutive patients with severe, symptomatic aortic stenosis undergoing TAVR from January 2012 to December 2015 were included. Primary outcomes of interest were the relationship of baseline TCP with 30-day and 1-year all-cause mortality. Secondary outcomes of interest were procedural complications and in-hospital mortality in the same subgroups. The prevalence of TCP (defined as platelet count <150 × 109/L) at baseline was 21.9%, of whom 4.0% had moderate/severe TCP (defined as platelet count <100 × 109/L). Compared to no or mild TCP, moderate/severe TCP at baseline was associated with a significantly higher 30-day mortality (23.3% vs 2.3% and 3.1%, respectively; P<.001) and 1-year mortality (40.0% vs 8.3% and 13.4%, respectively; P<.001). In Cox regression analysis, moderate/severe baseline TCP was an independent predictor of 30-day and 1-year mortality (hazard ratio [HR], 13.18; 95% confidence interval [CI], 4.49-38.64; P<.001 and HR, 5.90; 95% CI, 2.68-13.02; P<.001, respectively). CONCLUSIONS: In conclusion, baseline TCP is a strong predictor of mortality in TAVR patients, possibly identifying a specific subgroup of frail patients; therefore, it should be taken into account when addressing TAVR risk

Nuclear forces from chiral EFT: The unfinished business

In spite of the great progress we have seen in recent years in the derivation of nuclear forces from chiral effective field theory (EFT), some important issues are still unresolved. In this contribution, we discuss the open problems which have particular relevance for microscopic nuclear structure, namely, the proper renormalization of chiral nuclear potentials and sub-leading many-body forces.Comment: 16 pages, 3 figures; contribution to J. Phys. G, Special Issue, Focus Section: Open Problems in Nuclear Structur