Lattice chiral effective field theory with three-body interactions at next-to-next-to-leading order

We consider low-energy nucleons at next-to-next-to-leading order in lattice chiral effective field theory. Three-body interactions first appear at this order, and we discuss several methods for determining three-body interaction coefficients on the lattice. We compute the energy of the triton and low-energy neutron-deuteron scattering phase shifts in the spin-doublet and spin-quartet channels using Lüscher’s finite-volume method. In the four-nucleon system we calculate the energy of the -particle using auxiliary fields and projection Monte Carlo.     

Complex-mass renormalization in chiral effective field theory

We consider a low-energy effective field theory of vector mesons and Goldstone bosons using the complex-mass renormalization. As an application we calculate the mass and the width of the ρ meson.     

Neutron-deuteron scattering in chiral effective field theory

We perform a complete analysis of nd scattering at next-to-next-to-leading order (NNLO) in chiral effective field theory (EFT) and compare our predictions for selected observables with the ones based on conventional nuclear forces.Received: 1 November 2002, Published online: 15 July 2003PACS: 21.30.Cb Nuclear forces in vacuum - 21.45.+v Few-body systems     

Nuclear surface properties in relativistic effective field theory

We perform Hartree calculations of symmetric and asymmetric semi-infinite nuclear matter in the framework of relativistic models based on effective hadronic field theories as recently proposed in the literature. In addition to the conventional cubic and quartic scalar self-interactions, the extended models incorporate a quartic vector self-interaction, scalar-vector non-linearities and tensor couplings of the vector mesons. We investigate the implications of these terms on nuclear surface properties such as the surface energy coefficient, surface thickness, surface stiffness coefficient, neutron skin thickness and the spin-orbit force.     

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 1.4M⊙ star, where the theoretical range is due, in about equal amounts, to uncertainties in many-body forces and to the extrapolation to high densities.     

Dilute neutron matter on the lattice at next-to-leading order in chiral effective field theory

We discuss lattice simulations of the ground state of dilute neutron matter at next-to-leading order in chiral effective field theory. In a previous paper the coefficients of the next-to-leading-order lattice action were determined by matching nucleon-nucleon scattering data for momenta up to the pion mass. Here the same lattice action is used to simulate the ground state of up to 12 neutrons in a periodic cube using Monte Carlo simulations. We explore the density range from 2% to 8% of normal nuclear density and analyze the ground-state energy as an expansion about the unitarity limit with corrections due to finite scattering length, effective range, and P -wave interactions.     

Ground-state energy of dilute neutron matter at next-to-leading order in lattice chiral effective field theory

We present lattice calculations for the ground-state energy of dilute neutron matter at next-to-leading order in chiral effective field theory. This study follows a series of recent papers on low-energy nuclear physics using chiral effective field theory on the lattice. In this work we introduce an improved spin- and isospin-projected leading-order action which allows for a perturbative treatment of corrections at next-to-leading order and smaller estimated errors. Using auxiliary fields and Euclidean-time projection Monte Carlo, we compute the ground state of 8, 12, and 16 neutrons in a periodic cube, covering a density range from 2% to 10% of normal nuclear density.     

Few-nucleon forces and systems in chiral effective field theory

Chiral effective field theory provides a systematic framework to study nuclear forces based on the approximate and spontaneously broken chiral symmetry of QCD. I sketch the basic concepts of this method, outline the structure of the resulting few-nucleon forces and discuss some recent applications in the few-nucleon sector.     

Local three-nucleon interaction from chiral effective field theory

The three-nucleon (NNN) interaction derived within the chiral effective field theory at the next-to-next-to-leading order (N²LO) is regulated with a function depending on the magnitude of the momentum transfer. The regulated NNN interaction is then local in the coordinate space, which is advantageous for some many-body techniques. Matrix elements of the local chiral NNN interaction are evaluated in a three-nucleon basis. Using the ab initio no-core shell model (NCSM) the NNN matrix elements are employed in ³H and ⁴He bound-state calculations. Correspondence: P. Navrátil, Lawrence Livermore National Laboratory, L-414, P.O. Box 808, Livermore, CA 94551, USA     

Orthonormalization procedure for chiral effective nuclear field theory

We show that the -box expansion of nuclear many-body physics can be applied in nuclear effective field theory with explicit pions and external sources. We establish the corresponding power counting and give an algorithm for the construction of a hermitean and energy-independent potential for arbitrary scattering processes on nucleons and nuclei to a given order in the chiral expansion. Various examples are discussed in some detail.     

Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions

The density matrix expansion (DME) of Negele and Vautherin is a convenient tool to map finite-range physics associated with vacuum two- and three-nucleon interactions into the form of a Skyrme-like energy density functional (EDF) with density-dependent couplings. In this work, we apply the improved formulation of the DME proposed recently in arXiv:0910.4979 by Gebremariam et al. to the non-local Fock energy obtained from chiral effective field theory (EFT) two-nucleon (NN) interactions at next-to-next-to-leading-order (N²LO). The structure of the chiral interactions is such that each coupling in the DME Fock functional can be decomposed into a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the universal long-range pion exchanges. This motivates a new microscopically-guided Skyrme phenomenology where the density-dependent couplings associated with the underlying pion-exchange interactions are added to standard empirical Skyrme functionals, and the density-independent Skyrme parameters subsequently refit to data. A link to a downloadable Mathematica notebook containing the novel density-dependent couplings is provided.     

Three- and four-nucleon systems from chiral effective field theory

Recently developed chiral nucleon-nucleon (NN) forces at next-to-leading order (NLO), that describe NN phase shifts up to about 100 MeV fairly well, have been applied to 3N and 4N systems. Faddeev-Yakubovsky equations have been solved rigorously. The resulting 3N and 4N binding energies are in the same range as found using standard NN potentials. In addition, low-energy 3N scattering observables are very well reproduced as for standard NN forces. The long-standing A(y) puzzle is absent at NLO. The cutoff dependence of the scattering observables is rather weak.     

Nucleon propagation through nuclear matter in chiral effective field theory

We treat the propagation of a nucleon in nuclear matter by evaluating the ensemble average of the two-point function of the nucleon currents in the framework of chiral effective field theory. We first derive the effective parameters of the nucleon to one loop. The resulting formula for the effective mass has been known since before and gives an absurd value at normal nuclear density. We then modify it following Weinberg’s method for the two-nucleon system in the effective theory. Our results for the effective mass and the width of the nucleon are compared with those in the literature. PACS 11.30.Rd; 12.38.Lg; 12.39.Fe; 24.85.+p     

Candidate chiral nuclei in bromine isotopes based on triaxial relativistic mean field theory

Following the observation of candidate chiral doublet bands in ~(78,80)Br, triaxial deformations with corresponding configurations in odd-odd bromine isotopes have been investigated using adiabatic and configuration-fixed constrained triaxial relativistic-meanfield calculations with an aim of finding the boundary of chirality in the chain of Br isotopes. Several minima with triaxial deformation and the proper particle-hole configuration were obtained in ~(74,76,78,80,82)Br, where the chiral doublet bands have the possibility of occurrence. Furthermore, the possible existence of multiple chiral doublet(MχD) bands is demonstrated in ~(74,76,78,80,82)Br.Experiments to explore the chirality and MχD properties of Br isotopes are conducted to verify the predictions.