Generating functionals, consistency, and uniqueness in the integral equation theory of liquids

We discuss and illustrate through numerical examples the relations between generating functionals, thermodynamic consistency (in particular the virial-free energy one), and uniqueness of the solution, in the integral equation theory of liquids. We propose a new approach for deriving closures automatically satisfying such characteristics. Results from a first exploration of this program are presented and discussed.Comment: 27 pages, 5 figure

Computer simulation study of the closure relations in hard sphere fluids

We study, using Monte Carlo simulations, the cavity and the bridge functions of various hard sphere fluids: one component system, equimolar additive and non additive binary mixtures. In particular, we numerically check the assumption of local dependency of the bridge functions from the indirect correlation functions, on which most of the existing integral equation theories hinge. We find that this condition can be violated either in the region around the first and second neighbors shell, or inside the hard core, for the systems here considered. The violations manifest themselves clearly in the so called Duh-Haymet plots of the bridge functions versus the indirect correlation functions and become amplified as the coupling of the system increases.Comment: 24 pages, 13 figure

The two-nucleon electromagnetic charge operator in chiral effective field theory (χ\chiEFT) up to one loop

The electromagnetic charge operator in a two-nucleon system is derived in chiral effective field theory ($\chi$EFT) up to order $e\, Q$ (or N4LO), where $Q$ denotes the low-momentum scale and $e$ is the electric charge. The specific form of the N3LO and N4LO corrections from, respectively, one-pion-exchange and two-pion-exchange depends on the off-the-energy-shell prescriptions adopted for the non-static terms in the corresponding potentials. We show that different prescriptions lead to unitarily equivalent potentials and accompanying charge operators. Thus, provided a consistent set is adopted, predictions for physical observables will remain unaffected by the non-uniqueness associated with these off-the-energy-shell effects.Comment: 16 pages, 10 figure

Electromagnetic Structure and Reactions of Few-Nucleon Systems in χ\chiEFT

We summarize our recent work dealing with the construction of the nucleon-nucleon potential and associated electromagnetic currents up to one loop in chiral effective field theory ($\chi$EFT). The magnetic dipole operators derived from these currents are then used in hybrid calculations of static properties and low-energy radiative capture processes in few-body nuclei. A preliminary set of results are presented for the magnetic moments of the deuteron and trinucleons and thermal neutron captures on $p$, $d$, and $^3$He.Comment: Invited talk to the 19th International IUPAP Conference on Few-Body Problems in Physic

Electromagnetic processes in a χ\chiEFT framework

Recently, we have derived a two--nucleon potential and consistent nuclear electromagnetic currents in chiral effective field theory with pions and nucleons as explicit degrees of freedom. The calculation of the currents has been carried out to include N$^3$LO corrections, consisting of two--pion exchange and contact contributions. The latter involve unknown low-energy constants (LECs), some of which have been fixed by fitting the $np$ S- and P-wave phase shifts up to 100 MeV lab energies. The remaining LECs entering the current operator are determined so as to reproduce the experimental deuteron and trinucleon magnetic moments, as well as the $np$ cross section. This electromagnetic current operator is utilized to study the $nd$ and $n^3$He radiative captures at thermal neutron energies. Here we discuss our results stressing on the important role played by the LECs in reproducing the experimental data.Comment: Invited talk at the 5th International Conference on Quarks and Nuclear Physics, to appear in Chinese Physics