We construct a coordinate-space chiral potential, including ∆-isobar intermediate states in its two-pion-exchange component up to order Q 3 (Q denotes generically the low momentum scale). The contact interactions entering at next-to-leading and next-to-next-to-next-to-leading orders (Q 2 and Q 4 , respectively) are rearranged by Fierz transformations to yield terms at most quadratic in the relative momentum operator of the two nucleons. The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database, consisting of 2309 pp and 2982 np data (including, respectively, 148 and 218 normalizations) in the laboratory-energy range 0-300 MeV. For the total 5291 pp and np data in this range, we obtain a χ 2 /datum of roughly 1.3 for a set of three models characterized by long-and short-range cutoffs, RL and RS respectively, ranging from (RL, RS) = (1.2, 0.8) fm down to (0.8, 0.6) fm. The long-range (short-range) cutoff regularizes the one-and two-pion exchange (contact) part of the potential.

Nucleon-Nucleon potentials are commonplace in nuclear physics and are determined from a finite number of experimental data with limited precision sampling the scattering process. We study the statistical assumptions implicit in the standard least squares χ 2 fitting procedure and apply, along with more conventional tests, a tail sensitive quantile-quantile test as a simple and confident tool to verify the normality of residuals. We show that the fulfillment of normality tests is linked to a judicious and consistent selection of a nucleon-nucleon database. These considerations prove crucial to a proper statistical error analysis and uncertainty propagation. We illustrate these issues by analyzing about 8000 proton-proton and neutron-proton scattering published data. This enables the construction of potentials meeting all statistical requirements necessary for statistical uncertainty estimates in nuclear structure calculations.

The abstract of the above article contains a typographical error. Where the χ 2 values and number of data are stated, nn was printed instead of np. The correct text is as follows: "We obtain a χ 2 value of 2813 for pp and 3985 for np with a total of 2747 and 3691 pp and np data, respectively." Equation (2) of the above article contains an error in the number of operators O n . The correct expression to describe the NN interaction used in the partial-wave analysis is given bywhere O n is the set of operators. The first 18 operators correspond to the ones used in the AV18 basis. The remaining three operators further incorporate charge dependence, and each one can be written as a linear combination of the first 18 operators.The results and conclusions of the article are not affected by these typographical errors.

We determine the chiral constants of the Nucleon-Nucleon Two Pion Exchange potential deduced from Chiral Perturbation Theory. By using a coarse grained representation of the short distance interactions with 30 parameters, the Partial Wave Analysis fit gives χ 2 /ν = 1.08 to a mutually consistent set of 6713 data previously built from all published proton-proton and neutron proton scattering data from 1950 till 2013 with LAB energy below 350 MeV. We obtain (c 1 , c 3 , c 4 ) = (−0.41±1.08, −4.66±0.60, 4.31±0.17) GeV −1 with an almost 100% anti-correlation between c 1 and c 3 . We also provide the errors in the short distance parameters and propagate them to the deuteron properties and low partial waves phase shifts.

Background: Energy density functional methods provide a generic framework to compute properties of atomic nuclei starting from models of nuclear potentials and the rules of quantum mechanics. Until now, the overwhelming majority of functionals have been constructed either from empirical nuclear potentials such as the Skyrme or Gogny forces, or from systematic gradient-like expansions in the spirit of the density functional theory for atoms.Purpose: We seek to obtain a usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties.Methods: Our energy functional comprises two main components. The first component is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. Contributions to the mean field and the energy of this term are computed by expanding the spatial, finite-range components of the chiral potential onto Gaussian functions. The second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the unedf2 optimization protocol to determine the coupling constants of this energy functional. Results:We obtain a set of microscopically-constrained functionals for local chiral potentials from leading-order up to next-to-next-to-leading order with and without three-body forces and contributions from ∆ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, singleparticle shell structure in closed-shell nuclei and the fission barrier of 240 Pu. Quantitatively, they perform noticeable better than the more phenomenological Skyrme functionals. Conclusions:The inclusion of higher-order terms in the chiral perturbation expansion seems to produce a systematic improvement in predicting nuclear binding energies while the impact on other observables is not really significant. This result is especially promising since all the fits have been performed at the single-reference level of the energy density functional approach, where important collective correlations such as center-of-mass correction, rotational correction or zero-point vibrational energies have not been taken into account yet. * navarrop@ohio.edu † schunk1@llnl.gov ‡ dyhdalo.2@osu.edu § furnstahl.1@osu.edu ¶ bogner@nscl.msu.edu potentials. In light nuclei, the no-core shell model [3] or Quantum Monte-Carlo methods [4] are popular examples of such direct approaches; in heavier nuclei, alternative methods such as the coupled-cluster [5] or inmedium similarity renormalization group [6] can pro...