Density Functional Theory with Spatial-Symmetry Breaking and Configuration Mixing

This article generalizes the notion of the local density of a many-body system to introduce collective coordinates as explicit degrees of freedom. It is shown that the energy of the system can be expressed as a functional of this object. The latter can in turn be factorized as the product of the square of a collective wave function and a normalized collective-coordinate-dependent density. Energy minimization translates into a set of coupled equations, i.e. a local Schr\"odinger equation for the collective wave function and a set of Kohn-Sham equations for optimizing the normalized density at each point in the collective space. These equations reformulate the many-body problem exactly provided one is able to determine density- and collective-wave-function-dependent terms of the collective mass and potential which play a similar role to the exchange-correlation term in electronic Kohn-Sham density functional theory.Comment: 13 pages. Minor corrections, references and elements of discussion adde

Non-empirical pairing functional

The present contribution reports the first systematic finite-nucleus calculations performed using the Energy Density Functional method and a non-empirical pairing functional derived from low-momentum interactions. As a first step, the effects of Coulomb and the three-body force are omitted while only the bare two-nucleon interaction at lowest order is considered. To cope with the finite-range and non-locality of the bare nuclear interaction, the 1S0 channel of Vlowk is mapped onto a convenient operator form. For the first time, neutron-neutron and proton-proton pairing correlations generated in finite nuclei by the direct term of the two-nucleon interaction are characterized in a systematic manner. Eventually, such predictions are compared to those obtained from empirical local functionals derived from density-dependent zero range interactions. The characteristics of the latter are analyzed in view of that comparison and a specific modification of their isovector density dependence is suggested to accommodate Coulomb effects and the isovector trend of neutron gaps at the same time.Comment: To be printed in the Proceedings of the International Les Houches School on "Exotic Nuclei: New Challenges", May 7-18 2007, Les Houches, France, 9 pages, 2 figures. Minor modification

Chiral three-nucleon forces and pairing in nuclei

We present the first study of pairing in nuclei including three-nucleon forces. We perform systematic calculations of the odd-even mass staggering generated using a microscopic pairing interaction at first order in chiral low-momentum interactions. Significant repulsive contributions from the leading chiral three-nucleon forces are found. Two- and three-nucleon interactions combined account for approximately 70% of the experimental pairing gaps, which leaves room for self-energy and induced interaction effects that are expected to be overall attractive in nuclei.Comment: 4 pages, 3 figure

Non-empirical pairing energy density functional. First order in the nuclear plus Coulomb two-body interaction

We perform systematic calculations of pairing gaps in semi-magic nuclei across the nuclear chart using the Energy Density Functional method and a {\it non-empirical} pairing functional derived, without further approximation, at lowest order in the two-nucleon vacuum interaction, including the Coulomb force. The correlated single-particle motion is accounted for by the SLy4 semi-empirical functional. Rather unexpectedly, both neutron and proton pairing gaps thus generated are systematically close to experimental data. Such a result further suggests that missing effects, i.e. higher partial-waves of the NN interaction, the NNN interaction and the coupling to collective fluctuations, provide an overall contribution that is sub-leading as for generating pairing gaps in nuclei. We find that including the Coulomb interaction is essential as it reduces proton pairing gaps by up to 40%.Comment: 6 pages, 1 figure, accepted for publication in EPJ

Pairing in the Framework of the Unitary Correlation Operator Method (UCOM): Hartree-Fock-Bogoliubov Calculations

In this first in a series of articles, we apply effective interactions derived by the Unitary Correlation Operator Method (UCOM) to the description of open-shell nuclei, using a self-consistent Hartree-Fock-Bogoliubov framework to account for pairing correlations. To disentangle the particle-hole and particle-particle channels and assess the pairing properties of \VUCOM, we consider hybrid calculations using the phenomenological Gogny D1S interaction to derive the particle-hole mean field. In the main part of this article, we perform calculations of the tin isotopic chain using \VUCOM in both the particle-hole and particle-particle channels. We study the interplay of both channels, and discuss the impact of non-central and non-local terms in realistic interactions as well as the frequently used restriction of pairing interactions to the ${}^1S_0$ partial wave. The treatment of the center-of-mass motion and its effect on theoretical pairing gaps is assessed independently of the used interactions.Comment: 14 pages, 10 figures, to appear in Phys. Rev. C, title modified accordingl

Particle-Number Restoration within the Energy Density Functional formalism: Nonviability of terms depending on noninteger powers of the density matrices

We discuss the origin of pathological behaviors that have been recently identified in particle-number-restoration calculations performed within the nuclear energy density functional framework. A regularization method that removes the problematic terms from the multi-reference energy density functional and which applies (i) to any symmetry restoration- and/or generator-coordinate-method-based configuration mixing calculation and (ii) to energy density functionals depending only on integer powers of the density matrices, was proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041] and implemented for particle-number restoration calculations in [M. Bender, T. Duguet, D. Lacroix, arXiv:0809.2045]. In the present paper, we address the viability of non-integer powers of the density matrices in the nuclear energy density functional. Our discussion builds upon the analysis already carried out in [J. Dobaczewski \emph{et al.}, Phys. Rev. C \textbf{76}, 054315 (2007)]. First, we propose to reduce the pathological nature of terms depending on a non-integer power of the density matrices by regularizing the fraction that relates to the integer part of the exponent using the method proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041]. Then, we discuss the spurious features brought about by the remaining fractional power. Finally, we conclude that non-integer powers of the density matrices are not viable and should be avoided in the first place when constructing nuclear energy density functionals that are eventually meant to be used in multi-reference calculations.Comment: 17 pages, 12 figures, accepted for publication in PR

The neutron polaron as a constraint on nuclear density functionals

We study the energy of an impurity (polaron) that interacts strongly in a sea of fermions when the effective range of the impurity-fermion interaction becomes important, thereby mapping the Fermi polaron of condensed matter physics and ultracold atoms to strongly interacting neutrons. We present Quantum Monte Carlo results for this neutron polaron, and compare these with effective field theory calculations that also include contributions beyond the effective range. We show that state-of-the-art nuclear density functionals vary substantially and generally underestimate the neutron polaron energy. Our results thus provide constraints for adjusting the time-odd components of nuclear density functionals to better characterize polarized systems.Comment: 5 pages, 3 figures; v2 corresponds to the published versio

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 Skyme-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 {\it 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 (N$^2$LO). The structure of the chiral interactions is such that each coupling in the DME Fock functional can be decomposed into a cutoff-dependent coupling {\it constant} arising from zero-range contact interactions and a cutoff-independent coupling {\it 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 Mathematica notebook containing the novel density-dependent couplings is provided.Comment: 28 pages, 12 figures. Mathematica notebook provided with submission

Non-empirical nuclear energy functionals, pairing gaps and odd-even mass differences

First, we briefly outline some aspects of the starting project to design non-empirical energy functionals based on low-momentum vacuum interactions and many-body perturbation theory. Second, we present results obtained within an approximation of such a scheme where the pairing part of the energy density functional is constructed at first order in the nuclear plus Coulomb two-body interaction. We discuss in detail the physics of the odd-even mass staggering and the necessity to compute actual odd-even mass differences to analyze it meaningfully.Comment: 8 pages, 1 figure, proceedings of the International Conference on Nuclear Structure and Dynamics, Dubrovnik, Croatia, May 4 - 8, 200

Isovector splitting of nucleon effective masses, ab-initio benchmarks and extended stability criteria for Skyrme energy functionals

We study the effect of the splitting of neutron and proton effective masses with isospin asymmetry on the properties of the Skyrme energy density functional. We discuss the ability of the latter to predict observable of infinite matter and finite nuclei, paying particular attention to controlling the agreement with ab-initio predictions of the spin-isospin content of the nuclear equation of state, as well as diagnosing the onset of finite size instabilities, which we find to be of critical importance. We show that these various constraints cannot be simultaneously fulfilled by the standard Skyrme force, calling at least for an extension of its P-wave part.Comment: 17 pages, 9 figures; Minor changes, references added; Accepted for publication in Phys.Rev.