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T. Duguet

Publications and source records attributed to T. Duguet.

At least 73 records · Page 4Linked to original sources
arXiv2009

Symbolic computation of the Hartree-Fock energy from a chiral EFT three-nucleon interaction at N$^2$LO

We present the first of a two-part Mathematica notebook collection that implements a symbolic approach for the application of the density matrix expansion (DME) to the Hartree-Fock (HF) energy from a chiral effective field theory (EFT) three-nucleon interaction at N$^2$LO. The final output from the notebooks is a Skyrme-like energy density functional that provides a quasi-local approximation to the nonlocal HF energy. In this paper, we discuss the derivation of the HF energy and its simplification in terms of the scalar/vector-isoscalar/isovector parts of the one-body density matrix. Furthermore, a set of steps is described and illustrated on how to extend the approach to other three-nucleon interactions.

physics.comp-ph↗
arXiv2009

Non-empirical pairing energy functional in nuclear matter and finite nuclei

We study 1S0 pairing gaps in neutron and nuclear matter as well as in finite nuclei on the basis of microscopic two-nucleon interactions. Special attention is paid to the consistency of the pairing interaction and normal self-energy contributions. We find that pairing gaps obtained from low-momentum interactions depend only weakly on approximation schemes for the normal self-energy, required in present energy-density functional calculations, while pairing gaps from hard potentials are very sensitive to the effective-mass approximation scheme.

nucl-th↗
arXiv2009

Tensor part of the Skyrme energy density functional. II: Deformation properties of magic and semi-magic nuclei

We study systematically the impact of the time-even tensor terms of the Skyrme energy density functional, i.e. terms bilinear in the spin-current tensor density, on deformation properties of closed shell nuclei corresponding to 20, 28, 40, 50, 82, and 126 neutron or proton shell closures. We compare results obtained with three different families of Skyrme parameterizations whose tensor terms have been adjusted on properties of spherical nuclei: (i) TIJ interactions proposed in the first paper of this series [T. Lesinski et al., Phys. Rev. C 76, 014312 (2007)] which were constructed through a complete readjustment of the rest of the functional (ii) parameterizations whose tensor terms have been added perturbatively to existing Skyrme interactions, with or without readjusting the spin-orbit coupling constant. We analyse in detail the mechanisms at play behind the impact of tensor terms on deformation properties and how studying the latter can help screen out unrealistic parameterizations. It is expected that findings of the present paper are to a large extent independent of remaining deficiencies of the central and spin-orbit interactions, and will be of great value for the construction of future, improved energy functionals.

nucl-th↗
arXiv2009

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.

nucl-th↗
arXiv2009

New analysis method of the halo phenomenon in finite many-fermion systems. First applications to medium-mass atomic nuclei

A new analysis method to investigate halos in finite many-fermion systems is designed, as existing characterization methods are proven to be incomplete/inaccurate. A decomposition of the internal wave-function of the {$N$-body} system in terms of overlap functions allows a model-independent analysis of medium-range and asymptotic properties of the internal one-body density. The existence of a spatially decorrelated region in the density profile is related to the existence of three typical energy scales in the excitation spectrum of the {$(N-1)$-body} system. A series of model-independent measures, taking the internal density as the only input, are introduced. The new measures allow a quantification of the potential halo in terms of the average number of fermions participating to it and of its impact on the system extension. Those new "halo factors" are validated through simulations and applied to results obtained through energy density functional calculations of medium-mass nuclei. Performing spherical Hartree-Fock-Bogoliubov calculations with state-of-the-art Skyrme plus pairing functionals, a collective halo is predicted in drip-line Cr isotopes, whereas no such effect is seen in Sn isotopes.

nucl-th↗
arXiv2009

Halo phenomenon in finite many-fermion systems. Atom-positron complexes and large-scale study of atomic nuclei

The analysis method proposed in Ref. \cite{rotival07a} is applied to characterize halo properties in finite many-fermion systems. First, the versatility of the method is highlighted by applying it to light and medium-mass nuclei as well as to atom-positron and ion-positronium complexes. Second, the dependence of nuclear halo properties on the characteristics of the energy density functional used in self-consistent Hartree-Fock-Bogoliubov calculations is studied. It is found that (a) the low-density behavior of the pairing functional and the regularization/renormalization scheme must be chosen coherently and with care to provide meaningful predictions, (b) the impact of pairing correlations on halo properties is significant and is the result of two competing effects, (c) the detailed characteristics of the pairing functional has however only little importance, (d) halo properties depend significantly on any ingredient of the energy density functional that influences the location of single-particle levels; i.e. the effective mass, the tensor terms and the saturation density of nuclear matter. The latter dependencies give insights to how experimental data on medium-mass drip-line nuclei can be used in the distant future to constrain some characteristics of the nuclear energy density functional. Last but not least, large scale predictions of halos among all spherical even-even nuclei are performed using specific sets of particle-hole and particle-particle energy functionals. It is shown that halos in the ground state of medium-mass nuclei will only be found at the very limit of neutron stability and for a limited number of elements.

nucl-th↗
arXiv2009

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%.

nucl-th↗
arXiv2009

Configuration Mixing within the Energy Density Functional Formalism: Removing Spurious Contributions from Non-Diagonal Energy Kernels

Multi-reference calculations along the lines of the Generator Coordinate Method or the restoration of broken symmetries within the nuclear Energy Density Functional (EDF) framework are becoming a standard tool in nuclear structure physics. These calculations rely on the extension of a single-reference energy functional, of the Gogny or the Skyrme types, to non-diagonal energy kernels. There is no rigorous constructive framework for this extension so far. The commonly accepted way proceeds by formal analogy with the expressions obtained when applying the generalized Wick theorem to the non-diagonal matrix element of a Hamilton operator between two product states. It is pointed out that this procedure is ill-defined when extended to EDF calculations as the generalized Wick theorem is taken outside of its range of applicability. In particular, such a procedure is responsible for the appearance of spurious divergences and steps in multi-reference EDF energies, as was recently observed in calculations restoring particle number or angular momentum. In the present work, we give a formal analysis of the origin of this problem for calculations with and without pairing, i.e. constructing the density matrices from either Slater determinants or quasi-particle vacua. We propose a correction to energy kernels that removes the divergences and steps, and which is applicable to calculations based on any symmetry restoration or generator coordinate. The method is formally illustrated for particle number restoration and is specified to configuration mixing calculations based on Slater determinants.

nucl-th↗
arXiv2009

Particle-Number Restoration within the Energy Density Functional Formalism

We give a detailed analysis of the origin of spurious divergences and finite steps that have been recently identified in particle-number restoration calculations within the nuclear energy density functional framework. We isolate two distinct levels of spurious contributions to the energy. The first one is encoded in the definition of the basic energy density functional itself whereas the second one relates to the canonical procedure followed to extend the use of the energy density functional to multi-reference calculations. The first level of spuriosity relates to the long-known self-interaction problem and to the newly discussed self-pairing interaction process which might appear when describing paired systems with energy functional methods using auxiliary reference states of Bogoliubov or BCS type. A minimal correction to the second level of spuriosity to the multi-reference nuclear energy density functional proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041] is shown to remove completely the anomalies encountered in particle-number restored calculations. In particular, it restores sum-rules over (positive) particle numbers that are to be fulfilled by the particle-number-restored formalism. The correction is found to be on the order of several hundreds of keVs up to about 1 MeV in realistic calculations, which is small compared to the total binding energy, but often accounts for a substantial percentage of the energy gain from particle-number restoration and is on the same energy scale as the excitations one addresses with multi-reference energy density functional methods.

nucl-th↗
arXiv2009

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.

nucl-th↗
arXiv2007

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.

nucl-th↗
arXiv2007

The tensor part of the Skyrme energy density functional. I. Spherical nuclei

We perform a systematic study of the impact of the J^2 tensor term in the Skyrme energy functional on properties of spherical nuclei. In the Skyrme energy functional, the tensor terms originate both from zero-range central and tensor forces. We build a set of 36 parameterizations, which covers a wide range of the parameter space of the isoscalar and isovector tensor term coupling constants, with a fit protocol very similar to that of the successful SLy parameterizations. We analyze the impact of the tensor terms on a large variety of observables in spherical mean-field calculations, such as the spin-orbit splittings and single-particle spectra of doubly-magic nuclei, the evolution of spin-orbit splittings along chains of semi-magic nuclei, mass residuals of spherical nuclei, and known anomalies of charge radii. Our main conclusion is that the currently used central and spin-orbit parts of the Skyrme energy density functional are not flexible enough to allow for the presence of large tensor terms.

nucl-th↗
arXiv2006

Pairing correlations beyond the mean field

We discuss dynamical pairing correlations in the context of configuration mixing of projected self-consistent mean-field states, and the origin of a divergence that might appear when such calculations are done using an energy functional in the spirit of a naive generalized density functional theory.

nucl-th↗
arXiv2006

Tensor interaction contributions to single-particle energies

We calculate the contribution of the nucleon-nucleon tensor interaction to single-particle energies with finite-range $ G $ matrix potentials and with zero-range Skyrme potentials. The Skx Skyrme parameters including the zero-range tensor terms with strengths calibrated to the finite-range results are refitted to nuclear properties. The fit allows the zero-range proton-neutron tensor interaction as calibrated to the finite-range potential results and that gives the observed change in the single-particle gap $ε$(h$_{11/2}$)-$ε$(g$_{7/2}$) going from $^{114}$Sn to $^{132}$Sn. However, the experimental $\ell$ dependence of the spin-orbit splittings in $^{132}$Sn and $^{208}$Pb is not well described when the tensor is added, due to a change in the radial dependence of the total spin-orbit potential. The gap shift and a good fit to the $\ell$-dependence can be recovered when the like-particle tensor interaction is opposite in sign to that required for the $ G $ matrix.

nucl-th↗
arXiv2006

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.

nucl-th↗
arXiv2005

Do halos exist on the dripline of deformed nuclei?

A study of the effect of deformation and pairing on the development of halo nuclei is presented. Exploratory three-body $core+n+n$ calculations show that both the NN interaction and the deformation/excitation of the core hinder the formation of the halo. Preliminary self-consistent mean-field calculations are used to search for regions in the nuclear chart where halos could potentially develop. These are also briefly discussed.

nucl-th↗
arXiv2005

Pairing schemes for HFB calculations of nuclei

Several pairing schemes currently used to describe superfluid nuclei through Hartree-Fock-Bogolyubov (HFB) calculations are briefly reviewed. We put a particular emphasis on the regularization recipes used in connection with zero-range forces and on the density dependence which usually complement their definition. Regarding the chosen regularization process, the goal is not only to identify the impact it may or may not have on pairing properties of nuclei through spherical 1D HFB calculations but also to assess its tractability for systematic axial 2D and 3D mean-field and beyond-mean-field calculations.

nucl-th↗