arXiv subjects

K. Bennaceur

Publications and source records attributed to K. Bennaceur.

At least 37 records · Page 2Linked to original sources

arXiv2013

Spurious finite-size instabilities in nuclear energy density functionals

It is known that some well-established parametrizations of the EDF do not always provide converged results for nuclei and a qualitative link between this finding and the appearance of finite-size instabilities of SNM near saturation density when computed within the RPA has been pointed out. We seek for a quantitative and systematic connection between the impossibility to converge self-consistent calculations of nuclei and the occurrence of finite-size instabilities in SNM for the example of scalar-isovector (S=0, T=1) instabilities of the standard Skyrme EDF. We aim to establish a stability criterion based on computationally-friendly RPA calculations of SNM that is independent on the functional form of the EDF and that can be utilized during the adjustment of its coupling constants. Tuning the coupling constant $C^{ρΔρ}_{1}$ of the gradient term that triggers scalar-isovector instabilities of the standard Skyrme EDF, we find that the occurrence of instabilities in finite nuclei depends strongly on the numerical scheme used to solve the self-consistent mean-field equations. The link to instabilities of SNM is made by extracting the lowest density $ρ_{\text{crit}}$ at which a pole appears at zero energy in the RPA response function when employing the critical value of the coupling constant $C^{ρΔρ}_{1}$ extracted in nuclei. Our analysis suggests a two-fold stability criterion to avoid scalar-isovector instabilities: (i) The density $ρ_{\text{min}}$ corresponding to the lowest pole in the RPA response function should be larger than about 1.2 times the saturation density; (ii) one needs to verify that $ρ_{p}(q_{\text{pq}})$ exhibits a distinct global minimum and is not a decreasing function for large transferred momenta.

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arXiv2013

Quantum Hall Effect in Hydrogenated Graphene

The quantum Hall effect is observed in a two-dimensional electron gas formed in millimeter-scale hydrogenated graphene, with a mobility less than 10 $\mathrm{cm^{2}/V\cdot s}$ and corresponding Ioffe-Regel disorder parameter $(k_{F}λ)^{-1}\gg1$. In zero magnetic field and low temperatures, the hydrogenated graphene is insulating with a two-point resistance of order of $250 h/e^2$. Application of a strong magnetic field generates a negative colossal magnetoresistance, with the two-point resistance saturating within 0.5% of $h/2e^{2}$ at 45T. Our observations are consistent with the opening of an impurity-induced gap in the density of states of graphene. The interplay between electron localization by defect scattering and magnetic confinement in two-dimensional atomic crystals is discussed.

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arXiv2012

Skyrme pseudo-potential-based EDF parametrisation for spuriousity-free MR-EDF calculations

First exploratory steps towards a pseudo-potential-based Skyrme energy density functional for spuriousity-free multi-reference calculations are presented. A qualitatively acceptable fit can be accomplished by adding simple three- and four-body contact terms to the standard central plus spin-orbit two-body terms. To achieve quantitative predictive power, higher-order terms, e.g. velocity-dependent three-body terms, will be required.

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arXiv2012

Carrier drift velocity and edge magnetoplasmons in graphene

We investigate electron dynamics at the graphene edge by studying the propagation of collective edge magnetoplasmon (EMP) excitations. By timing the travel of narrow wave-packets on picosecond time scales around exfoliated samples, we find chiral propagation with low attenuation at a velocity which is quantized on Hall plateaus. We extract the carrier drift contribution from the EMP propagation and find it to be slightly less than the Fermi velocity, as expected for an abrupt edge. We also extract the characteristic length for Coulomb interaction at the edge and find it to be smaller than for soft, depletion edge systems.

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arXiv2012

Fitting Skyrme functionals using linear response theory

Recently, it has been recently shown that the linear response theory in symmetric nuclear matter can be used as a tool to detect finite size instabilities for different Skyrme functionals. In particular it has been shown that there is a correlation between the density at which instabilities occur in infinite matter and the instabilities in finite nuclei. In this article we present a new fitting protocol that uses this correlation to add new additional constraint in Symmetric Infinite Nuclear Matter in order to ensure the stability of finite nuclei against matter fluctuation in all spin and isospin channels. As an application, we give the parameters set for a new Skyrme functional which includes central and spin-orbit parts and which is free from instabilities by construction.

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arXiv2012

Effective theory for low-energy nuclear energy density functionals

We introduce a new class of effective interactions to be used within the energy-density-functional approaches. They are based on regularized zero-range interactions and constitute a consistent application of the effective-theory methodology to low-energy phenomena in nuclei. They allow for defining the order of expansion in terms of the order of derivatives acting on the finite-range potential. Numerical calculations show a rapid convergence of the expansion and independence of results of the regularization scale.

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arXiv2012

New parameterization of Skyrme's interaction for regularized multi-reference energy density functional calculations

[Background] Symmetry restoration and configuration mixing in the spirit of the generator coordinate method based on energy density functionals have become widely used techniques in low-energy nuclear structure physics. Recently, it has been pointed out that these techniques are ill-defined for standard Skyrme functionals, and a regularization procedure has been proposed to remove the resulting spuriosities from such calculations. This procedure imposes an integer power of the density for the density dependent terms of the functional. At present, only dated parameterizations of the Skyrme interaction fulfill this condition. [Purpose] To construct a set of parameterizations of the Skyrme energy density functional for multi-reference energy density functional calculations with regularization using the state-of-the-art fitting protocols. [Method] The parameterizations were adjusted to reproduce ground state properties of a selected set of doubly magic nuclei and properties of nuclear matter. Subsequently, these parameter sets were validated against properties of spherical and deformed nuclei. [Results] Our parameter sets successfully reproduce the experimental binding energies and charge radii for a wide range of singly-magic nuclei. Compared to the widely used SLy5 and to the SIII parameterization that has integer powers of the density, a significant improvement of the reproduction of the data is observed. Similarly, a good description of the deformation properties at $A\sim 80$ was obtained. [Conclusions] We have constructed new Skyrme parameterizations with integer powers of the density and validated them against a broad set of experimental data for spherical and deformed nuclei. These parameterizations are tailor-made for regularized multi-reference energy density functional calculations and can be used to study correlations beyond the mean-field in atomic nuclei.

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arXiv2012

Nuclear response for the Skyrme effective interaction with zero-range tensor terms. III. Neutron matter and neutrino propagation

The formalism of the linear response for the Skyrme energy density functional including tensor terms derived in articles [1,2] for nuclear matter is applied here to the case of pure neutron matter. As in article [2] we present analytical results for the response function in all channels, the Landau parameters and the odd-power sum rules. Special emphasis is given to the inverse energy weighted sum rule because it can be used to detect non physical instabilities. Typical examples are discussed and numerical results shown. Moreover, as a direct application, neutrino propagation in neutron matter is investigated through its neutrino mean free path at zero temperature. This quantity turns out to be very sensitive to the tensor terms of the Skyrme energy density functional.

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arXiv2012

Nuclear response for the Skyrme effective interaction with zero-range tensor terms. II. Sum rules and instabilities

The formalism of linear response theory for Skyrme forces including tensor terms presented in article [1] is generalized for the case of a Skyrme energy density functional in infinite matter. We also present analytical results for the odd-power sum rules, with particular attention to the inverse energy weighted sum rule, $M_{-1}$, as a tool to detect instabilities in Skyrme functionals.

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arXiv2011

Linear response in infinite nuclear matter as a tool to reveal finite size instabilities

Nuclear effective interactions are often modelled by simple analytical expressions such as the Skyrme zero-range force. This effective interaction depends on a limited number of parameters that are usually fitted using experimental data obtained from doubly magic nuclei. It was recently shown that many Skyrme functionals lead to the appearance of instabilities, in particular when symmetries are broken, for example unphysical polarization of odd-even or rotating nuclei. In this article, we show how the formalism of the linear response in infinite nuclear matter can be used to predict and avoid the regions of parameters that are responsible for these unphysical instabilities.

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arXiv2010

Transport and elastic scattering times as probes of the nature of impurity scattering in single and bilayer graphene

Both transport $τ_{tr}$ and elastic scattering times $τ_{e}$ are experimentally determined from the carrier density dependence of the magnetoconductance of monolayer and bilayer graphene. Both times and their dependences in carrier density are found to be very different in the monolayer and the bilayer. However their ratio $τ_{tr}/τ_{e} $is found to be of the order of $1.5 $ in both systems and independent of the carrier density. These measurements give insight on the nature (neutral or charged) and spatial extent of the scattering centers. Comparison with theoretical predictions yields that the main scattering mechanism in our graphene samples could be due to strong scatterers of short range, inducing resonant scattering, a likely candidate being vacancies.

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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.

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arXiv2009

Nuclear response for the Skyrme effective interaction with zero range tensor terms

The effects of a zero-range tensor component of the effective interaction on nuclear response functions are determined in the so-called RPA approach. Explicit formula in the case of symmetric homogeneous isotropic nuclear matter are given for each spin-isospin excitation channel. It is shown for a typical interaction with tensor couplings that the effects are quantitatively important, mainly in vector channels.

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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.

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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%.

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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.

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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.

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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.

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