Some challenges for Nuclear Density Functional Theory
We discuss some of the challenges that the DFT community faces in its quest for the truly universal energy density functional applicable over the entire nuclear chart.
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arXiv subjects
K. Bennaceur
Publications and source records attributed to K. Bennaceur.
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.
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Coordinate-space solution of the Skyrme-Hartree-Fock-Bogolyubov equations within spherical symmetry. The program HFBRAD (v1.0)
We describe the first version (v1.00) of the code HFBRAD which solves the Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov equations in the coordinate representation within the spherical symmetry. A realistic representation of the quasiparticle wave functions on the space lattice allows for performing calculations up to the particle drip lines. Zero-range density-dependent interactions are used in the pairing channel. The pairing energy is calculated by either using a cut-off energy in the quasiparticle spectrum or the regularization scheme proposed by A. Bulgac and Y. Yu.
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Microscopic determination of the nuclear incompressibility within the non-relativistic framework
The nuclear incompressibility $K_\infty$ is deduced from measurements of the Isoscalar Giant Monopole Resonance (ISGMR) in medium-heavy nuclei, and the resulting value turns out to be model dependent. Since the considered nuclei have neutron excess, it has been suggested that the model dependence is due to the different behaviour of the symmetry energy in different models. To clarify this issue, we make a systematic and careful analysis based on new Skyrme forces which span a wide range of values for $K_\infty$, for the value of the symmetry energy at saturation and for its density dependence. By calculating, in a fully self-consistent fashion, the ISGMR centroid energy in $^{208}$Pb we reach, for the first time within the non-relativistic framework, three important conclusions: (i) the monopole energy, and consequently the deduced value of $K_\infty$, depend on a well defined parameter related to the shape of the symmetry energy curve and called $K_{sym}$; (ii) Skyrme forces of the type of SLy4 predict $K_\infty$ around 230 MeV, in agreement with the Gogny force (previous estimates using Skyrme interactions having been plagued by lack of full self-consistency); (iii) it is possible to build forces which predict $K_\infty$ around 250 MeV, although part of this increase is due to our poor knowledge of the density dependence and effective mass.
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Skyrme forces with extended density dependence
A generalized parameterization of the Skyrme effective force is discussed. Preliminary results are presented for infinite symmetric and asymmetric nuclear matter. In particular, it is shown that an enlarged density dependence based on two terms allows to choose independently the incompressibility and the isoscalar effective mass.
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Compressibility, effective mass and density dependence in Skyrme forces
Generalized density dependence in Skyrme effective interactions is investigated to get forces valid beyond the mean field approximation. Preliminary results are presented for infinite symmetric and asymmetric nuclear matter up to pure neutron matter.
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Gamow Shell Model Description of Neutron-Rich Nuclei
This work presents the first continuum shell-model study of weakly bound neutron-rich nuclei involving multiconfiguration mixing. For the single-particle basis, the complex-energy Berggren ensemble representing the bound single-particle states, narrow resonances, and the non-resonant continuum background is taken. Our shell-model Hamiltonian consists of a one-body finite potential and a zero-range residual two-body interaction. The systems with two valence neutrons are considered. The Gamow shell model, which is a straightforward extension of the traditional shell model, is shown to be an excellent tool for the microscopic description of weakly bound systems. It is demonstrated that the residual interaction coupling to the particle continuum is important; in some cases, it can give rise to the binding of a nucleus.
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Coupling to the continuous spectrum and HFB approximation
We propose a new method to solve the Hartree-Fock-Bogoliubov equations for weakly bound nuclei whose purpose is to improve the treatment of the continuum when a finite range two-body interaction is used. We replace the traditional expansion on a discrete harmonic oscillator basis by a mixed eigenfunction expansion associated with a potential that explicitely includes a continuous spectrum. We overcome the problem of continuous spectrum discretization by using a resonance expansion.
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Pairing anti-halo effect
We discuss pairing correlations in weakly bound neutron rich nuclei, by using the coordinate-space Hartree-Fock-Bogolyubov approach which allows to take properly into account the coupling to particle continuum. We show that the additional pairing binding energy acts against a development of an infinite rms radius, even in situations when an l=0 single-particle orbital becomes unbound.
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Shell model description of 16O(p,gamma)17F and 16O(p,p)16O reactions
We present shell model calculations of both the structure of 17F and the reactions 16O(p,gamma)17F, 16O(p,p)16O. We use the ZBM interaction which provides a good description of the properties of 16O and neighbouring nuclei and, in particular it takes account for the complicated correlations in coexisting low-lying states of 16O.
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Structure effects on the Coulomb dissociation of 8B at relativistic energies
We investigate the Coulomb dissociation of 8B on 208Pb target at the beam energy of 250 MeV/nucleon, employing the cross sections for the radiative capture reaction 7Be(p,gamma)8B calculated within the Shell Model Embedded in the Continuum (SMEC) approach. In contrast to the situation at lower beam energies, the Coulomb breakup cross sections are found to be sensitive to the M1 transitions. Comparisons of SMEC and single-particle potential model predictions show that the Coulomb breakup cross sections at these high energies are sensitive to the structure model of 8B. Analysis of the preliminary data taken recently at GSI reveal that E2 multipolarity contributes up to 25 % to the cross sections even for the relative energies of p - 7Be below 0.25 MeV.
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Analysis of the 16O(p,gamma)17F capture reaction using the shell model embedded in the continuum
We apply the realistic shell model which includes the coupling between many-particle (quasi-)bound states and the continuum of one-particle scattering states, called the Shell Model Embedded in the Continuum, to the spectroscopy of mirror nuclei: 17F and 17O, as well as to the description of low energy cross section (the astrophysical S-factor) for E1, E2 and M1 components in the capture reaction: 16O(p,gamma)17F. With the same microscopic input we calculate the phase shifts and differential cross-section for the elastic scattering of protons on 16O.
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Continuum effects for the mean-field and pairing properties of weakly bound nuclei
Continuum effects in the weakly bound nuclei close to the drip-line are investigated using the analytically soluble Poschl-Teller-Ginocchio potential. Pairing correlations are studied within the Hartree-Fock-Bogoliubov method. We show that both resonant and non-resonant continuum phase space is active in creating the pairing field. The influence of positive-energy phase space is quantified in terms of localizations of states within the nuclear volume.
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Study of the $^7Be(p,γ)^8B$ and $^7Li(n,γ)^8Li$ capture reactions using the shell model embedded in the continuum
We apply the realistic shell model which includes the coupling between many-particle (quasi-)bound states and the continuum of one-particle scattering states to the spectroscopy of mirror nuclei: $^8$B and $^8$Li, as well as to the description of low energy cross sections (the astrophysical S factors) in the capture reactions:$^7Be(p,γ)^8B$ and $^7Li(n,γ)^8Li$.
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A study of nuclei of astrophysical interest in the continuum shell model
We present here the first application of realistic shell model (SM) including coupling between many-particle (quasi-)bound states and the continuum of one-particle scattering states to the spectroscopy of 8B and to the calculation of astrophysical factors in the reaction 7Be(p,gamma)8B.
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