arXiv subjects

V. Hellemans

Publications and source records attributed to V. Hellemans.

14 recordsLinked to original sources

arXiv2014

Solution of the Skyrme HF+BCS equation on a 3D mesh. II. A new version of the Ev8 code

We describe a new version of the EV8 code that solves the nuclear Skyrme-Hartree-Fock+BCS problem using a 3-dimensional cartesian mesh. Several new features have been implemented with respect to the earlier version published in 2005. In particular, the numerical accuracy has been improved for a given mesh size by (i) implementing a new solver to determine the Coulomb potential for protons (ii) implementing a more precise method to calculate the derivatives on a mesh that had already been implemented earlier in our beyond-mean-field codes. The code has been made very flexible to enable the use of a large variety of Skyrme energy density functionals that have been introduced in the last years. Finally, the treatment of the constraints that can be introduced in the mean-field equations has been improved. The code Ev8 is today the tool of choice to study the variation of the energy of a nucleus from its ground state to very elongated or triaxial deformations with a well-controlled accuracy.

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arXiv2014

Generalized seniority with realistic interactions in open-shell nuclei

Generalized seniority provides a truncation scheme for the nuclear shell model, based on pairing correlations, which offers the possibility of dramatically reducing the dimensionality of the nuclear shell-model problem. Systematic comparisons against results obtained in the full shell-model space are required to assess the viability of this scheme. Here, we extend recent generalized seniority calculations for semimagic nuclei, the Ca isotopes, to open-shell nuclei, with both valence protons and valence neutrons. The even-mass Ti and Cr isotopes are treated in a full major shell and with realistic interactions, in the generalized seniority scheme with one broken proton pair and one broken neutron pair. Results for level energies, orbital occupations, and electromagnetic observables are compared with those obtained in the full shell-model space. We demonstrate that, even for the Ti isotopes, significant benefit would be obtained in going beyond the approximation of one broken pair of each type, while the Cr isotopes require further broken pairs to provide even qualitative accuracy.

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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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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

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

Generalized seniority for the shell model with realistic interactions

The generalized seniority scheme has long been proposed as a means of dramatically reducing the dimensionality of nuclear shell model calculations, when strong pairing correlations are present. However, systematic benchmark calculations, comparing results obtained in a model space truncated according to generalized seniority with those obtained in the full shell model space, are required to assess the viability of this scheme. Here, a detailed comparison is carried out, for semimagic nuclei taken in a full major shell and with realistic interactions. The even-mass and odd-mass Ca isotopes are treated in the generalized seniority scheme, for generalized seniority v<=3. Results for level energies, orbital occupations, and electromagnetic observables are compared with those obtained in the full shell model space.

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arXiv2011

The tensor part of the Skyrme energy density functional. III. Time-odd terms at high spin

This article extends previous studies on the effect of tensor terms in the Skyrme energy density functional by breaking of time-reversal invariance. We have systematically probed the impact of tensor terms on properties of superdeformed rotational bands calculated within the cranked Hartree-Fock-Bogoliubov approach for different parameterizations covering a wide range of values for the isoscalar and isovector tensor coupling constants. We analyze in detail the contribution of the tensor terms to the energies and dynamical moments of inertia and study their impact on quasi-particle spectra. Special attention is devoted to the time-odd tensor terms, the effect of variations of their coupling constants and finite-size instabilities.

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arXiv2011

The platinum nuclei: concealed configuration mixing and shape coexistence

The role of configuration mixing in the Pt region is investigated. For this chain of isotopes, the nature of the ground state changes smoothly, being spherical around mass $A\sim 174$ and $A\sim 192$ and deformed around the mid-shell N=104 region. This has a dramatic effect on the systematics of the energy spectra as compared to the systematics in the Pb and Hg nuclei. Interacting Boson Model with configuration mixing calculations are presented for gyromagnetic factors, $\alpha$-decay hindrance factors, and isotope shifts. The necessity of incorporating intruder configurations to obtain an accurate description of the latter properties becomes evident.

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arXiv2008

Spectral properties of a tractable collective Hamiltonian

The spectral properties of a tractable collective model Hamiltonian are studied. The potential energy is truncated up to quartic terms in the quadrupole deformation variables, incorporating vibrational, $γ$-independent rotational and axially deformed rotational structures. These physically significant limits are analysed in detail and confronted with well-established approximation schemes. Furthermore, transitional Hamiltonians in between the limits are presented and discussed. All results are obtained within a recently presented Cartan-Weyl based framework to calculate $SU(1,1)\times SO(5)$ embedded quadrupole collective observables.

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arXiv2008

Configuration mixing in the neutron-deficient $^{186-196}$Pb isotopes

In this article we report the results of detailed interacting boson model calculations with configuration mixing for the neutron-deficient Pb isotopes. Calculated energy levels and $B(E2)$ values for $^{188-196}$Pb are discussed and some care is suggested concerning the current classification on the basis of level systematics of the $4_1^+$ and $6_1^+$ states in $^{190-194}$Pb. Furthermore, quadrupole deformations are extracted for $^{186-196}$Pb and the mixing between the different families (0p-0h, 2p-2h, and 4p-4h) is discussed in detail. Finally, the experimental and the theoretical level systematics are compared.

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arXiv2007

Criticality in the configuration-mixed interacting boson model : (1) $U(5)-\hat{Q}(χ)\cdot\hat{Q}(χ)$ mixing

The case of U(5)--$\hat{Q}(χ)\cdot\hat{Q}(χ)$ mixing in the configuration-mixed Interacting Boson Model is studied in its mean-field approximation. Phase diagrams with analytical and numerical solutions are constructed and discussed. Indications for first-order and second-order shape phase transitions can be obtained from binding energies and from critical exponents, respectively.

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arXiv2007

Quadrupole collective variables in the natural Cartan-Weyl basis

The matrix elements of the quadrupole collective variables, emerging from collective nuclear models, are calculated in the natural Cartan-Weyl basis of O(5) which is a subgroup of a covering $SU(1,1)\times O(5)$ structure. Making use of an intermediate set method, explicit expressions of the matrix elements are obtained in a pure algebraic way, fixing the $γ$-rotational structure of collective quadrupole models.

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arXiv2005

A theoretical description of energy spectra and two-neutron separation energies for neutron-rich zirconium isotopes

Very recently the atomic masses of neutron-rich Zr isotopes, from $^{96}$Zr to $^{104}$Zr, have been measured with high precision. Using a schematic Interacting Boson Model (IBM) Hamiltonian, the evolution from spherical to deformed shapes along the chain of Zr isotopes, describing at the same time the excitation energies as well as the two-neutron separation energies, can be rather well reproduced. The interplay between phase transitions and configuration mixing of intruder excitations in this mass region is succinctly addressed.

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arXiv2004

Configuration mixing in $^{188}$Pb : band structure and electromagnetic properties

In the present paper, we carry out a detailed analysis of the presence and mixing of various families of collective bands in $^{188}$Pb. Making use of the interacting boson model, we construct a particular intermediate basis that can be associated with the unperturbed bands used in more phenomenological studies. We use the E2 decay to construct a set of collective bands and discuss in detail the B(E2)-values. We also perform an analysis of these theoretical results (Q, B(E2)) to deduce an intrinsic quadrupole moment and the associated quadrupole deformation parameter, using an axially deformed rotor model.

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