arXiv subjects

P. -H. Heenen

Publications and source records attributed to P. -H. Heenen.

At least 19 recordsLinked to original sources

arXiv2019

Iterative approaches to the self-consistent nuclear energy density functional problem. Heavy ball dynamics and potential preconditioning

Large-scale applications of energy density functional (EDF) methods depend on fast and reliable algorithms to solve the associated non-linear self-consistency problem. When dealing with large single-particle variational spaces, existing solvers can become very slow, and their performance dependent on manual fine-tuning of numerical parameters. In addition, convergence can sensitively depend on particularities of the EDF's parametrisation under consideration. Using the widely-used Skyrme EDF as an example, we investigate the impact of the parametrisation of the EDF, both in terms of the operator structures present and the size of coupling constants, on the convergence of numerical solvers. We focus on two aspects of the self-consistency cycle, which are the diagonalisation of a fixed single-particle Hamiltonian on one hand and the evolution of the mean-field densities and potentials on the other. Throughout the article we use a coordinate-space representation, for which the behaviour of algorithms can be straightforwardly analysed. We propose two algorithmic improvements that are easily implementable in existing solvers, heavy-ball dynamics and potential preconditioning. We demonstrate that these methods can be made virtually parameter-free, requiring no manual fine-tuning to achieve near-optimal performance except for isolated cases. The combination of both methods decreases substantially the CPU time required to obtain converged results. The improvements are illustrated for the MOCCa code that solves the self-consistent HFB problem in a 3d coordinate space representation for parametrisations of the standard Skyrme EDF at next-to-leading order in gradients and its extension to next-to-next-to-leading order.

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arXiv2019

The impact of the surface energy coefficient on the deformation properties of atomic nuclei as predicted by Skyrme energy density functionals

In the framework of nuclear energy density functional (EDF) methods, many nuclear phenomena are related to the deformation of intrinsic states. Their accurate modeling relies on the correct description of the change of nuclear binding energy with deformation. The two most important contributions to the deformation energy have their origin in shell effects that are correlated to the spectrum of single-particle states, and the deformability of nuclear matter, that can be characterized by a model-dependent surface energy coefficient a_{surf}. With the goal of improving the global performance of nuclear EDFs through fine-tuning of their deformation properties, the purpose of this study is threefold. First, to analyze the impact of systematic variations of a_{surf} on properties of nuclei; second, to identify observables that can be safely used to narrow down the range of appropriate values of a_{surf} to be targeted in future parameter fits; third, to analyze the interdependence of a_{surf} with other properties of a nuclear EDF. Results for a large variety of relevant observables of deformed nuclei obtained from self-consistent mean-field calculations with a set of purpose-built SLy5sX parameterizations of the Skyrme EDF are correlated with the value of a_{surf}. The three main conclusions are that there is an evident preference for a comparatively low value of a_{surf}, as expected from the performance of existing parameterizations; that the isospin dependence of the surface energy also needs further finetuning in order to describe trends across the chart of nuclei; and that a satisfying simultaneous description of fission barriers and superdeformed states requires a better description of the single-particle spectra. [Note: The abstract has been abbreviated because of length restrictions imposed by the arXiv. See the paper for the full abstract.]

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arXiv2016

Symmetry-unrestricted Skyrme mean-field study of heavy nuclei

In the light of recent experimental developments, increasing attention is devoted to nuclear phenomena related to rotational excitations of exotic intrinsic nuclear configurations that often lack symmetries present in the majority of nuclei. Examples include configurations with a non-vanishing octupole moment. In order to describe this kind of states, we have developed a new computer code to solve the self-consistent mean-field equations, able to use most of today's effective Skyrme interactions and working in coordinate-space. We report on the development of MOCCa, a code based on the same principles as EV8, but offering the user individual control on many symmetry assumptions. In addition, the HF+BCS pairing treatment of EV8 has been generalised to the full machinery of Hartree-Fock-Bogoliubov transformations. We discuss as example the static fission barrier of $^{226}$Ra, prefacing extended studies in the region, using the recent series of Skyrme parameterizations SLy5s1 through SLy5s8.

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arXiv2015

Numerical accuracy of mean-field calculations in coordinate space

Background: Mean-field methods based on an energy density functional (EDF) are powerful tools used to describe many properties of nuclei in the entirety of the nuclear chart. The accuracy required on energies for nuclear physics and astrophysics applications is of the order of 500 keV and much effort is undertaken to build EDFs that meet this requirement. Purpose: The mean-field calculations have to be accurate enough in order to preserve the accuracy of the EDF. We study this numerical accuracy in detail for a specific numerical choice of representation for the mean-field equations that can accommodate any kind of symmetry breaking. Method: The method that we use is a particular implementation of 3-dimensional mesh calculations. Its numerical accuracy is governed by three main factors: the size of the box in which the nucleus is confined, the way numerical derivatives are calculated and the distance between the points on the mesh. Results: We have examined the dependence of the results on these three factors for spherical doubly-magic nuclei, neutron-rich $^{34}$Ne, the fission barrier of $^{240}$Pu and isotopic chains around Z = 50. Conclusions: Mesh calculations offer the user extensive control over the numerical accuracy of the solution scheme. By making appropriate choices for the numerical scheme the achievable accuracy is well below the model uncertainties of mean-field methods.

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arXiv2015

Collectivity in the light radon nuclei measured directly via Coulomb excitation

Background: Shape coexistence in heavy nuclei poses a strong challenge to state-of-the-art nuclear models, where several competing shape minima are found close to the ground state. A classic region for investigating this phenomenon is in the region around $Z=82$ and the neutron mid-shell at $N=104$. Purpose: Evidence for shape coexistence has been inferred from $α$-decay measurements, laser spectroscopy and in-beam measurements. While the latter allow the pattern of excited states and rotational band structures to be mapped out, a detailed understanding of shape coexistence can only come from measurements of electromagnetic matrix elements. Method: Secondary, radioactive ion beams of $^{202}$Rn and $^{204}$Rn were studied by means of low-energy Coulomb excitation at the REX-ISOLDE facility in CERN. Results: The electric-quadrupole ($E2$) matrix element connecting the ground state and first-excited $2^{+}_{1}$ state was extracted for both $^{202}$Rn and $^{204}$Rn, corresponding to ${B(E2;2^{+}_{1} \to 2^{+}_{1})=29^{+8}_{-8}}$ W.u. and $43^{+17}_{-12}$ W.u., respectively. Additionally, $E2$ matrix elements connecting the $2^{+}_{1}$ state with the $4^{+}_{1}$ and $2^{+}_{2}$ states were determined in $^{202}$Rn. No excited $0^{+}$ states were observed in the current data set, possibly due to a limited population of second-order processes at the currently-available beam energies. Conclusions: The results are discussed in terms of collectivity and the deformation of both nuclei studied is deduced to be weak, as expected from the low-lying level-energy schemes. Comparisons are also made to state-of-the-art beyond-mean-field model calculations and the magnitude of the transitional quadrupole moments are well reproduced.

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arXiv2015

Beyond mean-field study of elastic and inelastic electron scattering off nuclei

Electron scattering provides a powerful tool to determine charge distributions and transition densities of nuclei. This tool will soon be available for short-lived neutron-rich nuclei. [Purpose] Beyond mean-field methods have been successfully applied to the study of excitation spectra of nuclei in the whole nuclear chart. These methods permit to determine energies and transition probabilities starting from an effective in-medium nucleon-nucleon interaction but without other phenomenological ingredients. Such a method has recently been extended to calculate the charge density of nuclei deformed at the mean-field level of approximation [J. M. Yao et al., Phys. Rev. C86, 014310 (2012)]. The aim of this work is to further extend the method to the determination of transition densities between low-lying excited states. [Method] The starting point of our method is a set of Hartree-Fock-Bogoliubov wave functions generated with a constraint on the axial quadrupole moment and using a Skyrme energy density functional. Correlations beyond the mean field are introduced by projecting mean-field wave functions on angular-momentum and particle number and by mixing the symmetry restored wave functions.[Results] We give in this paper detailed formulae derived for the calculation of densities and form factors. These formulae are rather easy to obtain when both initial and final states are $0^+$ states but are far from being trivial when one of the states has a finite $J$-value. Illustrative applications to $^{24}$Mg and to the even-mass $^{58-68}$Ni have permitted to analyse the main features of our method, in particular the effect of deformation on densities and form factors. An illustration calculation of both elastic and inelastic scattering form factors is presented....

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arXiv2014

Beyond Mean-Field Calculations for Odd-A Nuclei

Beyond mean-field methods are very successful tools for the description of large-amplitude collective motion for even-even atomic nuclei. The state-of-the-art framework of these methods consists in a Generator Coordinate Method based on angular-momentum and particle-number projected triaxially deformed Hatree-Fock-Bogoliubov (HFB) states. The extension of this scheme to odd-mass nuclei is a long-standing challenge. We present for the first time such an extension, where the Generator Coordinate space is built from self-consistently blocked one-quasiparticle HFB states. One of the key points for this success is that the same Skyrme interaction is used for the mean-field and the pairing channels, thus avoiding problems related to the violation of the Pauli principle. An application to 25Mg illustrates the power of our method, as agreement with experiment is obtained for the spectrum, electromagnetic moments, and transition strengths, for both positive and negative parity states and without the necessity for effective charges or effective moments. Although the effective interaction still requires improvement, our study opens the way to systematically describe odd-A nuclei throughout the nuclear chart.

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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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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

Systematics of low-lying states of even-even nuclei in the neutron-deficient lead region from a beyond-mean-field calculation

Nuclei located in the neutron-deficient Pb region have a complex structure, rapidly evolving as a function of neutron and proton numbers. The most famous example is $^{186}$Pb where the three lowest levels are $0^+$ states, the two excited $0^+$ ones being located at low excitation energy around 600 keV. Coexisting structures with different properties are found in the neighboring nuclei. Many experiments have been performed over the last few years in which in-band and out-of-band $γ$ transition probabilities have been measured. A detailed interpretation of experimental data requires the use of a method going beyond a mean-field approach that permits to determine spectra and transition probabilities. Such methods have already been applied to selected isotopes in this mass region. Our aim is to provide a systematic investigation of this mass region in order to determine how well experimental data can be understood using a state-of-the-art method for nuclear structure. The starting point of our method is a set of mean-field wave functions generated with a constraint on the axial quadrupole moment and using a Skyrme energy density functional. Correlations beyond the mean field are introduced by projecting mean-field wave functions on angular-momentum and particle number and by mixing the symmetry restored wave functions as a function of the axial quadrupole moment. A detailed comparison with the available data is performed for energies, charge radii, spectroscopic quadrupole moments, $E0$ and $E2$ transition probabilities for the isotopic chains of neutron deficient Hg, Pb, Po and Rn. The connection between our results and the underlying mean field is also analyzed. Qualitative agreement with the data is obtained although our results indicate that the actual energy density functionals have to be improved further to achieve a quantitative agreement.

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arXiv2012

Structure of superheavy nuclei

Properties of transactinide nuclei needed for the interpretation of spectroscopic data and for the extrapolation to the expected "island of stability" of superheavy nuclei are reviewed from a theorist's point of view in the framework of self-consistent mean-field models.

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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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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

Symmetry restoration for odd-mass nuclei with a Skyrme energy density functional

In these proceedings, we report first results for particle-number and angular-momentum projection of self-consistently blocked triaxial one-quasiparticle HFB states for the description of odd-A nuclei in the context of regularized multi-reference energy density functionals, using the entire model space of occupied single-particle states. The SIII parameterization of the Skyrme energy functional and a volume-type pairing interaction are used.

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arXiv2010

Regularization of Multi-Reference Energy Density Functional Calculations

We report the first application of a recently proposed regularization procedure for multi-reference energy density functionals, which removes spurious divergent or non-continuous contributions to the binding energy, to a general configuration mixing. As an example, we present a calculation that corresponds to the particle-number and angular momentum projection of axially symmetric time-reversal invariant quasiparticle vacua of different quadrupole deformation for the nucleus O18. The SIII parameterization of the Skyrme energy functional is used.

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arXiv2010

Early onset of ground-state deformation in the neutron-deficient polonium isotopes

In-source resonant ionization laser spectroscopy of the even-$A$ polonium isotopes $^{192-210,216,218}$Po has been performed using the $6p^37s$ $^5S_2$ to $6p^37p$ $^5P_2$ ($λ=843.38$ nm) transition in the polonium atom (Po-I) at the CERN ISOLDE facility. The comparison of the measured isotope shifts in $^{200-210}$Po with a previous data set allows to test for the first time recent large-scale atomic calculations that are essential to extract the changes in the mean-square charge radius of the atomic nucleus. When going to lighter masses, a surprisingly large and early departure from sphericity is observed, which is only partly reproduced by Beyond Mean Field calculations.

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arXiv2010

Shape coexistence at the proton drip-line: First identification of excited states in 180Pb

Excited states in the extremely neutron-deficient nucleus, 180Pb, have been identified for the first time using the JUROGAM II array in conjunction with the RITU recoil separator at the Accelerator Laboratory of the University of Jyvaskyla. This study lies at the limit of what is presently achievable with in-beam spectroscopy, with an estimated cross-section of only 10 nb for the 92Mo(90Zr,2n)180Pb reaction. A continuation of the trend observed in 182Pb and 184Pb is seen, where the prolate minimum continues to rise beyond the N=104 mid-shell with respect to the spherical ground state. Beyond mean-field calculations are in reasonable correspondence with the trends deduced from experiment.

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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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