arXiv subjects

P. -G. Reinhard

Publications and source records attributed to P. -G. Reinhard.

At least 55 records · Page 3Linked to original sources

arXiv2018

Individual low-energy toroidal dipole state in $^{24}$Mg

The low-energy dipole excitations in $^{24}$Mg are investigated within the Skyrme quasiparticle random-phase-approximation (QRPA) for axial nuclei. The calculations with the force SLy6 reveal a remarkable feature: the lowest $I^πK=1^-1$ excitation (E = 7.92 MeV) in $^{24}$Mg is a vortical toroidal state (TS) representing a specific vortex-antivortex realization of well-known spherical Hill's vortex in a strongly deformed axial confinement. This is a striking example of an {\it individual} TS which can be much easier discriminated in experiment than the toroidal dipole resonance embracing many states. The TS acquires the lowest energy due to the huge prolate axial deformation in $^{24}$Mg. The result persists for different Skyrme parameterizations (SLy6, SVbas, SkM*). We analyze spectroscopic properties of the TS and its relation with the cluster structure of $^{24}$Mg. Similar TS could exist in other highly prolate light nuclei. They could serve as promising tests for various reactions to probe a vortical (toroidal) nuclear flow.

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arXiv2018

Wavelet signatures of $K$-splitting of the Isoscalar Giant Quadrupole Resonance in deformed nuclei from high-resolution (p,p$'$) scattering off $^{146,148,150}$Nd

The phenomenon of fine structure of the Isoscalar Giant Quadrupole Resonance (ISGQR) has been studied with high energy-resolution proton inelastic scattering at iThemba LABS in the chain of stable even-mass Nd isotopes covering the transition from spherical to deformed ground states. A wavelet analysis of the background-subtracted spectra in the deformed 146,148,150Nd isotopes reveals characteristic scales in correspondence with scales obtained from a Skyrme RPA calculation using the SVmas10 parameterization. A semblance analysis shows that these scales arise from the energy shift between the main fragments of the K = 0, 1 and K = 2 components.

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arXiv2017

Self-consistency in the phonon space of the particle-phonon coupling model

In the paper the non-linear generalization of the time blocking approximation (TBA) is presented. The TBA is one of the versions of the extended random-phase approximation (RPA) developed within the Green-function method and the particle-phonon coupling model. In the generalized version of the TBA the self-consistency principle is extended onto the phonon space of the model. The numerical examples show that this non-linear version of the TBA leads to the convergence of the results with respect to enlarging the phonon space of the model.

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arXiv2017

Deformation dependence of the isovector giant dipole resonance: The neodymium isotopic chain revisited

Proton inelastic scattering experiments at energy E_p = 200 MeV and a spectrometer scattering angle of 0 degree were performed on 144,146,148,150Nd and 152Sm exciting the IsoVector Giant Dipole Resonance (IVGDR). Comparison with results from photo-absorption experiments reveals a shift of resonance maxima towards higher energies for vibrational and transitional nuclei. The extracted photo-absorption cross sections in the most deformed nuclei, 150Nd and 152Sm, exhibit a pronounced asymmetry rather than a distinct double-hump structure expected as a signature of K-splitting. This behaviour can be related to the proximity of these nuclei to the critical point of the phase shape transition from vibrators to rotors with a soft quadrupole deformation potential. Self-consistent random-phase approximation (RPA) calculations using the SLy6 Skyrme force provide a relevant description of the IVGDR shapes deduced from the present data

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arXiv2017

Nuclear density-functional theory and fission of super-heavy elements

We review the prediction of fission properties of super-heavy elements (SHE) by self-consistent mean-field models thereby concentrating on the widely used Skyrme-Hartree-Fock (SHF) approach. We explain briefly the theoretical tools: the SHF model, the calibration of model parameters together with statistical analysis of uncertainties and correlations, and the involved computation of fission lifetimes. We present an overview of fission stability in comparison to other decay channels over the whole landscape of SHE reaching deep into the $r$-process domain. The main emphasis lies on a detailed discussion of the various ingredients determining eventually the fission properties. The main result is that fission is an involved process which explores many different influences with almost equal share, basic bulk properties (also known as liquid-drop model parameters), pairing strengths, and shell effects. %

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arXiv2017

Pairing and deformation effects in nuclear excitation spectra

We investigate effects of pairing and of quadrupole deformation on two sorts of nuclear excitations,$γ$-vibrational $K^π=2^+$ states and dipole resonances (isovector dipole, pygmy, compression, toroidal). The analysis is performed within the quasiparticle random-phase approximation (QRPA) based on the Skyrme energy functional using the Skyrme parametrization SLy6. Particular attention is paid to i) the role of the particle-particle (pp) channel in the residual interaction of QRPA, ii) comparison of volume pairing (VP) and surface pairing (SP), iii) peculiarities of deformation splitting in the various resonances. We find that the impact of the pp-channel on the considered excitations is negligible. This conclusion applies also to any other excitation except for the $K^π=0^+$ states. Furthermore, the difference between VP and SP is found small (with exception of peak height in the toroidal mode). In the low-energy isovector dipole (pygmy) and isoscalar toroidal modes, the branch $K^π=1^-$ is shown to dominate over $K^π=0^-$ one in the range of excitation energy $E <$ 8--10 MeV. The effect becomes impressive for the toroidal resonance whose low-energy part is concentrated in a high peak of almost pure $K^π=1^-$ nature. This peculiarity may be used as a fingerprint of the toroidal mode in future experiments. The interplay between pygmy, toroidal and compression resonances is discussed, the interpretation of the observed isoscalar giant dipole resonance is partly revised.

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arXiv2017

Optimizing phonon space in the phonon-coupling model

We present a new scheme to select the most relevant phonons in the phonon-coupling model, named here time-blocking approximation (TBA). The new criterion, based on the phonon-nucleon coupling strengths rather than on $B(EL)$ values, is more selective and thus produces much smaller phonon spaces in TBA. This is beneficial in two respects: first, it curbs down the computational cost, and second, it reduces the danger of double counting in the expansion basis of TBA. We use here TBA in a form where the coupling strength is regularized to keep the given Hartree-Fock ground state stable. The scheme is implemented in an RPA and TBA code based on the Skyrme energy functional. We first explore carefully the cutoff dependence with the new criterion and can work out a natural (optimal) cutoff parameter. Then we use the freshly developed and tested scheme to a survey of giant resonances and low-lying collective states in six doubly magic nuclei looking also on the dependence of the results when varying the Skyrme parametrization.

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arXiv2017

Towards the global description of nuclear charge radii: exploring the Fayans energy density functional

In this work, we study the odd-even effect in binding energies and charge radii, and systematic behavior of differential radii, to identify the underlying components of the effective nuclear interaction. We apply nuclear density functional theory using a family of Fayans and Skyrme energy density functionals fitted to similar datasets but using different optimization protocols. We inspect various correlations between differential charge radii, odd-even staggering in energies and radii, and nuclear matter properties. Detailed analysis is carried out for medium-mass and heavy semi-magic nuclei with a particular focus on the Ca chain. By making the surface and pairing terms dependent on density gradients, the Fayans functional offers the superb simultaneous description of odd-even staggering effects in energies and charge radii. Conversely, when the data on differential radii are added to the pool of fit-observables, the coupling constants determining the strengths of the gradient terms of Fayans functional are increased by orders of magnitude. The Skyrme functional optimized in this work with the generalized Fayans pairing term offers results of similar quality. We quantify these findings by performing correlation analysis based on the statistical linear regression technique. The nuclear matter parameters characterizing Fayans and Skyrme functionals optimized to similar datasets are fairly close.

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arXiv2017

Dissipation and energy balance in electronic dynamics of Na clusters

We investigate the impact of dissipation on the energy balance in the electron dynamics of metal clusters excited by strong electro-magnetic pulses. The dynamics is described theoretically by Time-Dependent Density-Functional Theory (TDDFT) at the level of Local Density Approximation (LDA) augmented by a self interaction correction term and a quantum collision term in Relaxation-Time Approximation (RTA). We evaluate the separate contributions to the total excitation energy, namely energy exported by electron emission, potential energy due to changing charge state, intrinsic kinetic and potential energy, and collective flow energy. The balance of these energies is studied as function of the laser parameters (frequency, intensity, pulse length) and as function of system size and charge. We also look at collisions with a highly charged ion and here at the dependence on the impact parameter (close versus distant collisions). Dissipation turns out to be small where direct electron emission prevails namely for laser frequencies above any ionization threshold and for slow electron extraction in distant collisions. Dissipation is large for fast collisions and at low laser frequencies, particularly at resonances.

cond-mat.mes-hall↗

arXiv2017

Forward-backward asymmetry of photoemission in C$_{60}$ excited by few-cycle laser pulses

We theoretically analyze angle-resolved photo-electron spectra (ARPES) generated by the interaction of C$_{60}$ with intense, short laser pulses. In particular, we focus on the impact of the carrier-envelope phase (CEP) onto the angular distribution. The electronic dynamics is described by time-dependent density functional theory, and the ionic background of $\csixty$ is approximated by a particularly designed jellium model. Our results show a clear dependence of the angular distributions onto the CEP for very short pulses covering only very few laser cycles, which disappears for longer pulses. For the specific laser parameters used in a recent experiments, a very good agreement is obtained. Furthermore, the asymmetry is found to depend on the energy of the emitted photoelectrons. The strong influence of the angular asymmetry of electron emission onto the CEP and pulse duration suggests to use this sensitivity as a means to analyze the structure of few-cycle laser pulses.

physics.atm-clus↗

arXiv2017

Deformation-induced splitting of isoscalar E0 giant resonance: Skyrme random-phase-approximation analysis

The deformation-induced splitting of isoscalar giant monopole resonance (ISGMR) is systematically analyzed in a wide range of masses covering medium, rare-earth, actinide, and superheavy axial deformed nuclei. The study is performed within the fully self-consistent quasiparticle random-phase-approximation (QRPA) method based on the Skyrme functional. Two Skyrme forces, one with a large (SV-bas) and one with a small (SkP) nuclear incompressibility, are considered. The calculations confirm earlier results that, due to the deformation-induced E0-E2 coupling, the isoscalar E0 resonance attains a double-peak structure and significant energy upshift. Our results are compared with available analytic estimations. Unlike earlier studies, we get a smaller energy difference between the lower and upper peaks and thus a stronger E0-E2 coupling. This in turn results in more pumping of E0 strength into the lower peak and more pronounced splitting of ISGMR. We also discuss widths of the peaks and their negligible correlation with deformation.

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arXiv2016

Carbon-oxygen-neon mass nuclei in superstrong magnetic fields

The properties of $\isotope[12]{C}$, $\isotope[16]{O}$, and $\isotope[20]{Ne}$ nuclei in strong magnetic fields $B\simeq 10^{17}\,$G are studied in the context of strongly magnetized neutron stars and white dwarfs. The SKY3D code is extended to incorporate the interaction of nucleons with the magnetic field and is utilized to solve the time-independent Hartree-Fock equations with a Skyrme interaction on a Cartesian three-dimensional grid. The numerical solutions demonstrate a number of phenomena, which include a splitting of the energy levels of spin-up and -down nucleons, spontaneous rearrangment of energy levels in $\isotope[16]{O}$ at a critical field, which leads to jump-like increases of magnetization and proton current in this nucleus, and evolution of the intrinsically deformed $\isotope[20]{Ne}$ nucleus towards a more spherical shape under increasing field strength. Many of the numerical features can be understood within a simple analytical model based on the occupation by the nucleons of the lowest states of the harmonic oscillator in a magnetic field.

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arXiv2016

Time-dependent density functional theory with twist-averaged boundary conditions

Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, 3D coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a box. For finite quantum systems (atoms, molecules, nuclei), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. These artifacts can be practically cured by introducing absorbing boundary conditions (ABC) through an absorbing potential in a certain boundary region sufficiently far from the described system. But also the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust) suffer artifacts from a finite computational box. In this regime, twist- averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we extend TABC to time-dependent framework and apply it to resolve the box artifacts for finite quantum systems using as test case small- and large-amplitude nuclear vibrations. We demonstrate that by using such a method, one can reduce finite volume effects drastically without adding any additional parameters. While they are almost equivalent in the linear regime, TABC and ABC differ in the nonlinear regime in their treatment of evaporated particles.

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arXiv2016

Sensitivity of the fusion cross section to the density dependence of the symmetry energy

It is the aim of this paper to discuss the impact of nuclear fusion on the EOS. This is a timely subject given the expected availability of increasingly exotic beams at rare isotope facilities\,\cite{balantekin2014}. In practice, we focus on $^{48}$Ca+$^{48}$Ca fusion. We employ three different approaches to calculate fusion cross-sections for a set of energy density functionals with systematically varying nuclear matter properties. Fusion calculations are performed using frozen densities, using a dynamic microscopic method based on density-constrained time-dependent Hartree-Fock (DC-TDHF) approach, as well as direct TDHF study of above barrier cross-sections. For these studies, we employ a family of Skyrme parametrizations with systematically varied nuclear matter properties. We find a slight preference for forces which deliver a slope of symmetry energy of $L\approx 50$\,MeV that corresponds to a neutron-skin thickness of $^{48}$Ca of $R_\mathrm{skin}\!=\!(0.180\!-\!0.210)$\,fm.

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arXiv2016

Application of an Extended Random Phase Approximation on Giant Resonances in Light, Medium and Heavy Mass Nuclei

We present results of the time blocking approximation (TBA) on giant resonances in light, medium and heavy mass nuclei. The TBA is an extension of the widely used random-phase approximation (RPA) adding complex configurations by coupling to phonon excitations. A new method for handling the single-particle continuum is developed and applied in the present calculations. We investigate in detail the dependence of the numerical results on the size of the single particle space and the number of phonons as well as on nuclear matter properties. Our approach is self-consistent, based on an energy-density functional of Skyrme type where we used seven different parameter sets. The numerical results are compared with experimental data.

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arXiv2016

Toroidal resonance: relation to pygmy mode, vortical properties and anomalous deformation splitting

We review a recent progress in investigation of the isoscalar toroidal dipole resonance (TDR). A possible relation of the TDR and low-energy dipole strength (also called a pygmy resonance) is analyzed. It is shown that the dipole strength in the pygmy region can by understood as a local manifestation of the collective vortical toroidal motion at the nuclear surface. Application of the TDR as a measure of the nuclear dipole vorticity is discussed. Finally, an anomalous splitting of the TDR in deformed nuclei is scrutinized.

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arXiv2016

Skyrme Random-Phase-Approximation description of lowest $K^π=2^+_γ$ states in axially deformed nuclei

The lowest quadrupole $γ$-vibrational $K^π=2^+$ states in axially deformed rare-earth (Nd, Sm, Gd, Dy, Er, Yb, Hf, W) and actinide (U) nuclei are systematically investigated within the separable random-phase-approximation (SRPA) based on the Skyrme functional. The energies $E_γ$ and reduced transition probabilities $B(E2)$ of $2^+_γ$-states are calculated with the Skyrme forces SV-bas and SkM$^*$. The energies of two-quasiparticle configurations forming the SRPA basis are corrected by using the pairing blocking effect. This results in a systematic downshift of $E_γ$ by 0.3-0.5 MeV and thus in a better agreement with the experiment, especially in Sm, Gd, Dy, Hf, and W regions. For other isotopic chains, a noticeable overestimation of $E_γ$ and too weak collectivity of $2^+_γ$-states still persist. It is shown that domains of nuclei with a low and high $2^+_γ$ -collectivity are related with the structure of the lowest 2-quasiparticle states and conservation of the Nilsson selection rules. The description of $2^+_γ$ states with SV-bas and SkM$^*$ is similar in light rare-earth nuclei but deviates in heavier nuclei. However SV-bas much better reproduces the quadrupole deformation and energy of the isoscalar giant quadrupole resonance. The accuracy of SRPA is justified by comparison with exact RPA. The calculations suggest that a further development of the self-consistent calculation schemes is needed for a systematic satisfactory description of the $2^+_γ$ states.

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arXiv2016

The phonon-coupling model for Skyrme forces

A short review on the self-consistent RPA based on a energy-density functional of the Skyrme type is given. We also present an extension of the RPA where the coupling of phonons to the single-particle states is considered. Within this approach we present numerical results which are compared with data. The self-consistent approach is compared with the Landau-Migdal theory. Here we derive from the self-consistent $ph$ interaction, the Landau-Migdal parameters as well as their density dependence. In the Appendix a new derivation of the reduced matrix elements of the $ph$ interaction is presented.

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