arXiv subjects

Paul-Gerhard Reinhard

Publications and source records attributed to Paul-Gerhard Reinhard.

30 records · Page 2Linked to original sources

arXiv2020

Future of Nuclear Fission Theory

There has been much recent interest in nuclear fission, due in part to a new appreciation of its relevance to astrophysics, stability of superheavy elements, and fundamental theory of neutrino interactions. At the same time, there have been important developments on a conceptual and computational level for the theory. The promising new theoretical avenues were the subject of a workshop held at the University of York in October 2019; this report summarises its findings and recommendations.

nucl-th↗

arXiv2020

Statistical aspects of nuclear mass models

We study the information content of nuclear masses from the perspective of global models of nuclear binding energies. To this end, we employ a number of statistical methods and diagnostic tools, including Bayesian calibration, Bayesian model averaging, chi-square correlation analysis, principal component analysis, and empirical coverage probability. Using a Bayesian framework, we investigate the structure of the 4-parameter Liquid Drop Model by considering discrepant mass domains for calibration. We then use the chi-square correlation framework to analyze the 14-parameter Skyrme energy density functional calibrated using homogeneous and heterogeneous datasets. We show that a quite dramatic parameter reduction can be achieved in both cases. The advantage of Bayesian model averaging for improving uncertainty quantification is demonstrated. The statistical approaches used are pedagogically described; in this context this work can serve as a guide for future applications.

nucl-th↗

arXiv2020

Rate for Laser-Induced Nuclear Dipole Absorption

Using the Brink-Axel hypothesis we derive the rate $R$ for nuclear dipole excitation by a laser pulse carrying $N \gg 1$ photons with average energy $\hbar ω_0 \approx 5$ MeV. As expected $R \propto (\hbar ω_0)^3$. The rate is also proportional to the aperure $α$ of the laser pulse. Perhaps less expected is the fact that $R \propto N$, irrespective of the degree of coherence of the laser pulse. The expression for $R$, derived for a nearly stationary laser pulse, is valid also for short times and can, thus, be used in simulations via rate equations of multiple nuclear dipole excitations by a single pulse. The explicit dependence of $R$ on the parameters of the laser pulse and on nuclear parameters given in the paper should help to optimize experiments on laser-nucleus reactions.

nucl-th↗

arXiv2017

The impact of the carrier envelope phase -- dependence on system and laser parameters

We investigate, from a theoretical perspective, photo-emission of electrons induced by ultra-short infrared pulses covering only a few photon cycles. In particular, we investigate the impact of the Carrier-Envelope Phase (CEP) of the laser pulse which plays an increasingly large role for decreasing pulse length. As key observable we look at the asymmetry of the angular distribution as function of kinetic energy of the emitted electrons. The focus of the present study lies on the system dependence of the reaction. To this end, we study two very different systems in comparison, an Ar atom and the Na9+ cluster. The study employs a fully quantum-mechanical description of electron dynamics at the level of Time-Dependent Density Functional Theory (TDDFT). We find a sensitive dependence on the system which can be related to the different spectral response properties. Results can be understood from an interplay of the ponderomotive motion driven by the external photon field and dynamical polarization of the system.

physics.atm-clus↗

arXiv2017

Central depression in nucleonic densities: Trend analysis in nuclear density-functional-theory approach

Central depression of nucleonic density, i.e., a reduction of density in the nuclear interior, has been attributed to many factors. E.g., bubble structures in superheavy (SH) nuclei are believed to be due to the electrostatic repulsion. In light nuclei, the mechanism has been discussed in terms of shell effects associated with occupations of s-orbits. The objective of this work is to reveal mechanisms behind the formation of central depression in nucleonic densities in light and heavy nuclei. We introduce several measures of the internal nucleonic density. Through the statistical analysis, we study the information content of these measures with respect to nuclear matter properties. We apply nuclear density functional theory with Skyrme functionals. Using the statistical tools of linear least square regression, we inspect correlations between various measures of central depression and model parameters, including nuclear matter properties. We study bivariate correlations with selected quantities as well as multiple correlations with groups of parameters. Detailed correlation analysis is carried out for $^{34}$Si for which a bubble structure has been reported recently, $^{48}$Ca, and N=82, 126, and 184 isotonic chains. We show that the central depression in medium-mass nuclei is very sensitive to shell effects, whereas for SH systems it is firmly driven by the electrostatic repulsion. An appreciable semi-bubble structure in proton density is predicted for $^{294}$Og, which is currently the heaviest nucleus known experimentally. Our correlation analysis reveals that the central density indicators in nuclei below $^{208}$Pb carry little information on parameters of nuclear matter; they are predominantly driven by shell structure. On the other hand, in the SH nuclei there exists a clear relationship between the central nucleonic density and symmetry energy.

nucl-th↗

arXiv2016

Laser-Matter Interaction: Classical Regime versus Quantum Regime

Doppler backscattering of optical laser photons on a "flying mirror" of relativistic electrons promises to yield coherent photons with MeV-range energies. We compare the nuclear interaction of such a laser pulse with the standard atom-laser interaction. The mean-field description of atoms must be replaced by a rate equation and the classical field strength, far too faint in nuclei, by the dipole transition rate. Significant nuclear excitation occurs for photon numbers much smaller than typical for atoms. That drastically reduces the requirements on the experimental realization of a "flying mirror".

nucl-th↗

arXiv2016

Stochastic TDHF in an exactly solvable model

We apply in a schematic model a theory beyond mean-field, namely Stochastic Time-Dependent Hartree-Fock (STDHF), which includes dynamical electron-electron collisions on top of an incoherent ensemble of mean-field states by occasional 2-particle-2-hole ($2p2h$) jumps. The model considered here is inspired by a Lipkin-Meshkov-Glick model of $Ω$ particles distributed into two bands of energy and coupled by a two-body interaction. Such a model can be exactly solved (numerically though) for small $Ω$. It therefore allows a direct comparison of STDHF and the exact propagation. The systematic impact of the model parameters as the density of states, the excitation energy and the bandwidth is presented and discussed. The time evolution of the STDHF compares fairly well with the exact entropy, as soon as the excitation energy is sufficiently large to allow $2p2h$ transitions. Limitations concerning low energy excitations and memory effects are also discussed.

physics.atm-clus↗

arXiv2016

Strong-field effects in the photo-emission spectrum of the C$_{60}$ fullerene

Considering C$_{60}$ as a model system for describing field emission from the extremity of a carbon nanotip, we explore electron emission from this fullerene excited by an intense, near-infrared, few-cycle laser pulse ($10^{13}$-$10^{14}~{\rm W/cm}^2$, 912 nm, 8-cycle). To this end, we use time-dependent density functional theory augmented by a self-interaction correction. The ionic background of C$_{60}$ is described by a soft jellium model. Particular attention is paid to the high energy electrons. Comparing the spectra at different emission angles, we find that, as a major result of this study, the photoelectrons are strongly peaked along the laser polarization axis forming a highly collimated electron beam in the forward direction, especially for the high energy electrons. Moreover, the high-energy plateau cut-off found in the simulations agrees well with estimates from the classical three-step model. We also investigate the build-up of the high-energy part of a photoelectron spectrum by a time-resolved analysis. In particular, the modulation on the plateau can be interpreted as contributions from intracycle and intercycle interferences.

physics.atm-clus↗

arXiv2014

Optimizing relativistic energy density functionals: covariance analysis

The stability of model parameters for a class of relativistic energy density functionals, characterized by contact (point-coupling) effective inter-nucleon interactions and density-dependent coupling parameters, is analyzed using methods of statistical analysis. A set of pseudo-observables in infinite and semi-infinite nuclear matter is used to define a quality measure $χ^2$ for subsequent analysis. We calculate uncertainties of model parameters and correlation coefficients between parameters, and determine the eigenvectors and eigenvalues of the matrix of second derivatives of $χ^2$ at the minimum. This allows to examine the stability of the density functional in nuclear matter, and to deduce weakly and strongly constrained combinations of parameters. In addition, we also compute uncertainties of observables that are not included in the calculation of $χ^2$: binding energy of asymmetric nuclear matter, surface thickness of semi-infinite nuclear matter, binding energies and charge radii of finite nuclei.

nucl-th↗

arXiv2013

Koopmans' condition in self-interaction corrected density functional theory

We investigate from a practitioner's point of view the computation of the ionization potential (IP) within density functional theory (DFT). DFT with (semi-)local energy-density functionals is plagued by a self-interaction error which hampers the computation of IP from the single-particle energy of the highest occupied molecular orbital (HOMO). The problem may be cured by a self interaction correction (SIC) for which there exist various approximate treatments. We compare the performance of the SIC proposed by Perdew and Zunger with the very simple average-density SIC (ADSIC) for a large variety of atoms and molecules up to larger systems as carbon rings and chains. Both approaches to SIC provide a large improvement to the quality of the IP if calculated from the HOMO level. The surprising result is that the simple ADSIC performs even better than the original Perdew-Zunger SIC (PZSIC) in the majority of the studied cases.

physics.atm-clus↗

arXiv2013

Time-Dependent Hartree-Fock Approach to Nuclear Pasta at Finite Temperature

We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation at temperatures of several MeV. The initial state consists of $α$ particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. This matter evolves into spherical, rod-like, and slab-like shapes and mixtures thereof. The simulations employ a full Skyrme interaction in a periodic three-dimensional grid. By an improved morphological analysis based on Minkowski functionals, all eight pasta shapes can be uniquely identified by the sign of only two valuations, namely the Euler characteristic and the integral mean curvature. In addition, we propose the variance in the cell density distribution as a measure to distinguish pasta matter from uniform matter.

nucl-th↗

arXiv2007

Violation of the `Zero-Force Theorem' in the time-dependent Krieger-Li-Iafrate approximation

We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the `Zero-Force Theorem'. By analyzing the time-dependent dipole moment of Na5 and Na9+, we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the `Zero-Force Theorem' and the `Generalized-Translation Invariance' of the potential, are discussed.

cond-mat.mtrl-sci↗