arXiv subjects

P. -G. Reinhard

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

At least 199 records · Page 11Linked to original sources

arXiv2003

Mapping exchange in relativistic Hartree-Fock

We show that formally for the standard ansatz relativistic point-coupling mean-field (RMF-PC) model a lagrangian density L is not equivalent in Hartree and Hartree-Fock approximations. The equivalency can be achieved only if we use a ``complete'' ansatz at the cost of introducing new parameters in the model. An approximate treatment of the exchange terms from standard RMF-PC indicates that these effects cannot be easily, if at all, absorbed by a Dirac-Hartree approximation.

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arXiv2002

Orbital magnetism in axially deformed sodium clusters: From scissors mode to dia-para magnetic anisotropy

Low-energy orbital magnetic dipole excitations, known as scissors mode (SM), are studied in alkali metal clusters. Subsequent dynamic and static effects are explored. The treatment is based on a self-consistent microscopic approach using the jellium approximation for the ionic background and the Kohn-Sham mean field for the electrons. The microscopic origin of SM and its main features (structure of the mode in light and medium clusters, separation into low- and high-energy plasmons, coupling high-energy M1 scissors and E2 quadrupole plasmons, contributions of shape isomers, etc) are discussed. The scissors M1 strength acquires large values with increasing cluster size. The mode is responsible for the van Vleck paramagnetism of spin-saturated clusters. Quantum shell effects induce a fragile interplay between Langevin diamagnetism and van Vleck paramagnetism and lead to a remarkable dia-para anisotropy in magnetic susceptibility of particular light clusters. Finally, several routes for observing the SM experimentally are discussed.

physics.atm-clus↗

arXiv2002

Separable RPA for self-consistent nuclear models

Self-consistent factorization of two-body residual interaction is proposed for arbitrary density- and current-dependent energy functionals. Following this procedure, a separable RPA (SRPA) method is constructed. SRPA considerably simplifies the calculations and demonstrates quick convergence to exact results. The method is tested for SkI3 and SkM* forces.

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arXiv2002

Scissors modes in triaxial metal clusters

We study the scissors mode (orbital M1 excitations) in small Na clusters, triaxial metal clusters ${\rm Na}_{12}$ and ${\rm Na}_{16}$ and the close-to-spherical ${{\rm Na}_9}^+$, all described in DFT with detailed ionic background. The scissors modes built on spin-saturated ground and spin-polarized isomeric states are analyzed in virtue of both macroscopic collective and microscopic shell-model treatments. It is shown that the mutual destruction of Coulomb and the exchange-correlation parts of the residual interaction makes the collective shift small and the net effect can depend on details of the actual excited state. The crosstalk with dipole and spin-dipole modes is studied in detail. In particular, a strong crosstalk with spin-dipole negative-parity mode is found in the case of spin-polarized states. Triaxiality and ionic structure considerably complicate the scissors response, mainly at expense of stronger fragmentation of the strength. Nevertheless, even in these complicated cases the scissors mode is mainly determined by the global deformation. The detailed ionic structure destroys the spherical symmetry and can cause finite M1 response (transverse optical mode) even in clusters with zero global deformation. But its strength turns out to be much smaller than for the genuine scissors modes in deformed systems.

physics.atm-clus↗

arXiv2002

Projection and ground state correlations made simple

We develop and test efficient approximations to estimate ground state correlations associated with low- and zero-energy modes. The scheme is an extension of the generator-coordinate-method (GCM) within Gaussian overlap approximation (GOA). We show that GOA fails in non-Cartesian topologies and present a topologically correct generalization of GOA (topGOA). An RPA-like correction is derived as the small amplitude limit of topGOA, called topRPA. Using exactly solvable models, the topGOA and topRPA schemes are compared with conventional approaches (GCM-GOA, RPA, Lipkin-Nogami projection) for rotational-vibrational motion and for particle number projection. The results shows that the new schemes perform very well in all regimes of coupling.

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arXiv2001

Nuclear Ground State Observables and QCD Scaling in a Refined Relativistic Point Coupling Model

We present results obtained in the calculation of nuclear ground state properties in relativistic Hartree approximation using a Lagrangian whose QCD-scaled coupling constants are all natural (dimensionless and of order 1). Our model consists of four-, six-, and eight-fermion point couplings (contact interactions) together with derivative terms representing, respectively, two-, three-, and four-body forces and the finite ranges of the corresponding mesonic interactions. The coupling constants have been determined in a self-consistent procedure that solves the model equations for representative nuclei simultaneously in a generalized nonlinear least-squares adjustment algorithm. The extracted coupling constants allow us to predict ground state properties of a much larger set of even-even nuclei to good accuracy. The fact that the extracted coupling constants are all natural leads to the conclusion that QCD scaling and chiral symmetry apply to finite nuclei.

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arXiv2001

The Z=82 shell closure in neutron-deficient Pb isotopes

Recent mass measurements show a substantial weakening of the binding energy difference delta_{2p} (Z,N) = E(Z-2,N) - 2 E(Z,N) + E(Z+2,N) in the neutron-deficient Pb isotopes. As delta_{2p} is often attributed to the size of the proton magic gap, it might be speculated that the reduction in delta_{2p} is related to a weakening of the spherical Z=82 shell. We demonstrate that the observed trend is described quantitatively by self-consistent mean-field models in terms of deformed ground states of Hg and Po isotopes.

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arXiv2001

Self-Consistent Separable RPA For Density- and Current-Dependent Forces

Self-consistent factorization of two-body residual interaction is proposed for arbitrary density- and current-dependent energy functionals. Following this procedure, a separable RPA (SRPA) method is constructed. SRPA dramatically simplifies the calculations and demonstrates quick convergence to exact results. The method is tested for SkM* forces.

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arXiv2001

Collectivity in the optical response of small metal clusters

The question whether the linear absorption spectra of metal clusters can be interpreted as density oscillations (collective ``plasmons'') or can only be understood as transitions between distinct molecular states is still a matter of debate for clusters with only a few electrons. We calculate the photoabsorption spectra of Na2 and Na5+ comparing two different methods: quantum fluid-dynamics and time-dependent density functional theory. The changes in the electronic structure associated with particular excitations are visualized in ``snapshots'' via transition densities. Our analysis shows that even for the smallest clusters, the observed excitations can be interpreted as intuitively understandable density oscillations. For Na5+, the importance of self-interaction corrections to the adiabatic local density approximation is demonstrated.

physics.atm-clus↗

arXiv2001

Shell stabilization of super- and hyperheavy nuclei without magic gaps

Quantum stabilization of superheavy elements is quantified in terms of the shell-correction energy. We compute the shell correction using self-consistent nuclear models: the non-relativistic Skyrme-Hartree-Fock approach and the relativistic mean-field model, for a number of parametrizations. All the forces applied predict a broad valley of shell stabilization around Z=120 and N=172-184. We also predict two broad regions of shell stabilization in hyperheavy elements with N approx 258 and N approx 308. Due to the large single-particle level density, shell corrections in the superheavy elements differ markedly from those in lighter nuclei. With increasing proton and neutron numbers, the regions of nuclei stabilized by shell effects become poorly localized in particle number, and the familiar pattern of shells separated by magic gaps is basically gone.

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arXiv2001

Pairing Interaction and Self-Consistent Densities in Neutron-Rich Nuclei

Particle and pairing densities in spherical even-even neutron-rich nuclei are studied within the Skyrme-Hartree-Fock-Bogoliubov approach with the density-dependent pairing interaction. The influence of the density dependence of the pairing interaction on asymptotic properties of nucleonic distributions are analyzed. It is demonstrated that the size of the neutron halo dramatically depends on the behavior of the pairing interaction at low density.

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arXiv2000

Mean-field models and superheavy elements

We discuss the performance of two widely used nuclear mean-field models, the relativistic mean-field theory (RMF) and the non-relativistic Skyrme-Hartree-Fock approach (SHF), with particular emphasis on the description of superheavy elements (SHE). We provide a short introduction to the SHF and RMF, the relations between these two approaches and the relations to other nuclear structure models, briefly review the basic properties with respect to normal nuclear observables, and finally present and discuss recent results on the binding properties of SHE computed with a broad selection of SHF and RMF parametrisations.

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arXiv2000

Twist Mode in Spherical Alkali Metal Clusters

A remarkable orbital quadrupole magnetic resonance, so-called twist mode, is predicted in alkali metal clusters where it is represented by $I^π=2^-$ low-energy excitations of valence electrons with strong M2 transitions to the ground state. We treat the twist by both macroscopic and microscopic ways. In the latter case, the shell structure of clusters is fully exploited, which is crucial for the considered size region ($8\le N_e\le 1314$). The energy-weighted sum rule is derived for the pseudo-Hamiltonian. In medium and heavy spherical clusters the twist dominates over its spin-dipole counterpart and becomes the most strong multipole magnetic mode.

cond-mat.mes-hall↗

arXiv2000

Ionic and electronic structure of sodium clusters up to N=59

We determined the ionic and electronic structure of sodium clusters with even electron numbers and 2 to 59 atoms in axially averaged and three-dimensional density functional calculations. A local, phenomenological pseudopotential that reproduces important bulk and atomic properties and facilitates structure calculations has been developed. Photoabsorption spectra have been calculated for $\mathrm{Na}_2$, $\mathrm{Na}_8$, and $\mathrm{Na}_9^+$ to $\mathrm{Na}_{59}^+$. The consistent inclusion of ionic structure considerably improves agreement with experiment. An icosahedral growth pattern is observed for $\mathrm{Na}_{19}^+$ to $\mathrm{Na}_{59}^+$. This finding is supported by photoabsorption data.

physics.atm-clus↗

arXiv2000

Pairing gaps from nuclear mean-field models

We discuss the pairing gap, a measure for nuclear pairing correlations, in chains of spherical, semi-magic nuclei in the framework of self-consistent nuclear mean-field models. The equations for the conventional BCS model and the approximate projection-before-variation Lipkin-Nogami method are formulated in terms of local density functionals for the effective interaction. We calculate the Lipkin-Nogami corrections of both the mean-field energy and the pairing energy. Various definitions of the pairing gap are discussed as three-point, four-point and five-point mass-difference formulae, averaged matrix elements of the pairing potential, and single-quasiparticle energies. Experimental values for the pairing gap are compared with calculations employing both a delta pairing force and a density-dependent delta interaction in the BCS and Lipkin-Nogami model. Odd-mass nuclei are calculated in the spherical blocking approximation which neglects part of the the core polarization in the odd nucleus. We find that the five-point mass difference formula gives a very robust description of the odd-even staggering, other approximations for the gap may differ from that up to 30% for certain nuclei.

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arXiv1999

Static Electric Dipole Polarizabilities of Na Clusters

The static electric dipole polarizability of $\mathrm{Na_N}$ clusters with even N has been calculated in a collective, axially averaged and a three-dimensional, finite-field approach for $2\le N \le 20$, including the ionic structure of the clusters. The validity of a collective model for the static response of small systems is demonstrated. Our density functional calculations verify the trends and fine structure seen in a recent experiment. A pseudopotential that reproduces the experimental bulk bond length and atomic energy levels leads to a substantial increase in the calculated polarizabilities, in better agreement with experiment. We relate remaining differences in the magnitude of the theoretical and experimental polarizabilities to the finite temperature present in the experiments.

physics.atm-clus↗

arXiv1999

Nuclear Skins and Halos in the Mean-Field Theory

Nuclei with large neutron-to-proton ratios have neutron skins, which manifest themselves in an excess of neutrons at distances greater than the radius of the proton distribution. In addition, some drip-line nuclei develop very extended halo structures. The neutron halo is a threshold effect; it appears when the valence neutrons occupy weakly bound orbits. In this study, nuclear skins and halos are analyzed within the self-consistent Skyrme-Hartree-Fock-Bogoliubov and relativistic Hartree-Bogoliubov theories for spherical shapes. It is demonstrated that skins, halos, and surface thickness can be analyzed in a model-independent way in terms of nucleonic density form factors. Such an analysis allows for defining a quantitative measure of the halo size. The systematic behavior of skins, halos, and surface thickness in even-even nuclei is discussed.

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arXiv1999

Shell Corrections of Superheavy Nuclei in Self-Consistent Calculations

Shell corrections to the nuclear binding energy as a measure of shell effects in superheavy nuclei are studied within the self-consistent Skyrme-Hartree-Fock and Relativistic Mean-Field theories. Due to the presence of low-lying proton continuum resulting in a free particle gas, special attention is paid to the treatment of single-particle level density. To cure the pathological behavior of shell correction around the particle threshold, the method based on the Green's function approach has been adopted. It is demonstrated that for the vast majority of Skyrme interactions commonly employed in nuclear structure calculations, the strongest shell stabilization appears for Z=124, and 126, and for N=184. On the other hand, in the relativistic approaches the strongest spherical shell effect appears systematically for Z=120 and N=172. This difference has probably its roots in the spin-orbit potential. We have also shown that, in contrast to shell corrections which are fairly independent on the force, macroscopic energies extracted from self-consistent calculations strongly depend on the actual force parametrisation used. That is, the A and Z dependence of mass surface when extrapolating to unknown superheavy nuclei is prone to significant theoretical uncertainties.

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