arXiv subjects
Publications and source records attributed to P. -G. Reinhard.
The density-constrained time-dependent Hartree-Fock (DC-TDHF) theory is a fully microscopic approach for calculating heavy-ion interaction potentials and fusion cross sections below and above the fusion barrier. We discuss recent applications of DC-TDHF method to fusion of light and heavy systems.
We investigate the possibility of the existence of the exotic torus configuration in the high-spin excited states of $^{40}$Ca. We here consider the spin alignments about the symmetry axis. To this end, we use a three-dimensional cranked Skyrme Hartree-Fock method and search for stable single-particle configurations. We find one stable state with the torus configuration at the total angular momentum $J=$ 60 $\hbar$ and an excitation energy of about 170 MeV in all calculations using various Skyrme interactions. The total angular momentum J=60 $\hbar$ consists of aligned 12 nucleons with the orbital angular momenta $Λ=+4$, +5, and +6 for spin up-down neutrons and protons. The obtained results strongly suggest that a macroscopic amount of circulating current breaking the time-reversal symmetry emerges in the high-spin excited state of $^{40}$Ca.
We discuss the possibility whether superheavy elements can be produced in Nature by the astrophysical rapid neutron capture process. To this end we have performed fully dynamical network r-process calculations assuming an environment with neutron-to-seed ratio large enough to produce superheavy nuclei. Our calculations include two sets of nuclear masses and fission barriers and include all possible fission channels and the associated fission yield distributions. Our calculations produce superheavy nuclei with A ~ 300 that however decay on timescales of days.
While bulk properties of stable nuclei are successfully reproduced by mean-field theories employing effective interactions, the dependence of the centroid energy of the electric giant dipole resonance on the nucleon number A is not. This problem is cured by considering many-particle correlations beyond mean-field theory, which we do within the "Quasiparticle Time Blocking Approximation". The electric giant dipole resonances in $^{16}$O, $^{40}$Ca, and $^{208}$Pb are calculated using two new Skyrme interactions.
We discuss in depth the validity and limitations of a theoretical scheme to evaluate photo-electron spectra (PES) through collecting the phase oscillations at a given measuring point. Problems appear if the laser pulse is still active when the first bunches of outgoing flow reach the measuring point. This limits the simple scheme for evaluation of PES to low and moderate laser intensities. Using a model of free particle plus dipole field, we develop a generalized scheme which is shown to considerably improve the results for high intensities.
We have optimized the parameters of extended relativistic mean-field model using a selected set of global observables which includes binding energies and charge radii for nuclei along several isotopic and isotonic chains and the iso-scalar giant monopole resonance energies for the $^{90}$Zr and $^{208}$Pb nuclei. The model parameters are further constrained by the available informations on the energy per neutron for the dilute neutron matter and bounds on the equations of state of the symmetric and asymmetric nuclear matter at supra-nuclear densities. Two new parameter sets BSP and IUFSU* are obtained, later one being the variant of recently proposed IUFSU parameter set. The BSP parametrization uses the contributions from the quartic order cross-coupling between $ω$ and $σ$ mesons to model the high density behaviour of the equation of state instead of the $ω$ meson self-coupling as in the case of IUFSU* or IUFSU. Our parameter sets yield appreciable improvements in the binding energy systematics and the equation of state for the dilute neutron matter. The importance of the quartic order $ω-σ$ cross coupling term of the extended RMF model, as often ignored, is realized.
We study the equilibration and relaxation processes within the time-dependent Hartree-Fock approach using the Wigner distribution function. On the technical side we present a geometrically unrestricted framework which allows us to calculate the full six-dimensional Wigner distribution function. With the removal of geometrical constraints, we are now able to extend our previous phase-space analysis of heavy-ion collisions in the reaction plane to unrestricted mean-field simulations of nuclear matter on a three-dimensional Cartesian lattice. From the physical point of view we provide a quantitative analysis on the stopping power in TDHF. This is linked to the effect of transparency. For the medium-heavy $^{40}$Ca+$^{40}$Ca system we examine the impact of different parametrizations of the Skyrme force, energy-dependence, and the significance of extra time-odd terms in the Skyrme functional. For the first time, transparency in TDHF is observed for a heavy system, $^{24}$Mg+$^{208}$Pb.
We study pre-equilibrium giant dipole resonance excitation and fusion in the neutron-rich system $^{132}$Sn+$^{48}$Ca at energies near the Coulomb barrier, and we compare photon yields and total fusion cross sections to those of the stable system $^{124}$Sn+$^{40}$Ca. The dynamic microscopic calculations are carried out on a three-dimensional lattice using both the Time-Dependent Hartree-Fock method and the Density Constrained TDHF method. We demonstrate that the peak of the GDR excitation spectrum occurs at a substantially lower energy than expected for an equilibrated system, thus reflecting the very large prolate elongation of the dinuclear complex during the early stages of fusion. Our theoretical fusion cross-sections for both systems agree reasonably well with recent data measured at HRIBF.
A new Skyrme-like energy density suitable for studies of strongly elongated nuclei has been determined in the framework of the Hartree-Fock-Bogoliubov theory using the recently developed model-based, derivative-free optimization algorithm POUNDerS. A sensitivity analysis at the optimal solution has revealed the importance of states at large deformations in driving the parameterization of the functional. The good agreement with experimental data on masses and separation energies, achieved with the previous parameterization UNEDF0, is largely preserved. In addition, the new energy density UNEDF1 gives a much improved description of the fission barriers in 240Pu and neighboring nuclei.
The recent high-resolution measurement of the electric dipole (E1) polarizability (alphad) in 208Pb [Phys. Rev. Lett. 107, 062502 (2011)] provides a unique constraint on the neutron-skin thickness of this nucleus. The neutron-skin thickness (rskin) of 208Pb is a quantity of critical importance for our understanding of a variety of nuclear and astrophysical phenomena. To assess the model dependence of the correlation between alphad and rskin, we carry out systematic calculations for 208Pb, 132Sn, and 48Ca based on the nuclear density functional theory (DFT) using both non-relativistic and relativistic energy density functionals (EDFs). Our analysis indicates that whereas individual models exhibit a linear dependence between alphad and rskin, this correlation is not universal when one combines predictions from a host of different models. By averaging over these model predictions, we provide estimates with associated systematic errors for rskin and alphad for the nuclei under consideration. We conclude that precise measurements of rskin in both 48Ca and 208Pb---combined with the recent measurement of alphad---should significantly constrain the isovector sector of the nuclear energy density functional.
We present a systematics of fission barriers and fission lifetimes for the whole landscape of super-heavy elements (SHE), i.e. nuclei with Z>100. The fission lifetimes are also compared with the alpha-decay half-lives. The survey is based on a self-consistent description in terms of the Skyrme-Hartree-Fock (SHF) approach. Results for various different SHF parameterizations are compared to explore the robustness of the predictions. The fission path is computed by quadrupole constrained SHF. The computation of fission lifetimes takes care of the crucial ingredients of the large-amplitude collective dynamics along the fission path, as self-consistent collective mass and proper quantum corrections. We discuss the different topologies of fission landscapes which occur in the realm of SHE (symmetric versus asymmetric fission, regions of triaxial fission, bi-modal fission, and the impact of asymmetric ground states). The explored region is extended deep into the regime of very neutron-rich isotopes as they are expected to be produced in the astrophysical r process.
We present a new method to calculate the total ion-ion interaction potential in terms of building blocks which we refer to as "single-particle interaction potentials". This allows also to compose the separate contributions from neutrons and protons to the interaction potentials. The method is applied to nuclear collisions via the use of time-dependent Hartree-Fock theory.
The multipole vortical, toroidal, and compression modes are analyzed. Following the vorticity concept of Ravenhall and Wambach, the vortical operator is derived and related in a simple way to the toroidal and compression operators. The strength functions and velocity fields of the modes are analyzed in $^{208}$Pb within the random-phase-approximation using the Skyrme force SLy6. Both convection and magnetization nuclear currents are taken into account. It is shown that the isoscalar (isovector) vortical and toroidal modes are dominated by the convection (magnetization) nuclear current while the compression mode is fully convective. The relation between the above concept of the vorticity to the hydrodynamical vorticity is briefly discussed.
Calculating the Wigner distribution function in the reaction plane, we are able to probe the phase-space behavior in time-dependent Hartree-Fock during a heavy-ion collision. We compare the Wigner distribution function with the smoothed Husimi distribution function. Observables are defined to give a quantitative measure for local and global equilibration. We present different reaction scenarios by analyzing central and non-central $^{16}O+$$^{16}O$ and $^{96}Zr+$$^{132}Zn$ collisions. It is shown that the initial phase-space volumes of the fragments barely merge. The mean values of the observables are conserved in fusion reactions and indicate a "memory effect" in time-dependent Hartree-Fock. We observe strong dissipation but no evidence for complete equilibration.
We investigate the presence of spatial localization in nuclei using a method that maps the nucleon same-spin pair probability and is based on the density-matrix. The method is used to study spatial localization of light nuclei within the Hartree-Fock approximation. We show that the method provides an alternative tool for studying spatial localization in comparison to the localization observed from maxima in the nuclear mass density.
We compare the systematics of binding energies computed within the standard and extended versions of the relativistic mean-field (RMF) model and the Skyrme Hartree-Fock (SHF) model. The general trends for the binding energies for super-heavy nuclei are significantly different for these models. The SHF models tend to underbind the superheavy nuclei, while, RMF models show just the opposite trend. The extended RMF model seems to provide remarkable improvements over the results obtained for the standard RMF model.
Low-energy E1 strength in neutron-rich $^{132-164}$Sn isotopes is analyzed in the framework of the Skyrme random phase approximation (RPA) with different Skyrme forces. A double folding procedure is applied to take into account the energy-dependent width effects beyond RPA. All the considered Skyrme forces indicate a soft prolate deformation in the open shell isotopes $^{142-164}$Sn. The integrated E1 strength in the energy region of the pygmy resonance grows with the neutron number. The influence of deformation on the integrated strength near the particle emission thresholds (which is of a keen astrophysical interest) is strictly suppressed by the mutual compensation effect for the branches of the giant dipole resonance. The results obtained are in a good agreement with the previous findings of the relativistic mean field model.
A variant of the basic Skyrme-Hartree-Fock (SHF) functional is considered dealing with a new form of density dependence. It employs only integer powers and thus will allow a more sound basis for projection schemes (particle number, angular momentum). We optimize the new functional with exactly the same adjustment strategy as used in an earlier study with a standard Skyrme functional. This allows direct comparisons of the performance of the new functional relative to the standard one. We discuss various observables: bulk properties of finite nuclei, nuclear matter, giant resonances, super-heavy elements, and energy systematics. The new functional performs at least as well as the standard one, but offers a wider range of applicability (e.g. for projection) and more flexibility in the regime of high densities.