Three-dimensional Time-dependent Hartree-Fock Calculations Research Articles

Microscopic study of16O+16Ofusion

We perform a study of $^{16}$O+$^{16}$O fusion at above and below the interaction barrier energies using three-dimensional time-dependent Hartree-Fock (TDHF) calculations at above barrier energies and density-constrained TDHF calculations for the entire energy range. We discuss the variations of the experimental data at above the barrier energies. Calculations reasonably reproduce the observed energy-dependent broad oscillations in the fusion excitation functions. These oscillations result from overcoming $L$-dependent fusion barriers. The role of the coupling to low-lying octupole states is also discussed.

Actinide collisions for QED and superheavy elements with the time-dependent Hartree-Fock theory and the Balian-Vénéroni variational principle

Collisions of actinide nuclei form, during very short times of few zs ($10^{-21}$ s), the heaviest ensembles of interacting nucleons available on Earth. Such collisions are used to produce super-strong electric fields by the huge number of interacting protons to test spontaneous positron-electron pair emission (vacuum decay) predicted by the quantum electrodynamics (QED) theory. Multi-nucleon transfer in actinide collisions could also be used as an alternative way to fusion in order to produce neutron-rich heavy and superheavy elements thanks to inverse quasifission mechanisms. Actinide collisions are studied in a dynamical quantum microscopic approach. The three-dimensional time-dependent Hartree-Fock (TDHF) code {\textsc{tdhf3d}} is used with a full Skyrme energy density functional to investigate the time evolution of expectation values of one-body operators, such as fragment position and particle number. This code is also used to compute the dispersion of the particle numbers (e.g., widths of fragment mass and charge distributions) from TDHF transfer probabilities, on the one hand, and using the Balian-Veneroni variational principle, on the other hand. A first application to test QED is discussed. Collision times in $^{238}$U+$^{238}$U are computed to determine the optimum energy for the observation of the vacuum decay. It is shown that the initial orientation strongly affects the collision times and reaction mechanism. The highest collision times predicted by TDHF in this reaction are of the order of $\sim4$ zs at a center of mass energy of 1200 MeV. According to modern calculations based on the Dirac equation, the collision times at $E_{cm}>1$ GeV are sufficient to allow spontaneous electron-positron pair emission from QED vacuum decay, in case of bare uranium ion collision. A second application of actinide collisions to produce neutron-rich transfermiums is discussed. A new inverse quasifission mechanism associated to a specific orientation of the nuclei is proposed to produce transfermium nuclei ($Z>100$) in the collision of prolate deformed actinides such as $^{232}$Th+$^{250}$Cf. The collision of the tip of one nucleus with the side of the other results in a nucleon flux toward the latter. The probability distributions for transfermium production in such a collision are computed. The produced nuclei are more neutron-rich than those formed in fusion reactions, thus, leading to more stable isotopes closer to the predicted superheavy island of stability. In addition to mass and charge dispersion, the Balian-Veneroni variational principle is used to compute correlations between $Z$ and $N$ distributions, which are zero in standard TDHF calculations.

Two different modes associated with the composite nucleus- the charge and mass distributions for exotic nuclear synthesis -

The mass-dependent structure of the composite nucleus is shown based on three-dimensional timedependent Hartree-Fock calculations with Skyrme interactions (SLy4d and SkM*). One remarkable result is that the isovector monopole excitation dominantly appears for collisions of heavy nuclei, and the isovector dipole excitation for those of light ones. Such a difference found in the dynamical structure of composite nucleus plays a role in the equilibration of charge.

Erratum to: Synthesis of exotic nuclei in heavy-ion collisions at higher energies

The charge equilibration upper energy-limit formula is proposed. It shows not only the basic mechanism of charge equilibration but also does imply the possibility of controlling the exotic nuclear synthesis. To understand the mechanism of charge equilibration, charge and mass distributions of final fragments of the heavy-ion collisions are studied based on three-dimensional time-dependent Hartree-Fock calculations with a Skyrme interaction.

Comparisons of two- and three-dimensional time-dependent Hartree-Fock calculations of the reactionsO16+O16andCa40+Ca40

Two-dimensional and three-dimensional time-dependent Hartree-Fock calculations have been performed over a wide range of angular momenta for $^{16}\mathrm{O}$ + $^{16}\mathrm{O}$ at ${E}_{\mathrm{lab}}=105$ MeV and for $^{40}\mathrm{Ca}$ + $^{40}\mathrm{Ca}$ at ${E}_{\mathrm{lab}}=192$ MeV. In all of the two-dimensional calculations it is assumed that the nuclear system is axially-symmetric about the line joining the mass centers of the colliding ions. Two very different two-dimensional, axially-symmetric models are considered. (a) In the first case, it is assumed that after the two ions interpenetrate the moment of inertia of the system attains the rigid-body value. (b) In the second model, each single-particle wave function is assumed to be multiplied by an extra phase factor which depends upon the azimuthal angle. This model yields an irrotational fluid flow. The results of time-dependent Hartree-Fock (TDHF) calculations with both of these models are compared with each other and with three-dimensional TDHF results. It is concluded that the two-dimensional calculations reproduce reasonably well the three-dimensional results for values of the angular momentum both below and above the three-dimensional fusion window. As the laboratory bombarding energy is decreased, there is better agreement between the two- and three-dimensional calculations, including cases in which the angular momentum is within the fusion region.NUCLEAR REACTIONS $^{16}\mathrm{O}(^{16}\mathrm{O}, x)$ and $^{40}\mathrm{Ca}(^{40}\mathrm{Ca}, x)$ in 2- and 3-dimensional time-dependent Hartree-Fock calculations. Comparisions between 2- and 3- dimensional results. Fusion and strongly damped collisions.

Three-dimensional time-dependent Hartree-Fock calculations ofO16+O16andCa40+Ca40fusion cross sections

Three-dimensional time-dependent Hartree-Fock calculations for the $^{16}\mathrm{O}$ + $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$ + $^{40}\mathrm{Ca}$ fusion excitation functions are presented. Results for the former system are in good agreement with experiment for ${E}_{\mathrm{lab}}\ensuremath{\le}120$ MeV and indicate a dynamical lower angular momentum limit to fusion for ${E}_{\mathrm{lab}}\ensuremath{\ge}54$ MeV. Results for $^{40}\mathrm{Ca}$ + $^{40}\mathrm{Ca}$ are compared with previous two-dimensional calculations. The low-energy fusion cross sections obtained for this system demonstrate the sensitivity of time-dependent Hartree-Fock calculations to the effective interaction used.