Single-particle dissipation in a time-dependent Hartree-Fock approach studied from a phase-space perspective

We study dissipation 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 ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ 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.

Figure 1

Global observables ${\beta }_k\left(t\right)$ (a), ${\gamma }_k\left(t\right)$ (b), $V_k\left(t\right)$ (c), and $Q_r^{20}\left(t\right)$ (d) are shown for a central ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ collision with a center-of-mass energy $E_{\mathrm{c}}.\mathrm{m}.=160$ MeV. Each curve corresponds to a different Skyrme force as indicated in the legend.

Figure 2

A still frame from a video of two-dimensional $z$-$k_z$ slice from the full six-dimensional Wigner distribution $f_{\mathrm{W}}^{\left(3\right)}(\mathbf{r},\mathbf{k})$ for a central ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ collision with a center-of-mass energy of $E_{\mathrm{c}}.\mathrm{m}.=160$ MeV [23].

Figure 3

Same as Fig. 2 with a center-of-mass energy of $E_{\mathrm{c}}.\mathrm{m}.=240$ MeV [23].

Figure 4

Global observables ${\beta }_k\left(t\right)$ (a), ${\gamma }_k\left(t\right)$ (b), $V_k\left(t\right)$ (c), and $Q_r^{20}\left(t\right)$ (d) are shown for a central ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ collision with fixed Skyrme interaction SkI4. Each curve corresponds to a different center-of-mass energy.

Figure 5

Global observables ${\beta }_k\left(t\right)$ (a), and $Q_r^{20}\left(t\right)$ (b) are shown for a central ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ collision with fixed Skyrme interaction SLy4.