Dissipation dynamics and spin-orbit force in time-dependent Hartree-Fock theory

We investigate the one-body dissipation dynamics in heavy-ion collisions of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ using a fully three-dimensional time-dependent Hartree-Fock (TDHF) theory with the modern Skyrme energy functional and without any symmetry restrictions. The energy dissipation is revealed to decrease in deep-inelastic collisions of the light systems as the bombarding energy increases owing to the competition between collective motion and single-particle degrees of freedom. The role of spin-orbit force is given particular emphasis in deep-inelastic collisions. The spin-orbit force causes a significant enhancement of the dissipation. The time-even coupling of spin-orbit force plays a dominant role at low energies, while the influence of time-odd terms is notable at high energies. About 40–65% of the total dissipation depending on the different parameter sets is predicted to arise from the spin-orbit force. The theoretical fusion cross section has a reasonably good agreement with the experimental data, considering that no free parameters are adjusted to reaction dynamics in the TDHF approach.

Figure 1

Final relative kinetic energy as a function of center-of-mass energy for head-on collisions of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$. The solid lines show the results of present studies using three Skyrme parametrizations, and the dashed lines are taken from Ref. [38] for comparison.

Figure 2

Percentage of energy dissipation as a function of center-of-mass energy for head-on collisions of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ with parametrization SLy4. The black, red, and blue lines represent the TDHF calculations involving full l*s, time-even l*s, and no l*s force.

Figure 3

Density profile of the separating ions at the same relative distance $R=8.3$ fm for three incident energies $E_{\mathrm{c}.\mathrm{m}.}=90$ MeV (top), 130 MeV (middle), and 170 MeV (bottom) for the head-on collisions of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ with the full l*s force.

Figure 4

Percentage of energy dissipation caused by the time-odd and time-even contributions of l*s force as a function of center-of-mass energy for head-on collisions of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ with parametrization SLy4.

Figure 5

Percentage of dissipated energy arising from l*s force as a function of center-of-mass energy for head-on collisions of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ with parametrizations SkM*, SLy4, and UNEDF1.