Shape evolution and collective dynamics of quasifission in the time-dependent Hartree-Fock approach

Background: At energies near the Coulomb barrier, capture reactions in heavy-ion collisions result either in fusion or in quasifission. The former produces a compound nucleus in statistical equilibrium, while the second leads to a reseparation of the fragments after partial mass equilibration without formation of a compound nucleus. Extracting the compound nucleus formation probability is crucial to predict superheavy-element formation cross sections. It requires a good knowledge of the fragment angular distribution which itself depends on quantities such as moments of inertia and excitation energies which have so far been somewhat arbitrary for the quasifission contribution.

Purpose: Our main goal is to utilize the time-dependent Hartee-Fock (TDHF) approach to extract ingredients of the formula used in the analysis of experimental angular distributions. These include the moment-of-inertia and temperature.

Methods: We investigate the evolution of the nuclear density in TDHF calculations leading to quasifission. We study the dependence of the relevant quantities on various initial conditions of the reaction process.

Results: The evolution of the moment of inertia is clearly nontrivial and depends strongly on the characteristics of the collision. The temperature rises quickly when the kinetic energy is transformed into internal excitation. Then, it rises slowly during mass transfer.

Conclusions: Fully microscopic theories are useful to predict the complex evolution of quantities required in macroscopic models of quasifission.

Figure 1

Effect of the moment of inertia on the angular distribution of the fragments computed with Eqs. (2) and (3). Both curves were calculated using $J_{\mathrm{CN}}=46$ and $T=1.2$ MeV.

Figure 2

Quasifission in the reaction ${}^{48}\mathrm{Ca}+{}^{249}\mathrm{Bk}$ at $E_{\mathrm{c}.\mathrm{m}.}=218$ MeV with impact parameter $b=2.0$ fm. Shown is a contour plot of the time evolution of the mass density. The actual numerical box is larger than the one shown in the frames.

Figure 3

DC-TDHF nucleus-nucleus potential for the ${}^{40}\mathrm{Ca}+{}^{238}\mathrm{U}$ central collision at $E_{\mathrm{c}.\mathrm{m}.}=211$ MeV and with the side orientation. Both the potentials for the incoming and outgoing channels are shown.

Figure 4

TDHF results showing the time-dependence of the ratio ${\Im }_0/{\Im }_{\mathrm{eff}}$ for the ${}^{48}\mathrm{Ca}+{}^{249}\mathrm{Bk}$ system at $E_{\mathrm{c}.\mathrm{m}.}=218$ MeV and for impact parameters ranging from $b=0.5$ to 3 fm. The arrows indicate the scission point of each trajectory.

Figure 5

TDHF results showing the time-dependence of the ratio ${\Im }_0/{\Im }_{\mathrm{eff}}$ for the ${}^{40}\mathrm{Ca}+{}^{238}\mathrm{U}$ system at energies $E_{\mathrm{c}.\mathrm{m}.}=208$ (solid blue curve) and 211 MeV (dashed red curve) for zero impact parameter.

Figure 6

TDHF results showing the time-dependence of the ratio ${\Im }_0/{\Im }_{\mathrm{eff}}$ for the ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ system at energy $E_{\mathrm{c}.\mathrm{m}.}=203$ MeV for zero impact parameter and two orientations of the ${}^{238}\mathrm{U}$ nucleus.

Figure 7

(a) TDHF results showing the time-dependence of the temperature for the ${}^{40}\mathrm{Ca}+{}^{238}\mathrm{U}$ system at energy $E_{\mathrm{c}.\mathrm{m}.}=211$ MeV for zero impact parameter and side orientation of the ${}^{238}\mathrm{U}$ nucleus. (b) The change of the width of the $K$ distribution, $K_0^2$ of Eq. (4), as a function of time for the same system.