Entrance channel dynamics of hot and cold fusion reactions leading to superheavy elements

We investigate the entrance channel dynamics for the reactions ${}^{70}\mathrm{Zn}+{}^{208}\mathrm{Pb}$ and ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ by using the fully microscopic time-dependent Hartree-Fock theory coupled with a density constraint. We calculate excitation energies and capture cross sections relevant for the study of superheavy formations. We discuss the deformation dependence of the ion-ion potential for the ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ system and perform an alignment angle averaging for the calculation of the capture cross section. The results show that this approach can generate results in good agreement with experiments and other theories.

Figure 1

Potential barriers $V(R)$ for the ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ system obtained from DC-TDHF calculations using Eq. (1) as a function of $E_{\mathrm{c}.\mathrm{m}.}$ energy and for selected orientation angles $\beta$ of the ${}^{238}\mathrm{U}$ nucleus. Also shown are the experimental c.m. energies.

Figure 2

Excitation energy $E^{*}(R)$ in a central collision for various $E_{\mathrm{c}.\mathrm{m}.}$ energies and for alignment angles $\beta =0^{°}$ and $\beta ={90}^{°}$ of the ${}^{238}\mathrm{U}$ nucleus.

Figure 3

Excitation energy in a central collision at the potential minimum inside the barrier $E_c^{*}$ as a function of $E_{\mathrm{c}.\mathrm{m}.}$ for the ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ and the ${}^{70}\mathrm{Zn}+{}^{208}\mathrm{Pb}$ systems. For the case of the ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ system, ${}^{238}\mathrm{U}$ alignment angles of $\beta =0^{°},{45}^{°},{90}^{°}$ are shown.

Figure 4

Dynamic alignment due to Coulomb excitation of ${}^{238}\mathrm{U}$. Shown is the orientation probability as a function of the Euler angle $\beta$ in a central collision at internuclear distances $R=1500\hspace{0.5em}\mathrm{fm}$ (dashed horizontal curve) and at $R=20\hspace{0.5em}\mathrm{fm}$ at c.m. energy of $E_{\mathrm{c}.\mathrm{m}.}=220\hspace{0.5em}\mathrm{MeV}$ (solid curve).

Figure 5

Capture cross sections for the ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ system as a function of $E_{\mathrm{c}.\mathrm{m}.}$ energy (black circles). Also shown are the experimental cross sections (red squares) [4].

Figure 6

Potential barriers $V(R)$ for the ${}^{70}\mathrm{Zn}+{}^{208}\mathrm{Pb}$ system obtained from DC-TDHF calculations using Eq. (1) for various $E_{\mathrm{c}.\mathrm{m}.}$ energies as indicated.

Figure 7

Excitation energy $E^{*}(R)$ for the ${}^{70}\mathrm{Zn}+{}^{208}\mathrm{Pb}$ system and for various $E_{\mathrm{c}.\mathrm{m}.}$ energies as indicated.

Figure 8

Cross sections (in microbarns) from Ref. [29] as a function of the $E_{\mathrm{lab}}$ energy for the ${}^{70}\mathrm{Zn}+{}^{208}\mathrm{Pb}$ system. The dotted curve shows the quasifission, the dashed curve shows the fusion, and the dotted-dashed curve shows the $1n$ evaporation residue cross section. Our calculations for the two experimental energies corresponding to the two potential energies leading to capture in Fig. 6 are shown as filled circles.