Dynamics of complete and incomplete fusion in heavy ion collisions

In order to study the influence of the strong Coulomb and nuclear interactions on the dynamics of complete and incomplete fusion, we construct a new four-variable master equation (ME) so that the deformations as well as the nucleon transfer are viewed as consistently governed by MEs in the potential energy surface of the system. The calculated yields of quasifission fragments and evaporation residue cross section (ERCS) are in agreement with experimental data of hot fusion reactions. Comparing cross sections by theoretical results and experimental data, we find the improved dinuclear sysytem model also describes the transfer cross sections reasonably. The production cross sections of new neutron-rich isotopes are estimated by the multinucleon transfer reactions.

Figure 1

Calculated mass yield the quasifission products as a function of the mass number of the fragment for the hot fusion reaction ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cm}$ at the bombarding energy corresponding to an excitation energy of the compound nucleus of 33 MeV.

Figure 2

The same as in Fig. 1, but for the hot fusion reactions ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ and ${}^{48}\mathrm{Ca}+{}^{244}\mathrm{Pu}$ at the bombarding energy corresponding to excitation energies of the compound nucleus of 38 and 42 MeV, respectively.

Figure 3

Transfer cross sections for the ${}^{64}\mathrm{Ni}+{}^{238}\mathrm{U}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}$=307.4 MeV. The number of transferred protons from ${}^{64}\mathrm{Ni}$ to ${}^{238}\mathrm{U}$ (negative number) is indicated. The measured cross sections are taken from Ref. [57].

Figure 4

The excitation functions for producing neutron-rich nuclei in the multinucleon transfer reaction ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cm}$ are presented by solid lines. The arrow indicates the expected maximal cross sections at $E_{\mathrm{c}.\mathrm{m}.}$ corresponding to the thresholds for neutron emission.

Figure 5

The predicted production cross sections for light neutron-rich nuclei in collisions of ${}^{248}\mathrm{Cm}$ with ${}^{48}\mathrm{Ca}$ at $E_{\mathrm{c}.\mathrm{m}.}=215.93$ MeV.

Figure 6

Comparison between the calculated ERCSs with the available experimental data for the reactions ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ [61], ${}^{244}\mathrm{Pu}$ [62], and ${}^{248}\mathrm{Cm}$ [61]. The measured ERCSs of the $3n, 4n$, and $5n$ channels are denoted by red solid squares, blue open cycles, and dark cyan open squares, respectively. The calculated results with the deformation at ground state and the dynamical deformation are denoted by dashed and solid lines, respectively.