Dynamical deformation in heavy ion reactions and the characteristics of quasifission products

The investigation of the characteristics of low-energy heavy ion reactions covering both fusion and quasifission is carried out within the dinuclear system (DNS) concept, which is developed to include the deformation variables of fragments in addition to the mass numbers of the fragments, so that the energy dissipation, nucleon exchange, and deformation evolutions of the colliding nuclei as well as their correlations are treated simultaneously, and the potential energy surface of the system is thus reaction-time dependent. The direct consequence of introducing the deformation of fragments as dynamical variables is that one must treat the orientation between the two deformed nuclei. This is solved by introducing a barrier function. It is found that the model can reproduce data about the mass, as well as the total kinetic energy and its dispersion, of the reaction products very well, revealing that the DNS model has a reasonable theoretical foundation and thus can reliably describe the reaction mechanism.

Figure 1

The potential of each DNS as a function of the internuclear distance $r$ of the nuclei leading to QF.

Figure 2

The potential energy surface for the reaction ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cm}$, which drives the nucleon transfer, and the deformation evolution, as a function of quadrupole deformations in the entrance channel $(A_1=48)$.

Figure 3

The evolution of the distribution function $P(A_1,{\beta }_1,{\beta }_2,t)$ (left) and the mass yield $Y_{\text{qf}}(A_1,{\beta }_1,{\beta }_2,t)$ (right) as a function of the fragment deformations of the reaction ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cm}$ for $A_1=48$.

Figure 4

(a) The evolution of the relative quasifission yield distribution $Y\left(A_1\right)$ of the reaction ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cm}$ at $E_{\text{c.m.}}=205$ MeV. The data are taken from Ref. [15]. (b) The energy surface as a function of $A_1$, with ${\beta }_1$ and ${\beta }_2$ being the values at which the energy surface is the lowest. The arrow in the figure indicates the injection channel.

Figure 5

The $〈\text{TKE}\left(A_1\right)〉$, the variance ${\sigma }_{\text{TKE}}^2\left(A_1\right)$ of TKE, and the relative mass yield $Y\left(A_1\right)$ of the QF products in the reaction ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cm}$ at $E_{\text{c.m.}}=205$ MeV. The quantities in the left column are the ones calculated with the shell correction, those in the middle are calculated with the shell corrections being witched off, and those in the right column are calculated with the damped shell corrections. The blue dashed lines are the results obtained by LDM [39]. The experimental data are from Ref. [15].

Figure 6

$〈\text{TKE}\left(A_1\right)〉$, the variance ${\sigma }_{\text{TKE}}^2\left(A_1\right)$ of QF fragments with only tip-tip orientation in the reaction ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cm}$ at $E_{\text{c.m.}}=205\mathrm{MeV}$. The black squares represent the experimental data from Ref. [15].