Quasifission and fission rates and their lifetimes in asymmetric reactions forming ${}^{216}\mathrm{Ra}$ within a dinuclear system approach

Background: The study of evolution of asymmetric dinuclear systems (DNSs) formed in heavy ion collisions is a topic of intense research. The DNS evolution leads to a variety of reaction channels such as deep inelastic, complete fusion, quasifission, fast fission, fusion-fission, and evaporation of particles. The time evolution of the DNS in the quasifission process and the role of relevant parameters are still not fully understood.

Purpose: The influence of the entrance channel mass asymmetry on the time evolution of an excited and rotating DNS, populated via four reactions with different entrance channel mass asymmetry parameters which all lead to the compound nucleus ${}^{216}\mathrm{Ra}$, is explored.

Method: The driving potential, emission barriers for the binary decay (namely the quasifission and intrinsic fusion barriers), rate of the quasifission channel, and the lifetime of an excited DNS, as well as the fission rate and fission lifetime of the compound nucleus ${}^{216}\mathrm{Ra}$ formed in the ${}^{12}\mathrm{C}+{}^{204}\mathrm{Pb},{}^{19}\mathrm{F}+{}^{197}\mathrm{Au},{}^{30}\mathrm{Si}+{}^{186}\mathrm{W}$, and ${}^{48}\mathrm{Ca}+{}^{168}\mathrm{Er}$ reactions, are calculated by the dinuclear system approach.

Results: Our results show that the intrinsic fusion barrier values are equal to zero for the ${}^{12}\mathrm{C}+{}^{204}\mathrm{Pb}$ and ${}^{19}\mathrm{F}+{}^{197}\mathrm{Au}$ reactions. Therefore, the quasifission signature is extremely hindered for these reactions, while the ${}^{30}\mathrm{Si}+{}^{186}\mathrm{W}$ and ${}^{48}\mathrm{Ca}+{}^{168}\mathrm{Er}$ calculated results contain quasifission contributions. Provided the quasifission rate is nonzero, the quasifission rate increases with increasing orbital angular momentum $\ell$ of the composite system for a given excitation energy $E_{CN}^{*}$ of the compound nucleus. On the other hand, the quasifission lifetime decreases moderately with increasing $\ell$. Furthermore, both quasifission and fission rates increase with increasing excitation energy $E_{CN}^{*}$, while the quasifission and fission lifetimes decrease with increasing $E_{CN}^{*}$ for a given $\ell$.

Conclusions: Although these reactions with different entrance channels populate the same compound nucleus ${}^{216}\mathrm{Ra}$ at similar excitation energies, the fused system presents different behaviors for different entrance channel mass asymmetry parameters. In the ${}^{30}\mathrm{Si}+{}^{186}\mathrm{W}$ and ${}^{48}\mathrm{Ca}+{}^{168}\mathrm{Er}$ reactions having smaller entrance channel mass asymmetry, the quasifission signature dominates over the complete fusion process. Because of the small quasifission barrier for these reactions, the lifetime of the DNS is short and its $E_{\mathrm{DNS}}^{*}$ excitation energy is not sufficient to overcome the saddle point along the way to fusion. Instead, in the ${}^{12}\mathrm{C}+{}^{204}\mathrm{Pb}$ and ${}^{19}\mathrm{F}+{}^{197}\mathrm{Au}$ reaction systems, at $E_{\mathrm{DNS}}^{*}$ excitation energy higher than the threshold energy, the DNS has sufficient energy and time to reach a compound nucleus. In other words, the model calculations predict that the quasifission rate is negligible for the reactions with higher entrance channel mass asymmetry and complete fusion is a dominant decay channel.

Figure 1

The driving potential $U_{dr}\left(Z_1\right)$ calculated for $\ell =0\hslash$ and $40\hslash$ for the DNS formed in the reactions leading to the formation of the same compound nucleus ${}^{216}\mathrm{Ra}$ versus the charge number of the lighter fragment of the DNS based on the DNS approach.

Figure 2

(a) The intrinsic fusion barrier $B_{\mathrm{fus}}^{*}$ predicted for the DNS formed in the reactions leading to the compound nucleus ${}^{216}\mathrm{Ra}$ as a function of the charge $Z_1$ of the lighter fragment of the DNS for three different values of the angular momentum, $\ell =0\hslash ,30\hslash$, and $50\hslash$, respectively, based on the DNS model. (b) The behavior of the intrinsic fusion barrier $B_{\mathrm{fus}}^{*}$ versus $\ell$ is plotted for the ${}^{30}\mathrm{Si}+{}^{186}\mathrm{W}$ and ${}^{48}\mathrm{Ca}+{}^{168}\mathrm{Er}$ reactions at $E_{CN}^{*}=60\mathrm{MeV}$. (c) The intrinsic fusion barrier $B_{\mathrm{fus}}^{*}$ predicted for the DNS formed in the reactions leading to the compound nucleus ${}^{216}\mathrm{Ra}$ as a function of the $Z_1$ and $\ell$ values.

Figure 3

(a) The quasifission barrier $B_{qf}$ predicted for the DNS formed in the reactions leading to the compound nucleus ${}^{216}\mathrm{Ra}$ as a function of the charge $Z_1$ of the lighter fragment of the DNS for three different values of the angular momentum, $\ell =0\hslash ,30\hslash$, and $50\hslash$, respectively, based on the DNS model. (b) The behavior of the quasifission barrier $B_{qf}^{*}$ versus $\ell$ for the studied reactions at $E_{CN}^{*}=60$ MeV. (c) The quasifission barrier $B_{qf}^{*}$ predicted for the DNS formed in the reactions leading to the compound nucleus ${}^{216}\mathrm{Ra}$ as a function of the $Z_1$ and $\ell$ values.

Figure 4

The dependence of the quasifission rate ${\mathrm{\Lambda }}_{qf}$ of the DNS decay versus the angular momentum $\ell$ within the framework of the DNS model for the ${}^{12}\mathrm{C}+{}^{204}\mathrm{Pb},{}^{19}\mathrm{F}+{}^{197}\mathrm{Au},{}^{30}\mathrm{Si}+{}^{186}\mathrm{W}$, and ${}^{48}\mathrm{Ca}+{}^{168}\mathrm{Er}$ asymmetric reactions are reported in (a), (b), (c), and (d), respectively.

Figure 5

The behavior of the lifetime ${\tau }_{\mathrm{DNS}}$ of the excited DNS versus the angular momentum $\ell$ within the framework of the DNS model for the ${}^{12}\mathrm{C}+{}^{204}\mathrm{Pb},{}^{19}\mathrm{F}+{}^{197}\mathrm{Au},{}^{30}\mathrm{Si}+{}^{186}\mathrm{W}$, and ${}^{48}\mathrm{Ca}+{}^{168}\mathrm{Er}$ asymmetric reactions are shown in (a), (b), (c), and (d), respectively.

Figure 6

The behavior of the maximum values of angular momentum ${\ell }_m$ for the reactions leading to the formation of the same compound nucleus ${}^{216}\mathrm{Ra}$ versus the excitation energy $E_{CN}^{*}$.

Figure 7

The dependence of the DNS decay rate ${\mathrm{\Lambda }}_{qf}$ versus the excitation energy $E_{CN}^{*}$ for the DNSs formed in the ${}^{12}\mathrm{C}+{}^{204}\mathrm{Pb},{}^{19}\mathrm{F}+{}^{197}\mathrm{Au},{}^{30}\mathrm{Si}+{}^{186}\mathrm{W}$, and ${}^{48}\mathrm{Ca}+{}^{168}\mathrm{Er}$ reactions are shown in (a), (b), (c), and (d), respectively.

Figure 8

The behavior of the lifetime ${\tau }_{\mathrm{DNS}}$ of the excited DNS formed via the different entrance channels versus the excitation energy $E_{CN}^{*}$ at the given angular momentum $\ell$ within the framework of the DNS approach.

Figure 9

(a) The calculated (dots) quasifission rate ${\mathrm{\Lambda }}_{qf}$ for the DNS formed in the reactions forming the compound nucleus ${}^{216}\mathrm{Ra}$ as a function of the charge $Z_1$ of the lighter fragment in the DNS within the DNS model at the excitation energy $E_{CN}^{*}=60\mathrm{MeV}$ and at the angular momentum $\ell =30\hslash$. (b) Obtained results for ${\mathrm{\Lambda }}_{qf}$ against $Z_1$ and $E_{CN}^{*}$. (c) The behavior of ${\mathrm{\Lambda }}_{qf}$ versus $Z_1$ and $\ell$.

Figure 10

The fission rate ${\mathrm{\Lambda }}_{\mathrm{fis}}$ (curves from top to bottom) and the fission lifetime ${\tau }_{\mathrm{fis}}$ (curves from bottom to top)for the ${}^{12}\mathrm{C}+{}^{204}\mathrm{Pb}$ reaction are calculated within the framework of the DNS model versus the excitation energy $E_{CN}^{*}$ at the same values of angular momentum $\ell$ in (a) and (b), respectively.

Figure 11

The fission rate ${\mathrm{\Lambda }}_{\mathrm{fis}}$ (curves from top to bottom) and the fission lifetime ${\tau }_{\mathrm{fis}}$ (curves from bottom to top) for the ${}^{48}\mathrm{Ca}+{}^{168}\mathrm{Er}$ reaction are obtained within the framework of the DNS model versus the excitation energy $E_{CN}^{*}$ at the same values of angular momentum $\ell$ in (a) and (b), respectively.