Isotopic dependence of the evaporation residue cross section in the synthesis of superheavy nuclei

The formation of superheavy nuclei via hot fusion reactions ${}^{48}\mathrm{Ca}$$+{}^A$Ra and ${}^{48}\mathrm{Ca}$$+{}^A$Th is systematically studied within the diffusion model. The effect of the isotopic composition of actinide target on the production cross section is analyzed in detail. The results show that, as a general trend, the evaporation residue cross section exponentially depends on the difference of the effective fission barrier hight and neutron separation energy in units of the temperature. By means of this exponential relationship, the possible optimal isotopic composition of the colliding nuclei can be easily figured out before the experiment.

Figure 1

The transmission probability $T_{l=0}(E)$ as a function of the center-of mass energy for the reactions ${}^{48}\mathrm{Ca}+{}^{224,226,228}\mathrm{Ra}$. The arrows indicate the positions corresponding to the peak of the $\mathit{ER}$ excitation function for each reaction.

Figure 2

The potential energies along the asymmetric fission valley for the reaction systems ${}^{48}\mathrm{Ca}+{}^{223,228}\mathrm{Ra}$ and ${}^{48}\mathrm{Ca}+{}^{227,232}\mathrm{Th}$.

Figure 3

The neutron flow driving potential for the systems ${}^{48}\mathrm{Ca}+{}^{232}\mathrm{Th}$. The open and solid circles represent the potential at $s=0.5$ and 2.5 fm, respectively. The dashed and solid lines are the parabolic fit of the data.

Figure 4

The fusion probability as a function of mass asymmetry η for the reactions ${}^{48}\mathrm{Ca}$$+{}^A$Ra and ${}^{48}\mathrm{Ca}$$+{}^A$Th. The lines are the least-square fit of the data to guide the eye.

Figure 5

The difference of the effective fission barrier height and neutron separation energy in units of the temperature (upper panel) and the ($\mathit{ER}$) cross sections of the $3n$ channel (lower panel) as a function of the target mass for the reactions ${}^{48}\mathrm{Ca}$$+{}^A$Ra.

Figure 6

Same as Fig. 1, but for the reactions ${}^{48}\mathrm{Ca}$$+{}^A$Th. The experimental $\mathit{ER}$ cross section of the ${}^{48}\mathrm{Ca}+{}^{232}\mathrm{Th}$ $\to {}^{277}110+3n$ reaction is taken from Ref. [30].

Figure 7

The logarithm of the $\mathit{ER}$ cross section as a function of $d$ for the reactions ${}^{48}\mathrm{Ca}$$+{}^A$Ra and ${}^{48}\mathrm{Ca}$$+{}^A$Th. The lines are the linear fit of the data. The experimental $\mathit{ER}$ cross section of the ${}^{48}\mathrm{Ca}+{}^{232}\mathrm{Th}$ $\to {}^{277}110+3n$ reaction is taken from Ref. [30].