Role of the “window” component of the friction tensor in the formation of superheavy nuclei

Formation of superheavy nuclei is greatly hindered by the inner barrier and strong dissipation on the way from the contact point of two colliding nuclei to the compound nucleus configuration. One of the dissipation mechanisms is related to the exchange of particles across the window between two nuclei in relative motion, which is the “window” term in the “wall-plus-window” formula. By means of the dynamic analysis for the symmetric systems ${}^{132}\mathrm{Xe}$ + ${}^{132}\mathrm{Xe}$ and ${}^{136}\mathrm{Xe}$ + ${}^{136}\mathrm{Xe}$, we have shown that the window component of friction tensor retards the elongation of the fusing composite nucleus, decreases the height of the inner barrier, and hence increases the fusion probability. Therefore, the friction associated with “window” term enhances the formation cross sections of superheavy nuclei. Besides, we have shown the mass difference (in units of the temperature) of the fission and neutron emission saddle points as a function of mass number of the hassium isotopes, which may provide a useful reference for synthesis and study of the nuclei adjacent to the doubly magic nucleus ${}^{270}\mathrm{Hs}$.

Figure 1

Different components of friction tensor in the wall-plus-window formula as a function of $n/R_0$ for the system ${}^{132}\mathrm{Xe}$ + ${}^{132}\mathrm{Xe}$ at contact. They are the window (${\gamma }_{ss}^{w}indow$, dash-dotted line), radial (${\gamma }_{ss}^{w}all$, dashed line), neck (${\gamma }_{nn}^{w}all$, dash-dot-dotted line), and coupling term between radial and neck (${\gamma }_{sn}^{w}all$, short dashed line) degrees of freedom in the wall formula. The solid line represents the sum of ${\gamma }_{ss}^{\mathrm{wall}}+{\gamma }_{ss}^{\mathrm{window}}$.

Figure 2

Probability distributions of $s_{\mathrm{inj}}$ (a) and the inner barrier height distributions (b) for the system ${}^{132}\mathrm{Xe}$ + ${}^{132}\mathrm{Xe}$ at $E_{\mathrm{c}.\mathrm{m}.}=311$ MeV. The solid and open circles in panels (a) and (b) represent the results calculated with and without the window term in the friction tensor, respectively.

Figure 3

Fusion probabilities for the system ${}^{132}\mathrm{Xe}$ + ${}^{132}\mathrm{Xe}$ at $E_{\mathrm{c}.\mathrm{m}.}=311$ MeV. Only the component with the angular momentum $l=0$ is shown. The solid and dashed lines represent the results calculated with and without the window term in the friction tensor.

Figure 4

The evaporation residue cross sections for the ${}^{136}\mathrm{Xe}$ + ${}^{136}\mathrm{Xe}$ reaction calculated in two conditions, i.e., with (solid line) and without (dashed line) the window term in the wall-plus-window formula. The dash-dotted line shows the cross sections calculated using the friction of the wall term in Eq. (2) only, but with reduction factor $k=1.0$. The insert illustrates the nuclear shape in the symmetric valley, in which the thin and thick solid lines are obtained with reduction factors $k=0.25$ and $k=1.0$, respectively. The hollow bar in panel (a) shows the upper limit of the experimental $\mathrm{ER}$ cross sections in this reaction [3].

Figure 5

Same as Fig. 4, but for the ${}^{132}\mathrm{Xe}$ + ${}^{132}\mathrm{Xe}$ reaction.

Figure 6

The difference of the effective fission barrier hight and neutron separation energy in units of the temperature as a function of the mass number for the hassium isotopes. The arrows indicate the mass numbers of the ${}^{132}\mathrm{Xe}$ + ${}^{132}\mathrm{Xe}$ and ${}^{136}\mathrm{Xe}$ + ${}^{136}\mathrm{Xe}$ systems.