Orientation effects on evaporation residue cross sections in ${}^{48}\mathrm{Ca}$-induced hot fusion reactions

Within the framework of the dinuclear system model, the evaporation residue (ER) cross sections of superheavy nuclei in ${}^{48}\mathrm{Ca}$-induced hot fusion reactions with different entrance orientations are investigated. The production cross sections are obtained by calculating the average ER cross sections for different orientations of deformed colliding nuclei. The average results are in good agreement with the experimental data. The orientation effects on ER cross sections are investigated through studying the orientation dependence of the capture cross sections and the fusion probability. It is found that the fusion probabilities with the polar orientation of the target are higher than those with the equatorial orientation at lower incident energies, while the opposite behavior can be seen at high incident energy regions. The production cross sections for synthesizing $Z=119$ and 120 by fusion reactions of ${}^{48}\mathrm{Ca}$ with actinide targets are predicted.

Figure 1

Fusionlike shape parametrization for two ellipsoidal nuclei.

Figure 2

The interaction potentials in the entrance channel as a function of relative distance with different colliding orientations of the target for the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$. The minimum value of the potential well is at $R=R_m$. Potential well depth $B_{\mathrm{QF}}$ is used as a quasifission barrier. The position of the barrier is denoted by $R_B$.

Figure 3

The driving potential (a) and the QF barrier (b) of DNS for the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ as a function of the mass asymmetry $\eta$ at different orientations of heavy fragment ${\theta }_2$.

Figure 4

The value of the inner fusion barrier $B_{\mathrm{fus}}$ (a) and nucleus-nucleus potential at the minimum of the potential pocket $V\left(R_m\right)$ (b) as a function of ${\theta }_2$ for the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$.

Figure 5

(a) Capture cross sections for the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$. The capture cross sections for ${\theta }_2=0^{\circ },{45}^{\circ }$, and ${90}^{\circ }$ are denoted by dashed, dotted, and dot-dashed lines, respectively. The experimental data [40] are denoted by solid squares. (b) Dependence of the fusion probabilities on excitation energies $\left(J=0\right)$ for different ${\theta }_2$ in the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$. (c) ER cross sections for the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$. The solid lines and the dashed lines denote the calculated ER cross sections of the $3n$ and the $4n$ channels, respectively. The thick solid and dashed lines denote the averaged results. The experimental data [6] of the $3n$ and the $4n$ channels are denoted by solid squares and circles, respectively.

Figure 6

The maximal values of calculated ER cross sections (a) and the optimal excitation energies (b) as a function of ${\theta }_2$ in the $3n$ and the $4n$ channels in the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$.

Figure 7

Comparison of calculated ER cross sections with the available experimental data for the reactions ${}^{48}\mathrm{Ca}+{}^{237}\mathrm{Np}$ [7], ${}^{243}\mathrm{Am}$ [4], ${}^{244}\mathrm{Pu}$ [3, 10], ${}^{248}\mathrm{Cm}$ [6], ${}^{249}\mathrm{Bk}$ [8, 9], and ${}^{249}\mathrm{Cf}$ [5] to produce elements $Z=113–118$.

Figure 8

(a) Dependence of the fusion probability on excitation energies $\left(J=0\right)$ and ${\theta }_2$ in the reaction ${}^{48}\mathrm{Ca}+{}^{252}\mathrm{Es}$ $\to$ ${}^{(300-xn)}$119. (b) ER cross sections as a function of the excitation energy for the reaction ${}^{48}\mathrm{Ca}+{}^{252}\mathrm{Es}$. The solid lines and the dashed lines denote the calculated ER cross sections in the $3n$ and the $4n$ channels, respectively. The thick solid lines and the thick dashed lines denote the averaged results.

Figure 9

The same as in Fig. 8, but for the reaction ${}^{48}\mathrm{Ca}+{}^{257}\mathrm{Fm}$ $\to$ ${}^{(305-xn)}$120.