Formation of superheavy nuclei in ${}^{36}\mathrm{S}+{}^{238}\mathrm{U}$ and ${}^{64}\mathrm{Ni}+{}^{238}\mathrm{U}$ reactions

We describe the capture, fusion, fission, and evaporation residue formation cross sections of superheavy nuclei within the proposed earlier two-stage dynamical model. The approaching of the projectile nucleus to the target nucleus is described in the first stage of the model. In the second stage, the evolution of the system formed after the touching of the projectile and target nuclei is considered. The evolution of the system on both stages is described by the Langevin equations. The transport coefficients of these equations for the shape degrees of freedom are calculated within the microscopic linear-response theory. The mutual orientation of the colliding ions, the tunneling through the Coulomb barrier in the entrance channel and the shell effects in the potential energy on both stages of the calculations are taking into account. The obtained results are compared with the available experimental data and other theoretical predictions.

Figure 1

The nuclear shapes versus $\alpha$ and ${\alpha }_1$ at ${\alpha }_4=-0.2$ (dotted lines), 0.0 (solid lines), and 0.2 (dashed lines).

Figure 2

Collective coordinates of the system, which consist of two separated nuclei. The shape of the system is determined by four parameters, namely, by the distance $r$ between the centers of mass of the colliding nuclei, by the deformation parameters of the target (${\alpha }_t$) and projectile (${\alpha }_p$) nuclei, and by the orientational parameter ${\theta }_t$, which is an angle between the symmetrical axis of the deformed in the ground-state target nucleus and the line connecting centers of mass of the colliding nuclei.

Figure 3

The potential energy $V_{\mathrm{pot}}^I$ (18) of colliding ions ${}^{36}\mathrm{S}+{}^{238}\mathrm{U}$ and ${}^{64}\mathrm{Ni}+{}^{238}\mathrm{U}$ in the fusion channel for $L=0$, ${\theta }_t=0$ (solid) and ${\theta }_t={90}^{\mathrm{o}}$ (dashed). Dotted horizontal lines are the reaction energy $E_x=E_{\mathrm{cm}}+Q$.

Figure 4

The deformation energy $E_{\mathrm{def}}$ at $T=0$ of the combined system formed in the reaction ${}^{64}\mathrm{Ni}+{}^{238}\mathrm{U}$ as a function of the parameters ${\alpha }_4$ and $\alpha$ (${\alpha }_1$ is fixed by the mass asymmetry of ${}^{64}\mathrm{Ni}+{}^{238}\mathrm{U}$) system. The dashed line corresponds to fixed distance $r=14.4$ fm between the centers of mass of ions for the nose-to-nose touching configuration, and the solid line ($r=12.55$) corresponds to side-to-side configuration (see Fig. 3). The circle marks the point where potential energy is minimal with respect to variations of ${\alpha }_4$.

Figure 5

The dependence of the potential energy of the system ${}^{302}120$ on the parameters $\alpha$ and ${\alpha }_1$ (${\alpha }_4=0$). The circle shows the approximate position of the initial point of evolution of the mono-system formed in the reaction ${}^{64}\mathrm{Ni}+{}^{238}\mathrm{U}$. The arrows show the possible directions of evolution of the mono-system: dot: deep-inelastic collision, dashes: quasifission, solid: fission.

Figure 6

The same as in Fig. 5, but for the ${}^{274}\mathrm{Hs}$ nucleus, formed in the reaction ${}^{36}\mathrm{S}+{}^{238}\mathrm{U}$.

Figure 7

The deformation energy of ${}^{274}\mathrm{Th}$ at $T=0$ minimized with respect to ${\alpha }_4$. The white line marks the position of the fission barrier.

Figure 8

(a) The probability $P\left(E_n\right)$ [Eq. (25)] of neutron emission per time unit as a function of neutron kinetic energy $E_n$ for a few values of excitation energy $E^{*}$ of compound nucleus ${}^{274}\mathrm{Hs}$. (b) The dependence of the number of trajectories that stay at the ground-state region ($\alpha \le 0.1$) after emission of 1, 2, 3, 4, and 5 neutrons on the excitation energy $E^{*}$ of the compound nucleus. The initial excitation energy $E^{*}=47.3$ MeV is marked by the circle.

Figure 9

The Coulomb barrier penetration cross sections (solid line) for the reaction (a) ${}^{36}\mathrm{S}+{}^{238}\mathrm{U}$ and (b) ${}^{64}\mathrm{Ni}+{}^{238}\mathrm{U}$ as function of the reaction energy $E_x=E_{\mathrm{c}.\mathrm{m}.}+Q$. Closed circles are the experimental data on capture cross sections [22]. The cross sections of the fission of the compact system, corresponding to the fragment mass asymmetry $A/2\pm 20$ are shown by the dashed line (calculations) and open circles (experimental data [22]).

Figure 10

The dependence of fusion cross section, obtained for the reaction ${}^{36}\mathrm{S}+{}^{238}\mathrm{U}\to {}^{274-x}\mathrm{Hs}+xn$ and ${}^{64}\mathrm{Ni}+{}^{238}\mathrm{U}\to {}^{302-x}120+xn$, on the number of emitted neutrons.

Figure 11

(a) The dependence of the total fusion cross sections of the isotopes obtained in the reactions ${}^{36}\mathrm{S}+{}^{238}\mathrm{U}\to {}^{274}\mathrm{Hs}$ and ${}^{64}\mathrm{Ni}+{}^{238}\mathrm{U}\to {}^{302}120$ on the initial excitation energy $E_x$. The triangles are the results from Ref. [28] at $E_x=29.0$ MeV $\left(▴\right)$ and $E_x=33.2$ MeV $\left(▾\right)$. (b) The evaporation residues formation cross sections for the same reactions. The up $\left(▵\right)$ and down $(▿)$ triangles mark the data obtained in Ref. [28]. The right triangle, the stars, and the left triangle are the results from Refs. [29] $(▹)$, [26] $\left(★\right)$, and [27, 30] $(◃)$.