Isotopic dependence of superheavy nuclear production in hot fusion reactions

The dependence of the evaporation residue cross section (ERCS)'s ability to produce superheavy nuclei (SHN) on the isospin of colliding nuclei is analyzed within the dinuclear system concept. ERCSs are discussed in detail and compared with existing experimental data. The fusion probabilities and surviving probabilities depend sensitively on the neutron numbers of the target and projectile nuclei. In most cases a neutron excess in the system can increase the producing cross section of a new nuclide of SHN. Some predicted ERCSs for the new isotopes of SHN were found to be as large as about 1–8 pb, which is large enough to be realized experimentally with the current existing technology. Element 120 may be produced by ${}^{50}\mathrm{Ti}+{}^{251,252}\mathrm{Cf}$, with the ERCS being about 0.03 pb, and element 119 may be produced by the reaction channel ${}^{50}\mathrm{Ti}+{}^{248,249}\mathrm{Bk}$, with the ERCS being about 0.1 pb via $3n$ and $4n$ emission channels, respectively. Radioactive projectiles are not much more favorable in comparison to stable projectiles.

Figure 1

Contour plot of the driving potential for the reaction systems (a) ${}^{48}\mathrm{Ca}+{}^{242}\mathrm{Pu}$ and (b) ${}^{50}\mathrm{Ti}+{}^{242}\mathrm{Pu}$ as functions of the neutron and proton numbers of fragment 1. Incident channels are indicated. Thick central (red) lines indicate the valley of the potential.

Figure 2

Calculated ERCSs compared with available experimental data for the reactions ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ [52], ${}^{48}\mathrm{Ca}+{}^{237}\mathrm{Np}$ [53], ${}^{48}\mathrm{Ca}+{}^{242}\mathrm{Pu}$ [52], ${}^{48}\mathrm{Ca}+{}^{244}\mathrm{Pu}$ [55], ${}^{48}\mathrm{Ca}+{}^{243}\mathrm{Am}$ [54], ${}^{48}\mathrm{Ca}+{}^{245}\mathrm{Cm}$ [56], ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cm}$ [52], ${}^{48}\mathrm{Ca}+{}^{249}\mathrm{Bk}$ [57], and ${}^{48}\mathrm{Ca}+{}^{249}\mathrm{Cf}$ [56]. Measured ERCSs of the $2n$, $3n$, $4n$, and $5n$ channels are denoted by filled black circles, filled (red) squares, open (blue) circles, and open (dark cyan) squares, respectively. Calculated results are denoted by solid lines.

Figure 3

Top: Isospin dependence of the maximal evaporation residue cross sections from the hot fusion reactions (a) ${}^{48}\mathrm{Ca}+{}^A\mathrm{U}$, (b) ${}^{48}\mathrm{Ca}+{}^A\mathrm{Pu}$, (c) ${}^{48}\mathrm{Ca}+{}^A\mathrm{Cm}$, and (d) ${}^{48}\mathrm{Ca}+{}^A\mathrm{Cf}$ as functions of the target mass number $A$, for the $3n$ and $4n$ emission channels. The corresponding experimental data are represented by the open squares ($3n$) and open circles ($4n$) with error bars. Bottom: Corresponding excitation energies of the compound nuclei.

Figure 4

The same as Fig. 3, but for ${}^{50}\mathrm{Ti}$-induced hot fusion reactions.

Figure 5

The same as Fig. 3, but for ${}^{50}\mathrm{Ca}$-induced hot fusion reactions.

Figure 6

The same as Fig. 3, but for ${}^{48}\mathrm{Ca}+{}^A\mathrm{Np}$, ${}^{48}\mathrm{Ca}+{}^A\mathrm{Am}$, and ${}^{48}\mathrm{Ca}+{}^A\mathrm{Bk}$.

Figure 7

The same as Fig. 6, but for ${}^{50}\mathrm{Ti}$-induced hot fusion reactions.

Figure 8

Calculated maximal ERCSs for ${}^{248}\mathrm{Cm}$-based hot fusion reactions. According to the increasing mass number of the projectile, results are shown by black, red, blue, green, and dark cyan circles.