Synthesis of neutron-rich superheavy nuclei with radioactive beams within the dinuclear system model

The production of neutron-rich superheavy nuclei with $Z=105–118$ in neutron evaporation channels is investigated within the dinuclear system model. The different stable and radioactive beam-induced hot fusion reactions are studied systematically. The prospect for synthesizing neutron-rich superheavy nuclei using radioactive beams is evaluated quantitatively based on the beam intensities proposed by Argonne Tandem Linac Accelerator System [B. B. Back and C. L. Jiang, Argonne National Laboratory Report No. ANL-06/55, 2006 (unpublished)]. All possible combinations (with projectiles of $Z=16–22$ and half-lives longer than 1 ms; with targets of half-lives longer than 30 days), which can be performed in available experimental equipment, for producing several unknown neutron-rich superheavy nuclei in neutron evaporation channels are investigated and the most promising reactions are predicted. It is found that the stable beams still show great advantages for producing most of superheavy nuclei. The calculated results are also compared with production cross sections in the $\mathrm{p}xn$ and $\alpha xn$ evaporation channels [Hong et al., Phys. Lett. B 764, 42 (2017)]. We find that the radioactive beam-induced reactions are comparable to the stable beam-induced reactions in charged particle evaporation channels. To obtain more experimental achievements, the beam intensities of modern radioactive beam facilities need to be further improved in the future.

Figure 1

The discovery time [11] of the nuclei $Z\ge 104.$

Figure 2

(a) The ${\log }_{10}$ value of the half-life ($\mathrm{s}$) [11] and (b) the ${\log }_{10}$ value of the beam intensity ($\mathrm{p}/\mathrm{s}$) [52] for the nuclei with $10\le Z\le 25$.

Figure 3

(a) The PES as a function of $Z$ and $N$ of the fragment 1 for the system ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ (in MeV). The red line denotes the minimum trajectory in the PES. The entrance position is marked by a blue point. (b) The driving potential $U\left(\eta \right)$ as a function of the mass asymmetry degree of freedom. The entrance position is pointed out by a black hollow arrow. The red solid arrow denotes the BG point.

Figure 4

(a) The calculated capture cross sections, (b) survival probabilities $W_{\mathrm{sur}}$, (c) complete fusion probability $P_{\mathrm{CN}}$, and (d) evaporation residue cross section ${\sigma }_{ER}$ as a function of excitation energy $E_{\mathrm{CN}}^{*}$ in the reaction ${}^{48}\mathrm{Ca}({}^{238}\mathrm{U},xn)$. The experimental data of the capture cross sections are taken from Ref. [64]. The experimental data of ER cross sections are taken from Ref. [13]. The experimental data of $3n$ and $4n$ are denoted by the green squares and blue circles, respectively.

Figure 5

The comparison of calculated ER cross sections with the experimental data [13, 16, 65, 65] for the reactions (a) ${}^{48}\mathrm{Ca}+{}^{242}\mathrm{Pu}$, (b) ${}^{48}\mathrm{Ca}+{}^{243}\mathrm{Am}$, (c) ${}^{48}\mathrm{Ca}+{}^{244}\mathrm{Pu}$, (d) ${}^{48}\mathrm{Ca}+{}^{245}\mathrm{Cm}$, (e) ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cm}$, and (f) ${}^{48}\mathrm{Ca}+{}^{249}\mathrm{Bk}$.

Figure 6

The predicted excitation functions of the favorable reactions for producing neutron-rich SHN (a) ${}^{271}\mathrm{Db}$, (b) ${}^{272}\mathrm{Sg}$, (c)${}^{273}\mathrm{Sg}$, (d) ${}^{276}\mathrm{Bh}$, (e) ${}^{278}\mathrm{Hs}$, (f) ${}^{279}\mathrm{Mt}$, (g) ${}^{282}\mathrm{Ds}$, and (h) ${}^{283}\mathrm{Rg}$. The thick lines denote the corresponding evaporation channels. The black solid arrows denote the maximal ER cross sections and optimal incident energies.

Figure 7

The same as Fig. 6, but for producing neutron-rich SHN (a) ${}^{286}\mathrm{Cn}$, (b) ${}^{287}\mathrm{Nh}$, (c) ${}^{288}\mathrm{Nh}$, (d) ${}^{290}\mathrm{Fl}$, (e) ${}^{291}\mathrm{Mc}$, and (f) ${}^{292}\mathrm{Mc}$.

Figure 8

The predicted excitation functions as a function of the excitation energy for producing neutron-rich SHN (a), (b) ${}^{294}\mathrm{Lv}$, (c), (d) ${}^{295}\mathrm{Lv}$, (e), (f) ${}^{295}\mathrm{Og}$, and (g), (h) ${}^{296}\mathrm{Og}$. Left panels are the predicted optimal radioactive beam-induced reactions. Right panels are the predicted stable beam-induced reactions.