The production cross sections of superheavy nuclei in hot fusion reactions are investigated systematically. In hot fusion reactions, the capture cross section can be obtained by calculating the weighted average of the transmission probability for different orientations of deformed colliding nuclei. An analytical formula for calculating the value of the fusion probability is proposed, which is suitable for both hot and cold fusion reactions. The orientation effects are considered empirically in calculating the fusion probability. The method proposed in the present work reproduces the measured evaporation residue (ER) cross sections in hot fusion reactions acceptably well. The formula also gives reasonable results for fusion probability in cold fusion reactions. Using this method the evaporation residue cross sections for synthesizing $Z=119$ and 120 are predicted. It is found that for hot fusion reaction's larger maximal ER cross section of the $4n$ channel corresponds to lower optimal incident energy.

In order to produce more unknown neutron-rich nuclei around N=126, the transfer reactions 136Xe + 198Pt, 136–144Xe + 208Pb, and 132Sn + 208Pb are investigated within the framework of the dinuclear system (DNS) model. The influence of neutron excess of projectile on production cross sections of target-like products is studied through the reactions 136,144Xe + 208Pb. We find that the radioactive projectile 144Xe with much larger neutron excess is favorable to produce neutron-rich nuclei with charge number less than the target rather than produce transtarget nuclei. The incident energy dependence of yield distributions of fragments in the reaction 132Sn + 208Pb are also studied. The production cross sections of neutron-rich nuclei with Z=72–77 are predicted in the reactions 136–144Xe + 208Pb and 132Sn + 208Pb. It is noticed that the production cross sections of unknown neutron-rich nuclei in the reaction 144Xe + 208Pb are at least two orders of magnitude larger than those in the reaction 136Xe + 208Pb. The radioactive beam induced transfer reactions 139,144Xe + 208Pb, considering beam intensities proposed in SPIRAL2 (Production System of Radioactive Ion and Acceleration On-Line) project as well, for production of neutron-rich nuclei around the N=126 shell closure are investigated for the first time. It is found that, in comparison to the stable beam 136Xe, the radioactive beam 144Xe shows great advantages for producing neutron-rich nuclei with N=126 and the advantages get more obvious for producing nuclei with less charge number

The dynamic mechanics in the multinucleon transfer reaction ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$ at an incident energy of $E_{\mathrm{c}.\mathrm{m}.}=450$ MeV is investigated by using the improved quantum molecular dynamics model (ImQMD). The lifetime of the neck directly influences the nucleon exchange and energy dissipation between the projectile and the target. The total-kinetic-energy–mass distributions and excitation energy division of primary binary fragments and the mass distributions of primary fragments at different impact parameters are calculated. The thermal equilibrium between two reaction partners has been observed at the lifetime of a neck larger than $480\mathrm{fm}/c$. By using the statistical decay code gemini to describe the de-excitation process of the primary fragments, the isotope production cross sections from Pt to At are compared with the prediction by the dinuclear system and GRAZING model. The calculations indicate that the GRAZING model is suitable for estimating the isotope production cross sections only for $\mathrm{\Delta }Z=-1$ to +2; the DNS + gemini calculations underestimate the cross sections in the neutron-rich and neutron-deficient regions; and the ImQMD + gemini calculations give reasonable predictions of the isotope production cross sections for $\mathrm{\Delta }Z=-3$ to 0.

The main progresses in the multinucleon transfer reactions at energies close to the Coulomb barrier are reviewed. After a short presentation of the experimental progress and theoretical progress, the predicted production cross sections for unknown neutron-rich heavy nuclei and the trans-uranium nuclei are presented.

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.

Within the framework of dinuclear system model, the synthesis of the superheavy elements (SHEs) $Z=119$ and $Z=120$ is investigated. The entrance channel effects on capture cross section, fusion probability, survival probability, and evaporation residue cross section are investigated. We calculate the production cross sections in 276 possible reactions (with stable projectiles of $Z=20$–30 and targets with the half-lives longer than 20 days) and show the promising ones for the synthesizing SHEs $Z=119$ and $Z=120$. It is found that the systems ${}^{44}\mathrm{Ca}+{}^{252}\mathrm{Es}$ and ${}^{40}\mathrm{Ca}+{}^{257}\mathrm{Fm}$ are the most favorable to produce the SHEs $Z=119$ and $Z=120$ with maximal production cross sections (optimal incident energies) of 4.32 pb (204.27 MeV) and 1.24 pb (205.66 MeV), respectively.