Influence of the nuclear dynamical deformation on production cross sections of superheavy nuclei

The superheavy nuclear production mechanism can be described by fusion reactions with the dinuclear system concept, in which the deformations of the two nuclei are assumed to stay at their ground state with nucleons transferring between them. Actually the two nuclei have to deform due to very strong nuclear and Coulomb interactions between them. These deformations can be analytically described by a Fokker-Planck equation, and by combining them with a master equation that describes the nucleon transfer between nuclei the superheavy nuclear production cross sections can be investigated systematically. The calculated results are in good agreement with available data, and the evaporation residue cross sections for synthesizing the superheavy nuclei $Z=119$ and 120 are predicted.

Figure 1

The time evolution of mean values of the fragment deformations for the reaction ${}^{48}\mathrm{Ca}+{}^{242}\mathrm{Pu}$, and for the other systems for the same composite system, but with different combinations.

Figure 2

The PES for the reaction ${}^{48}\mathrm{Ca}+{}^{242}\mathrm{Pu}$ as a function of mass asymmetry.

Figure 3

(a) Fusion probabilities as a function of the excitation energy using the ground-state deformation (GSD) vs the dynamical deformation (DyD). (b) Calculated excitation functions of ERCS taking the dynamical deformation (solid line) and the ground deformation of the two nuclei (dashed line) compared with the available experimental data [23] for the reaction ${}^{48}\mathrm{Ca}+{}^{242}\mathrm{Pu}$.

Figure 4

Comparison between the calculated ERCSs with the available experimental data for the reactions ${}^{48}\mathrm{Ca}$ + ${}^{238}\text{U}$ [23], ${}^{237}\text{Np}$ [24], ${}^{243}\text{Am}$ [25], ${}^{244}\mathrm{Pu}$ [26], ${}^{245}\text{Cm}$ [27], ${}^{248}\mathrm{Cm}$ [23], ${}^{249}\mathrm{Bk}$ [28], and ${}^{249}\mathrm{Cf}$ [27]. The measured ERCSs of the $3n,4n$, and $5n$ channels are denoted by red (gray) solid squares, blue (gray) open cycles, and dark cyan (gray) open squares, respectively. The calculated results with the deformation at ground state and the dynamical deformation are denoted by dashed and solid lines, respectively.

Figure 5

ERCSs of yet undiscovered superheavy nuclei $Z=119$ and 120 predicted by considering the dynamical nuclear deformation in DNS model by solid lines. The dashed lines show those only considering the nuclear ground-state deformation.

Figure 6

Maximal values of experimentally available ERCSs for ${}^{48}\mathrm{Ca}$-induced reactions leading to SHN with $Z=112$–118, compared with the theoretical values. The calculated maximal ERCSs for ${}^{50}\mathrm{Ti}$- (or ${}^{48}\mathrm{Ca}$- and ${}^{54}\mathrm{Cr}$-) induced reactions leading to SHN with $Z=119$ and 120 are also shown. For each superheavy nucleus, the charge and mass numbers are given. The experimental values are shown by black solid squares $({}^{288}114$ and ${}^{292}116$ are shown by black open stars) with error bars. Theoretical results calculated by the dynamical deformation are shown by red (gray) dots and those by the ground-state deformation by black circles.