Unified description of fusion and multinucleon transfer processes within the dinuclear system model

To compare fusion-evaporation (FE) and multinucleon transfer (MNT) approaches and make more reliable predictions for producing superheavy nuclei, the unified description of FE and MNT processes is performed in the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ within the (DNS) model. We extend the fusion concept in the DNS model based on the deformation degree of freedom. Our calculations support the experimental result [Nishio et al., Phys. Rev. C 77, 064607 (2008)] that compact configuration enhances the fusion probability. The experimental production cross sections of isotopes in FE and MNT processes can be simultaneously reproduced. By comparing the production cross sections in the MNT reaction ${}^{238}\mathrm{U}+{}^{248}\mathrm{Cm}$ with the FE reactions ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ and ${}^{54}\mathrm{Cr}+{}^{248}\mathrm{Cm}$, we find that the FE process shows great advantages of cross sections for producing Cn isotopes and is the only approach that could produce superheavy elements beyond oganesson.

Figure 1

(a) PES as a function of mass asymmetry $\eta$ and ${\beta }_2$ for the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$. The wine line connects the B.G. points for different ${\beta }_2$. The injection point is denoted with the black solid circle. (b) Potential energy as a function of mass asymmetry with ${\beta }_2=0$ for the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$. The B.G. point and inner fusion barrier is denoted.

Figure 2

(a) Comparison of calculated capture cross sections with experimental data [85] in the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$. (b) Calculated fusion probability as a function of incident energy within the dns-sysu code. The angular momentum is $J=30\hslash$. (c) ER cross sections in the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ for producing Cn isotopes. The experimental data [9] are denoted with circles and squares.

Figure 3

(a) The fusion probability $P_{\text{CN}}$ as a function of ${\beta }_2$ for the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ at different incident energies. The angular momentum is $J=30\hslash$. (b) The inner fusion barrier $B_{\text{fus}}$ as a function of ${\beta }_2$. The horizontal dotted line denotes the $B_{\text{fus}}=0$.

Figure 4

Comparison of calculated ER cross sections with the available experimental data for the reactions ${}^{48}\mathrm{Ca}+{}^{243}\mathrm{Am}$ [11], ${}^{244}\mathrm{Pu}$ [12, 13], ${}^{248}\mathrm{Cm}$ [14], and ${}^{249}\mathrm{Cf}$ [15].

Figure 5

(a) Mass distribution of primary fragments in the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ at different incident energies. (b) Production cross sections of Ac, Th, Pa, U, and Np isotopes in the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ at $E_{\text{c.m.}}=196$ MeV. The experimental data are from Ref. [86].

Figure 6

Cross sections as a function of incident energy for producing SHN ${}^{281-285}\mathrm{Cn}$ and neutron rich unknown isotopes ${}^{60}\mathrm{Ca}, {}^{200}\mathrm{W}, {}^{245}\mathrm{U}$, and ${}^{246}\mathrm{Np}$ in the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$.

Figure 7

The probabilities of compound nucleus formation and production of symmetry fragments with $(A_{\text{CN}}/2-12)<A<(A_{\text{CN}}/2+12)$ as a function of incident energy with angular momentum $J=30\hslash$ (a) and entrance angular momentum at $E_{\text{c.m.}}=204$ MeV (b) in the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$. The red dotted lines denote the interaction time of diffusion process, which corresponds to the vertical axis on the right side.

Figure 8

TKE-mass distributions of MNT products in the reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ at (a) $E_{\text{c.m.}}=180$ and (b) 196 MeV, respectively.

Figure 9

Cross sections for producing SHN in MNT reaction ${}^{238}\mathrm{U}+{}^{248}\mathrm{Cm}$ ($E_{\text{c.m.}}=800$ MeV). The horizontal dashed and dotted lines denote a maximal synthesis cross section of ${}^{281–285}\mathrm{Cn}$ and ${}^{298–300}120$ in FE reaction ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ and ${}^{54}\mathrm{Cr}+{}^{248}\mathrm{Cm}$, respectively.