Predictions of synthesizing elements with $Z=119$ and 120 in fusion reactions

Within the framework of the dinuclear system model, the experimentally accessible projectile-target combinations are predicted for the production of new superheavy elements with $Z=119$ and $Z=120$. The entrance channel effect and the isotopic dependence of targets and projectiles on the capture, fusion, and survival stages of the fusion reaction are discussed. The reactions ${}^{45}\mathrm{Sc}+{}^{249}\mathrm{Cf}$ and ${}^{50}\mathrm{V} + {}^{246}\mathrm{Cm}$ are found to be promising candidates for the synthesis of the element with $Z=119$, achieving the maximal evaporation residue cross sections of 0.288 pb at an incident energy of 211.2 MeV and 0.237 pb at an incident energy of 226.2 MeV, respectively. Meanwhile, the element with $Z=120$ can be synthesized through the reaction ${}^{46}\mathrm{Ti} + {}^{249}\mathrm{Cf}$ with a maximal evaporation residue cross section of 0.040 pb at 221.8 MeV.

Figure 1

Comparison of the calculated results with the available experimental data [9, 11, 23, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96]. The calculated ER cross sections in the $2n, 3n, 4n$, and $5n$ channels are denoted by the red dashed lines, black solid lines, blue dash-dot lines, and green dotted lines, respectively. The black arrows denote the positions of the Coulomb barrier heights in side-side collisions $V_{\mathrm{B}}^{\mathrm{side}}$ [29, 97]. The experimental data for the $2n$-, $3n$-, $4n$-, and $5n$-emission channels are presented by the solid red inverted triangles, black circles, blue squares, and green triangles with the error bars, respectively.

Figure 2

(a) The predicted maximal ER cross sections for producing the isotopes of the SHE with $Z=119$ (red solid line) and 120 (black dash-dot line). (b) The $B_{\mathrm{n}}$ of the compound nuclei which form the isotopes with $Z=119$ (red solid lines) and 120 (black dash-dot lines). (c) The $B_{\mathrm{f}}^{\mathrm{M}}$ of the compound nuclei which form the isotopes with $Z=119$ (red solid lines) and 120 (black dash-dot lines).

Figure 3

The calculated capture cross sections (a), fusion probabilities (b), and ER cross sections (c) of the reactions ${}^{45}\mathrm{Sc}+{}^{249}\mathrm{Cf}$ (solid lines) and ${}^{50}\mathrm{V}+{}^{244}\mathrm{Cm}$ (dash-dot lines). The ER cross sections in the $3n$- and $4n$-emission channels are denoted by the blue and red lines, respectively. The calculation uncertainties are given by the shaded areas.

Figure 4

The driving potential as a function of mass asymmetry. The $B_{\mathrm{fus}}$ values of the reactions ${}^{45}\mathrm{Sc}+{}^{249}\mathrm{Cf}$ and ${}^{50}\mathrm{V}+{}^{244}\mathrm{Cm}$ are represented by the green solid line arrow and red dashed line arrow, respectively.

Figure 5

The predicted ER cross sections of the reactions ${}^{51}\mathrm{V}+{}^{245}\mathrm{Cm}$ (a) and ${}^{51}\mathrm{V}+{}^{248}\mathrm{Cm}$ (b). The $3n$- and $4n$-emission channels are indicated by the blue solid and red dotted lines, respectively. The ER cross sections of the $3n+4n$ channels in the reaction ${}^{51}\mathrm{V}+{}^{248}\mathrm{Cm}$ are indicated by the black dash-dot line. The optimal reaction energy of the reaction ${}^{51}\mathrm{V}+{}^{248}\mathrm{Cm}$ in the $3n+4n$ channels from Ref. [29] and from this work are represented by the green dashed and black dash-dot lines, respectively. The calculation uncertainties are given by the shaded areas.

Figure 6

The calculated capture cross sections (a), fusion probabilities (b), and survival probabilities (c) of the reactions ${}^{51}\mathrm{V}+{}^{245}\mathrm{Cm}$ (solid lines) and ${}^{51}\mathrm{V}+{}^{248}\mathrm{Cm}$ (dash-dot lines). The survival probabilities in the $3n$- and $4n$-emission channels are denoted by the blue and red lines, respectively.

Figure 7

The predicted maximal ER cross sections for producing the isotopes of the SHE with $Z=120$ with ${}^{249}\mathrm{Cf}$ target and ${}^{46–50}\mathrm{Ti}$ beams.

Figure 8

The predicted ER cross sections of the reactions ${}^{46}\mathrm{Ti}+{}^{249}\mathrm{Cf}$ (a), ${}^{48}\mathrm{Ti}+{}^{249}\mathrm{Cf}$ (b), and ${}^{50}\mathrm{Ti}+{}^{249}\mathrm{Cf}$ (c). The $3n$- and $4n$-emission channels are indicated by the solid and dotted lines, respectively. The calculation uncertainties are given by the shaded areas.

Figure 9

The calculated capture cross sections (a), fusion probabilities (b), and survival probabilities (c) of the reactions ${}^{46}\mathrm{Ti}+{}^{249}\mathrm{Cf}$ (solid lines), ${}^{48}\mathrm{Ti}+{}^{249}\mathrm{Cf}$ (dash-dot lines) and ${}^{50}\mathrm{Ti}+{}^{249}\mathrm{Cf}$ (dashed lines). The survival probabilities in the $3n$- and $4n$-emission channels are denoted by the blue and red lines, respectively.