Synthesis of superheavy element<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>120</mml:mn></mml:mrow></mml:math>via<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Ti</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>50</mml:mn></mml:mrow></mml:mmultiscripts><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">Cf</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:mmultiscripts></mml:math>hot fusion reactions

Synthesis of superheavy element $120$ in terms of the $^{50}\mathrm{Ti}+^{249\ensuremath{-}252}\mathrm{Cf}$ fusion-evaporation reactions is evaluated and discussed. It is found that the reactions of $^{250,251}\mathrm{Cf}(^{50}\mathrm{Ti},3n)^{297,298}120$ and $^{251,252}\mathrm{Cf}(^{50}\mathrm{Ti},4n)^{297,298}120$ are relatively favorable with the maximum evaporation-residue cross sections of $0.12$, $0.09$, $0.11$, and $0.25$ pb, respectively. However, $^{252}\mathrm{Cf}$ may be difficult to be target because its spontaneous fission will bring about serious background in the experiment. Fusion probabilities for different target-projectile combinations leading to the formation of surperheavy nucleus $^{302}120$ are estimated with the ``fusion-by-diffusion'' model and presented as a function of the Coulomb parameter ${Z}_{1}{Z}_{2}/({A}_{1}^{1/3}+{A}_{2}^{1/3})$. Among the reactions $^{50}\mathrm{Ti}+^{252}\mathrm{Cf}$, $^{54}\mathrm{Cr}+^{248}\mathrm{Cm}$, $^{58}\mathrm{Fe}+^{244}\mathrm{Pu}$, and $^{64}\mathrm{Ni}+^{238}\mathrm{U}$, the reaction $^{50}\mathrm{Ti}+^{252}\mathrm{Cf}$ has the largest fusion probability. Synthesis of superheavy element $120$ is of essential importance for determining whether the magic proton shell should be at $Z=114$ or at higher proton numbers $Z=120--126$. Therefore, the experiment to produce isotopes with $Z=120$ in the fusion reactions $^{50}\mathrm{Ti}+^{250,251}\mathrm{Cf}$ is of great interest.

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