Applications of Skyrme energy-density functional to fusion reactions for synthesis of superheavy nuclei

The Skyrme energy-density functional approach has been extended to study massive heavy-ion fusion reactions. Based on the potential barrier obtained and the parametrized barrier distribution the fusion (capture) excitation functions of a lot of heavy-ion fusion reactions are studied systematically. The average deviations of fusion cross sections at energies near and above the barriers from experimental data are less than 0.05 for $92%$ of 76 fusion reactions with ${Z}_{1}{Z}_{2}<1200$. For the massive fusion reactions, for example, the $^{238}\mathrm{U}$-induced reactions and $^{48}\mathrm{Ca}+^{208}\mathrm{Pb}$, the capture excitation functions have been reproduced remarkably well. The influence of structure effects in the reaction partners on the capture cross sections is studied with our parametrized barrier distribution. By comparing the reactions induced by double-magic nucleus $^{48}\mathrm{Ca}$ and by $^{32}\mathrm{S}$ and $^{35}\mathrm{Cl}$, the ``threshold-like'' behavior in the capture excitation function for $^{48}\mathrm{Ca}$-induced reactions is explored and an optimal balance between the capture cross section and the excitation energy of the compound nucleus is studied. Finally, the fusion reactions with $^{36}\mathrm{S}$, $^{37}\mathrm{Cl}$, $^{48}\mathrm{Ca}$, and $^{50}\mathrm{Ti}$ bombarding $^{248}\mathrm{Cm}$, $^{247,249}\mathrm{Bk}$, $^{250,252,254}\mathrm{Cf}$, and $^{252,254}\mathrm{Es}$, as well as the reactions leading to the same compound nucleus with $Z=120$ and $N=182$, are studied further. The calculation results for these reactions are useful for searching for the optimal fusion configuration and suitable incident energy in the synthesis of superheavy nuclei.

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