Optimal reaction for synthesis of superheavy element 117

Abstract

Fusion reactions leading to the formation of superheavy element 117 are systematically analyzed. Among the reactions considered, the $^{250}\mathrm{Bk}(^{48}\mathrm{Ca},4n)^{294}\mathrm{117}$ reaction has the largest evaporation residue (ER) cross section of about 2 pb. However, this reaction is hard to realize experimentally because it is difficult to accumulate sufficient amount of target material due to the short lifetime of $^{250}\mathrm{Bk}$ nucleus. For the reaction $^{48}\mathrm{Ca}+^{249}\mathrm{Bk}$, our estimation shows that the ER cross sections in $3n$ and $4n$ channels may be expected to be greater than 1 pb. Therefore, $^{48}\mathrm{Ca}$ and $^{249}\mathrm{Bk}$ should be the optimal projectile-target combination for synthesis of superheavy element 117 in practice. In addition, as a main result of systematic analysis, we find that the ER cross section exponentially depends on the mass difference (in unit of temperature) of fission and neutron emission saddle points. Therefore, it is of essential importance for the successful synthesis of superheavy nuclei to select the isotopic composition of projectile and/or target so as the mass difference of fission and neutron emission saddle points as large as possible. Entrance channel effects are examined by means of a comparison of the reactions $^{48}\mathrm{Ca}+^{245}\mathrm{Bk}$, $^{50}\mathrm{Ti}+^{243}\mathrm{Am}$, and $^{55}\mathrm{Mn}+^{238}\mathrm{U}$ leading to the same compound nucleus $^{293}\mathrm{117}$. The ER cross sections of the reactions $^{50}\mathrm{Ti}+^{243}\mathrm{Am}$ and $^{55}\mathrm{Mn}+^{238}\mathrm{U}$ are much smaller than that of $^{48}\mathrm{Ca}+^{245}\mathrm{Bk}$.