Optimal colliding energy for the synthesis of superheavy element $Z$=119

Abstract

The evaporation residue (ER) cross section of 3n and 4n channels related to the synthesis of superheavy element (SHE) with the charge number $Z=119$ in the $^{51}$V+$^{248}$Cm reaction has been calculated by the dinuclear system (DNS) model as a sum of the partial cross sections of the corresponding channels. The angular momentum distribution of the compound nucleus is estimated by the dynamical trajectory calculations of the capture probability which is considered as the DNS formation probability. The fusion probability decreases by the increase of the DNS angular momentum due to its influence on the intrinsic fusion barrier $B_{\rm fus}^*$. The range $α_2=60^{\circ} ÷70^{\circ}$ of the orientation angle of the axial symmetry axis of the deformed target nucleus $^{248}$Cm is favorable for the formation of the compound nucleus. The fusion probability decreases at around $α_2=90^{\circ}$ since the number of the partial waves contributing to the capture decreases. Therefore, it is important to calculate the capture cross section dynamically. The 4n channel cross section of the SHE synthesis is larger than the 3n channel cross section maximum value of the ER cross section is 12.3 fb at $E_{\rm c.m.}$=232 MeV.