ECC3: a global model for evaporation residue cross sections in the synthesis of superheavy nuclei

Abstract

We present ECC3, an efficient model for evaporation residue (ER) cross sections in heavy-ion fusion reactions from light systems to superheavy-element synthesis. The ER cross section is factorized into capture, described by the universal empirical coupled channel (ECC2) model; compound-nucleus formation, given by the Zagrebaev-Greiner empirical Fermi function of the charge product; and survival against fission, obtained from a simplified HIVAP-type statistical-decay cascade. The capture sector is inherited unchanged from ECC2 and reproduces 348 measured capture excitation functions with a logarithmic RMSD of 0.29. A single set of model parameters for the formation and survival of compound nuclei is fitted to 60 measured ER excitation functions with the corresponding RMSD of 0.27. About 95\% of both the capture and ER systems are reproduced within a factor of four. Because the fitted parameters are constrained by light, medium-mass and superheavy systems rather than anchored to the measured superheavy region, extrapolation to unmeasured reactions is well controlled. The model also resolves the individual $xn$ channels. It reproduces the measured $3n$--$5n$ excitation functions of ${}^{19}$F+${}^{188}$Os and the systematic charge dependence of the maximal channel cross section for ${}^{48}$Ca-, ${}^{50}$Ti- and ${}^{54}$Cr-induced reactions. For the three element-119 reactions ${}^{50}$Ti+${}^{249}$Bk, ${}^{54}$Cr+${}^{243}$Am and ${}^{51}$V+${}^{248}$Cm, it predicts $4n$ dominance, with maximum cross sections of 13.2 fb, 2.64 fb and 1.56 fb, respectively.

arXiv comment30 pages. 7 figures