Stopping powers and ranges for the heaviest atoms

Slowing down and stopping of the heaviest atoms, products of the fusion-evaporation nuclear reactions, during their passage through the Dubna gas-filled recoil separator has been studied using TRIM simulations. The study is important for experiments on the synthesis of super-heavy elements (SHEs) with atomic numbers around ZP = 114 produced with accelerated heavy ion (HI) beams and extracted with a separator for their detection. The average Mylar stopping power (SP) values obtained with the simulations for HIs with 82 ⩽ ZP ⩽ 92 reveal almost the same magnitudes, allowing extrapolation to the region of ZP > 92. Similar extrapolation of the ranges in an He + Ar gas mixture leads to rather small values for the heaviest atoms (ZP ⩾ 102) as compared to the range for U. The extrapolated values have large uncertainties and should be verified with different approaches. Available SP data obtained for HIs with 18 ⩽ ZP ⩽ 92 at energies E < 20 MeV/u have been analysed within various semi-empirical approaches. The analysis has shown that existing parameterizations give Mylar SP values for ZP ⩾ 82 that are very different from each other at energies of interest (around 0.1 MeV/u). We propose to use a general approach based on the HI effective charge parameterization obtained with available SP data for HIs and the hydrogen SP and effective charge corresponding to the same velocity and stopping medium as those for HIs. In this manner, the SPs of the gases H2, He, C4H10, and Ar as well as those of the solids Mylar, C, Al, and Ti have been obtained for any atoms with ZP ⩾ 18 (including the heaviest ones) at their reduced velocities 0.03 ⩽ Vred ⩽ 5.0. The SP values derived in such a way seem to be more reliable compared to the existing semi-empirical calculations and can be used in the conditioning of experiments on the synthesis of SHEs.