EBD3: Systematic description of evaporation residue cross sections from light to superheavy nuclear systems

摘要: We propose an empirical formula, EBD3, for the systematic description of evaporation residue cross sections (σ_ER) in heavy-ion fusion reactions across a wide range of projectile-target combinations, from light asymmetric systems to superheavy element synthesis. The model decomposes the total cross section into a capture cross section calculated with an improved barrier distribution approach, a macroscopic survival probability accounting for quasi-fission and fusion-fission competition, and energy-dependent damping terms governing the compound nucleus de-excitation. A scale factor is introduced to absorb residual effects from angular momentum, dissipation, and shell structure. The model is validated against 189 experimental data points from 35 hot fusion, yielding a global root-mean-square deviation (RMSD) of 0.349 in log₁₀ (σ_ER) , corresponding to an average deviation factor of approximately 2.2. For 50 data points from hot fusion superheavy systems with Z≧110, the RMSD is 0.372 (factor of 2.4). The predicted optimal incident energies for 23 hot-fusion reactions leading to superheavy nuclei agree with experimental values with an RMSD of 2.50 MeV. These results demonstrate that EBD3 provides a reliable and computationally efficient framework for estimating evaporation residue cross sections and guiding experimental searches for new isotopes.