You not find specific equation to calculation the threshold fluence energy ( F) (J/ cm2) to able ablation the metal (Cu), but usually the equation to find the fluene energy for different metals depend on the properties of this metals and parameters of laser it use. Kindly ,read this paper .
The thresh limit Is it related to concentration if so one can analyses from micro gram to nano gram with spectral devises like spectrometer AAS.ICP-AES
Most models neglect e-p interaction, so that there are a differences between theory and experimentally (We have seen in our works). so that we will modified it in new our book .this effect more dominate in long lambda (Λ, λ) .other factor depending on bonds type in unit cell (lattice) .this details and others will contains in our book.