Etching index to fission tracks

A practical procedure is proposed to standardize etching degrees for materials having different critical angles. Assuming that V_q and V_t are constant through the etching process, the increase of the track densities is considered to be proportional to the enlargement in the maximum track width. The density observable at time (T_t) after the saturation is given by ρ_t = ρη_o cos² θ + η_s (dρ/dW)W_s + (dρ/dW)(W_t - W_s), were ρ is the 'true' track density for a reference material, θ is the critical ange η₀ the optical counting efficiency for tracks intersecting the original surface, η_s that for tracks revealed by bulk etching from the start of the saturation time, and W_s and W_t the maximum track widths at times of the saturation (T_s) and (T_t). The sum of the former two is equal to the saturated density (ρ_s), and the last to the additional density after the saturation. The etching index at time (T_t) after the saturation is defined as the ratio of ρ_t to ρ cos² θ: EI_t = ρ_t/[(ρ_s - η_s(dρ/dW)W_s)/ η_o]. The counting efficiency for latent tracks (η_s) can be evaluated by integrating (dρ/dW) from W = 0 to W_s, taking into account consideration the appearance of the bulk etched tracks, and can also be calculated when the track geometry is assumed. It must be stressed that this efficiency is unchangeable by the resolving power of microscopes used. On the other hand, η_o would be greatly affected by the resolving power in most cases, and cannot be logically evaluated because it is the product of two kinds of obscure factors: η₁ for track length correction and η_u for many other unknowns. However, the former will be roughly given by η_o = W_r/R, where W_r is the resolving power measured separately, or estimated by the minimum track width which corresponds to just after the incubation period on the line tied to the origin and W_t. R is the etchable track length. In conclusion, using the available value of ρ cos² θ, objective comparison of track densities is possible, because it depends essentially not on the etching efficiency only, but also the resolving power of microscopes used.