Diagnostic diagrams of forbidden lines have been a useful tool for observers in astrophysics for many decades now. They are used to obtain information on the basic physical properties of thin gaseous nebulae. Some diagnostic diagrams are in wavelength domains which were difficult to take either due to missing wavelength coverage or low resolution of older spectrographs. Furthermore, most of the diagrams were calculated using just the species involved as a single atom gas, although several are affected by well-known fluorescence mechanisms as well. Additionally the atomic data have improved up to the present time. Aim of this work was a recalculation of well-known, but also of sparsely used, unnoted diagnostics diagrams. The new diagrams provide observers with modern, easy-to-use recipes to determine electron temperature and densities. The new diagnostic diagrams are calculated using large grids of parameter space in the photoionization code CLOUDY. For a given basic parameter (e.g. electron density or temperature) the solutions with cooling-heating-equilibrium are chosen to derive the diagnostic diagrams. Empirical numerical functions are fitted to provide formulas usable in e.g. data reduction pipelines. The resulting diagrams differ significantly from those used up to now and will improve the thermodynamic calculations. To our knowledge, for the first time detailed directly applicable fit formulas are given, leading to electron temperature or density from the line ratios.
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