Relativistic atomic structure calculations for electric dipole E1, electric quadrupole E2 and magnetic dipole M1 transition probabilities among the first 80 fine-structure levels of Fe VI, dominated by configurations 3d^3, 3d^24s, and 3d^24p, are carried out using the Breit-Pauli version of the code Superstructure. Experimental energies are used to improve the accuracy of these transition probabilities. Employing the 80-level collision-radiative (CR) model with these dipole and forbidden

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... ion probabilities, and Iron Project R-matrix collisional data, we present a number of [Fe VI] line ratios applicable to spectral diagnostics of photoionized H II regions. It is shown that continuum fluorescent excitation needs to be considered in CR models in order to interpret the observed line ratios of optical [Fe VI] lines in planetary nebulae NGC 6741, IC 351, and NGC 7662. The analysis leads to parametrization of line ratios as function of, and as constraints on, the electron density and temperature, as well as the effective radiation temperature of the central source and a geometrical dilution factor. The spectral diagnostics may also help ascertain observational uncertainties. The method may be generally applicable to other objects with intensive background radiation fields, such as novae and active galactic nuclei. The extensive new Iron Project radiative and collisional calculations enable a consistent analysis of many line ratios for the complex iron ions.