  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 transition 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.
