1 Introduction

Recently a wealth of optical and UV spectra in Fe VI have been observed from gaseous nebulae and hot H II regions in general, and from hot white dwarfs (Jordan et al. 1995). Emission lines from transitions among the first 19 fine-structure levels dominated by the ground configuration ${\rm 3d^3}$ also appear in nova V 1016 Cygni (Mammano & Ciatti 1975) and RR Telescoppii (McKenna et al. 1997). Optical spectra of [Fe VI] have been observed for many transitions in planetary Nebulae such as NGC 6741 (Hyung & Aller 1997a), NGC 7662 (Hyung & Aller 1997b), IC 351 (Feibelman et al. 1996), and others. It is therefore interesting to simulate these spectra using accurate atomic data from the Iron Project (Hummer et al. 1993) obtained using ab initio calculations.

Given the state-of-the-art observational accuracy of astrophysical work, it is necessary to use accurate atomic radiative and electron impact excitation (EIE) data in order to calculate accurately the intensities ratios of prominent density and temperature sensitive lines of [Fe VI]. In the collisional-radiative (hereafter CR) model, all of the level contributions are coupled together and need to be considered. Furthermore, we have recently shown (Chen & Pradhan 2000; hereafter CP00) that in addition to EIE and spontaneous radiative decay, level populations in Fe VI are significantly affected by fluorescent excitation (hereafter FLE) via a radiation backgound, typically a UV continuum. From an atomic physics point of view this requires additional physical mechanisms to be included in the atomic model in order to correctly predict the line intensities. In fact, it was demonstrated in CP00 that the observed [Fe VI] optical line ratios in the high excitation planetary nebula (hereafter PNe) NGC 6741 can not be interpreted without taking account of the FLE mechanism (as proposed by Lucy 1995; see also Bautista et al. 1996), which depends on strong dipole allowed excitations from the ground, or low-lying levels, and cascades into the upper levels of observed transitions.

In order to implement the FLE mechanism in the CR model therefore, one needs both the forbidden and the dipole allowed transition probabilities, in addition to the EIE rate coefficients. Accurate EIE collison strengths and rate coefficients of Fe VI have recently been computed under the IP by the Ohio-State group using the R-matrix method. The excitation rate coefficients differ considerably from previous works (IP.XXXVII, Chen & Pradhan 1999b; hereafter CP99b). The present work has a two-fold aim: (i) to compute transition proabilities Fe VI, and (ii) to use a CR model with FLE to compute line intensity ratios as possible temperature and density diagnostics. It is further shown that, following CP00, the radiation temperature of the central source and the distance of the emission region may be determined if the FLE mechanism is operative. The extended CR model takes account of the two competing excitation mechanisms, due to electron excitation (EIE), and photon excitations (FLE).

A large number of line ratios of [Fe VI] are examined. Density and temperature diagnostics line ratios are determined and applied to interpret observational data from a sample of planetary nebulae. The spectral diagnostics developed herein should have general applications to various other astrophysical sources.