Fe XIV green/Fe XIII infrared line ratio diagnostics

We consider the first 27-level atomic model of Fe XIII (5.9 K < log T_{e} < 6.4 K) to estimate its ground level populations, taking account of electron as well as proton collisional excitations and de-excitations, radiative cascades, radiative excitations and de-excitations. Radiative cascade is important but the effect of dilution factor is negligible at higher electron densities. The ^{3}P_{1}-^{3}P_{0} and ^{3}P_{2}-^{3}P_{1} transitions in the ground configuration 3s^{2} 3p^{2} of Fe XIII result in two forbidden coronal emission lines in the infrared region, namely 10747 and 10798 Å. While the 5303 Å green line is formed in the 3s^{2} 3p ground configuration of Fe XIV as a ^2P_{3/2}-^{2}P_{1/2} magnetic dipole transition. The line-widths of simultaneously observed Fe XIV green and Fe XIII infrared forbidden coronal emission lines can be a useful diagnostic tool to deduce temperature and nonthermal velocity in the largescale coronal structures using intensity ratios of the lines as the temperature signature, instead of assuming ion temperature to be equal to the electron temperature. Since the line intensity ratios I_{G5303}/I_{IR10747} and I_{G5303}/I_{IR10798} have very weak density dependence, they are ideal monitors of temperature mapping in the solar corona. The computed ratios will be compared with the recently obtained observations in our next paper.