Electron densities in the coronae of the Sun and Procyon from extreme-ultraviolet emission line ratios in Fe XI

New R-matrix calculations of electron impact excitation rates for Fe XI are used to determine theoretical emission line ratios applicable to solar and stellar coronal observations. These are subsequently compared to solar spectra of the quiet Sun and an active region made by the Solar EUV Rocket Telescope and Spectrograph (SERTS-95), as well as Skylab observations of two flares. Line blending is identified, and electron densities of 10(9.3), 10(9.7), greater than or equal to 10(10.8), and greater than or equal to 10(11.3) cm(-3) are found for the quiet Sun, active region, and the two flares, respectively. Observations of the F5 IV-V star Procyon, made with the Extreme Ultraviolet Explorer (EUVE) satellite, are compared and contrasted with the solar observations. It is confirmed that Procyon's average coronal conditions are very similar to those seen in the quiet Sun, with N-e = 10(9.4) cm(-3). In addition, although the quiet Sun is the closest solar analog to Procyon, we conclude that Procyon's coronal temperatures are slightly hotter than solar. A filling factor of 25(-12)(+38)% was derived for the corona of Procyon.