  Previously-unexplored diagnostics of O IV in the extreme ultraviolet region
260-280 A are used to derive a temperature and density for a solar flare kernel
observed on 2012 March 9 with the Extreme ultraviolet Imaging Spectrometer on
the Hinode satellite. Seven lines from the 2s 2p^2 - 2s 2p 3s transition array
between 271.99 and 272.31 A are both temperature and density sensitive relative
to the line at 279.93 A. The temperature, T, is constrained with the
268.02/279.93 ratio, giving a value of log (T/K)=5.10 +/- 0.03. The ratio
272.13/279.93 then yields an electron number density, N_e, of log (N_e/cm^-3) =
12.55 with a lower limit of 11.91, and an upper limit of 14.40. The O IV
emitting volume is estimated to be 0.4 arcsec (300 km) across. Additional O IV
lines at 196, 207 and 260 A are consistent with the derived temperature and
density but have larger uncertainties from the radiometric calibration and
blending. Density diagnostics of O V and Mg VII from the same spectrum are
consistent with a constant pressure of 10^17.0 K cm^-3 through the transition
region. The temperature derived from O IV supports recent results that O IV is
formed around 0.15 dex lower at high densities compared to standard
"zero-density" ionization balance calculations.
