High coronal electron densities in a solar flare from Fe XXI and Fe XXII X-ray line measurements

New calculations of the intensities of the Fe XXI 2p(2)-2p41 X-ray lines using the distorted wave method are described and compared with observations made by a crystal spectrometer on the Solar Maximum Mission about 6 minutes after the peak of a very intense flare. The comparison enables the electron density of the flare to be derived, the value being about 2 or 3 x 10(12) cm(-3). Some nearby Fe XXII X-ray lines, scanned 1 minute after flare peak, give an even higher value, 10(13) cm(-3). This is the first time corroborated values of such high densities have been obtained from ions emitted at temperatures as high as similar to 10 MK. They imply very rapid radiation cooling rates and have other important consequences for flare models.