  We introduce a new technique for determining x-ray fluorescence line energies
and widths, and we present measurements made with this technique of 22 x-ray L
lines from lanthanide-series elements. The technique uses arrays of
transition-edge sensors, microcalorimeters with high energy-resolving power
that simultaneously observe both calibrated x-ray standards and the x-ray
emission lines under study. The uncertainty in absolute line energies is
generally less than 0.4 eV in the energy range of 4.5 keV to 7.5 keV. Of the
seventeen line energies of neodymium, samarium, and holmium, thirteen are found
to be consistent with the available x-ray reference data measured after 1990;
only two of the four lines for which reference data predate 1980, however, are
consistent with our results. Five lines of terbium are measured with
uncertainties that improve on those of existing data by factors of two or more.
These results eliminate a significant discrepancy between measured and
calculated x-ray line energies for the terbium Ll line (5.551 keV). The line
widths are also measured, with uncertainties of 0.6 eV or less on the
full-width at half-maximum in most cases. These measurements were made with an
array of approximately one hundred superconducting x- ray microcalorimeters,
each sensitive to an energy band from 1 keV to 8 keV. No energy-dispersive
spectrometer has previously been used for absolute-energy estimation at this
level of accuracy. Future spectrometers, with superior linearity and energy
resolution, will allow us to improve on these results and expand the
measurements to more elements and a wider range of line energies.
