A reassessment of absolute energies of the x-ray L lines of lanthanide metals

Abstract

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 xray 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.

A practical superconducting-microcalorimeter X-ray spectrometer for beamline and laboratory science

“…One must take care in fitting data to known line shapes, in order to avoid biased results. An accurate model of the energy-response function of the TES is required (a pure Gaussian response may be inadequate 33,34 ). To minimize bias, fits should be maximum-likelihood fits that account for the Poisson distribution of counts in a histogram bin.…”

“…73 "Smoothing" means that the spline does not strictly interpolate the calibration points, which in turn reduces the danger that the calibration curve will over-fit the uncertain, detailed structure of the data. In the most thorough absoluteenergy calibration of TES X-ray spectra to date, Fowler et al 34 used the NIST-metrology spectrometer (Sec. IV C) to derive an energy scale, based on the K lines of high-purity foils of Ti, Cr, Mn, Fe, and Co, whose absolute accuracy over the 4.5 to 7 keV range was estimated to be 0.4 eV.…”

“…9). To account for this effect, spectra acquired with these sensors must be analyzed 34 via a Bortels function, 107 which is the convolution of a Gaussian with a single-sided exponential and a delta function. The physical mechanism that causes this low-energy tail is an active area of research, but we speculate that some fraction of the X-ray energy absorbed in the Bi resides in an energy state with a thermal decay time that is much longer than τ TES .…”

“…The seven deployed and five planned spectrometers are designed for the applications of time-resolved absorption and emission spectroscopy with a tabletop, broadband source, [23][24][25][26][27] synchrotron-based X-ray emission and absorption spectroscopy, 22 synchrotron-based energy-resolved scattering, 28,29 particle-induced X-ray emission at an accelerator beamline, 30,31 X-ray spectroscopy of hadronic atoms produced by accelerator beamlines, 32,33 metrology of X-ray lines excited by a laboratory tube source, 34 and study of highly ionized atoms and molecules at electron-beam ion traps. 35,36 Sec.…”

Energy of the Th229 Nuclear Clock Isomer Determined by Absolute γ -ray Energy Difference

“…The third error is the error due to an inappropriate functional form for the calibration curve. A cubic spline curve with natural boundary conditions [31] was tested as a calibration curve, resulting in an energy discrepancy of 0.25 eV. We therefore determined the overall systematic error by taking a root sum square of both errors (0.22 eV and 0.25 eV), which is 0.33 eV.…”