Absolute energies and emission line shapes of the L x-ray transitions of lanthanide metals

Abstract

We use an array of transition-edge sensors, cryogenic microcalorimeters with 4 eV energy resolution, to measure L x-ray emission-line profiles of four elements of the lanthanide series: praseodymium, neodymium, terbium, and holmium. The spectrometer also surveys numerous x-ray standards in order to establish an absolute-energy calibration traceable to the international system of units for the energy range 4 keV to 10 keV. The new results include emission line profiles for 97 lines, each expressed as a sum of one or more Voigt functions; improved absolute energy uncertainty on 71 of these lines relative to existing reference data; a median uncertainty on the peak energy of 0.24 eV, four to ten times better than the median of prior work; and six lines that lack any measured values in existing reference tables. The 97 lines comprise nearly all of the most intense L lines from these elements under broad-band x-ray excitation. The work improves on previous measurements made with a similar cryogenic spectrometer by the use of sensors with better linearity in the absorbed energy and a gold x-ray absorbing layer that has a Gaussian energy-response function. It also employs a novel sample holder that enables rapid switching between science targets and calibration targets with excellent gain balancing. Most of the results for peak energy values shown here should be considered as replacements for the currently tabulated standard reference values, while the line shapes given here represent a significant expansion of the scope of available reference data.

Energy calibration of nonlinear microcalorimeters with uncertainty estimates from Gaussian process regression

“…We asked how far in error the intermediate (Co Kα) energy estimate would be if the curve were the linear interpolation of the Mn and Cu Kα peaks for each possible choice of y and x functions. gives results intermediate between p and log p. In any calibration space, the linear-interpolation error is larger at higher photon energy for these data (from a study of lanthanide metal emission [3]).…”

“…In previous work [3,4], we argued that the smoothing spline is the best way to generalize the calibration x-y relationship. It does not interpolate the anchor points exactly but strikes a compromise between fidelity to the data and minimal curvature.…”

“…The x and y functions can be picked by the principle that the spline function should "do the least work." For example, in the case of TES calibration from 4 keV to 10 keV for a study of rare-earth L lines [3], we found it best to spline y(E, p) = p/E, which we called the sensor gain, as a function of x(p) = p. Consider the Kα lines of Mn, Co, and Cu at approximately 6 keV, 7 keV, and 8 keV. We asked how far in error the intermediate (Co Kα) energy estimate would be if the curve were the linear interpolation of the Mn and Cu Kα peaks for each possible choice of y and x functions.…”

“…With polynomial fits, approximation is accomplished by weighted least-squares fits to a polynomial of degree lower than the number of anchor points. Though splines normally interpolate their data, several methods to approximate with splines exist; we have previously found best results with a cubic smoothing spline [3].…”

Transition edge sensor based detector: from X-ray to $γ$-ray

“…Since the transition region is very narrow, the resistance of TES is extremely sensitive to the change of temperature. The temperature coefficient of resistance(α I ) of TES is much higher than that of traditional semiconductor thermometers, so it has been used in many cutting-edge scientific researches [2][3][4][5][6][7][8]. For the sake of brevity, this article will mainly introduce the work in the field of X-ray and γ ray.…”