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.

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

X-ray emission spectroscopy optimization for chemical speciation in laboratory

A nonrelativistic variant of the quantum theory for the resonant inelastic-scattering process of two x-ray photons in the deep $1s$-shell ionization threshold energy region of a free many-electron atom is established. A quantitative estimate for the magnitude of the observed differential cross section is given.

Resonant inelastic scattering of two x-ray photons by a many-electron atom

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 6 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.

High-accuracy MCDHF Cu Kα and Cu Kβ diagram spectra and major satellites are presented. Spectral eigenvalues reach a theoretical expansion convergence of 0.03 eV or 0.00025%, with gauge and amplitude convergence to 0.7% for Cu Kα diagram spectra. Dominant theoretical spectral eigenvalues are shown to be within 0.032 eV of experimental data. Ab initio shake-off contributions are presented in terms of total probability from each subshell and as separated single and double shake probabilities. Discrepancies between theory and experiment in copper X-ray spectra arise from profile asymmetries, relativistic terms and shake spectra not yet accounted for. These results and this improved agreement provide key fundamental parameters for processes towards XFEL evolution and resolving key discrepancies between theory and experiment. 

Theory of copper Kα and Kβ diagram lines, satellite spectra, and ab initio determination of single and double shake probabilities

The $K\ensuremath{\beta}$ x-ray spectra of the elements from Ca to Ge have been systematically investigated using a high-resolution antiparallel double-crystal x-ray spectrometer. Each $K{\ensuremath{\beta}}_{1,3}$ natural linewidth has been corrected using the instrumental function of this type of x-ray spectrometer, and the spin doublet energies have been obtained from the peak position values in $K{\ensuremath{\beta}}_{1,3}$ x-ray spectra. For all studied elements the corrected $K{\ensuremath{\beta}}_{1}$ x-ray lines FWHM increase linearly as a function of $Z$. However, for $K{\ensuremath{\beta}}_{3}$ x-ray lines this dependence is generally not linear in the case of $3d$ elements but increases from Sc to Co elements. It has been found that the contributions of satellite lines are considered to be $[KM]$ shake processes. Our theoretically predicted synthetic spectra of Ca, Mn, Cu, and Zn are in very good agreement with our high-resolution measurements, except in the case of Mn, due to the open-shell valence configuration effect (more than 7000 transitions for diagram lines and more than $100\phantom{\rule{0.16em}{0ex}}000$ transitions for satellite lines) and the influence of the complicated structure of the metallic Mn.

Structure of high-resolution K β 1 , 3 x-ray emission spectra for the elements from Ca to Ge

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Structure of high-resolution K β 1 , 3 x-ray emission spectra for the elements from Ca to Ge