LAUSR

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.