The K${\ensuremath{\alpha}}_{2}^{h}$ (${L}^{\mathrm{\ensuremath{-}}n}$; n=0--5) hypersatellite spectrum of sodium has been detected for various electron-impact energies in the range of 15\ensuremath{\le}${E}_{0}$\ensuremath{\le}200 keV. The measured energies of the transitions are in agreement with results of previous experiments at low electron energies and theoretical predictions. For the strongest hypersatellite, which corresponds to a ${K}^{\mathrm{\ensuremath{-}}2}$\ensuremath{\rightarrow}${K}^{\mathrm{\ensuremath{-}}1}$${L}^{\mathrm{\ensuremath{-}}1}$ transition, the natural width has been determined. The natural linewidth was found to be ${\ensuremath{\Gamma}}_{K}^{h}$=2.2\ifmmode\pm\else\textpm\fi{}0.4 eV, which is much larger than predicted. Furthermore, the electron double-ionization cross section of the K shell has been obtained. Within the investigated energy region the cross section decreases by about a factor of 4 with increasing electron-impact energy. This energy dependence suggests the dominance of direct double ionization in comparison to the shake-off process.
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