The natural line widths, asymmetric indices, and CK transitions in Ca to Ge

We have investigated systematically the $K\alpha_{\mathrm{1,2}}$ spectra in elements Ca to Ge using a high-resolution anti-parallel double-crystal X-ray spectrometer in order to elucidate the physical meaning of the asymmetry in the spectral profile. Lowe \textit{et al}. [PRA83, 060501] reported that the [\textit{1s3d}] shake-off probability for Sc at 42 {\%}, whichis the highest reported value. Chantler \textit{et al}. [J. Phys. B46, 015002] concluded that the symmetric profile of the observed Ti $K\alpha_{\mathrm{1}}$ emission line is different from the results of the Cu $K\alpha_{\mathrm{1,2}}$ obtained by Deutsch \textit{et al}.[ PRA51, 283]. To shed some light on this issue, we focused on the implications of the inclusion of the main [\textit{1s3d}] shake processes, asymmetric index, and natural line widths in 3$d$ elements. Our experimental results yielded the [\textit{1s3p}, \textit{3d}] shake probability for the 3d elements. For the [\textit{1s3p, 3d}] shake probability on Sc, we have obtained experimentally and theoretically (MCDF and the sudden approximation) the values \textasciitilde 25{\%} and 10{\%}, respectively. In both approaches, it is found that the shake-off related peaks appear between the $K\alpha_{\mathrm{1}}$ and $K\alpha _{\mathrm{2}}$ lines. Moreover, the observed Sc $K\alpha _{\mathrm{1\thinspace }}$line approaches a symmetric profile, unlike the another 3d's $K\alpha_{\mathrm{1}}$ line profile. The asymmetry index of $K\alpha_{\mathrm{1}}$ in 3$d$ elements from Sc to Zn is ascribed to the 3$d$ spectator hole.