We present $R$-matrix calculations of photoabsorption and photoionization cross sections across the K-edge of Mg, Si, S, Ar, and Ca ions with more than 10 electrons. The calculations include the effects of radiative and Auger damping by means of an optical potential. The wave functions are constructed from single-electron orbital bases obtained using a Thomas--Fermi--Dirac statistical model potential. Configuration interaction is considered among all states up to $n=3$. The damping processes affect the resonances converging to the K-thresholds causing them to display symmetric profiles of constant width that smear the otherwise sharp edge at the photoionization threshold. These data are important for modeling of features found in photoionized plasmas.
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