We are concerned with improving the diagnostic potential of the K lines and edges of elements with low cosmic abundances that are observed in the X-ray spectra of supernova remnants, galaxy clusters and accreting black holes and neutron stars. Since accurate photoabsorption and photoionization cross sections are needed in their spectral models, they have been computed for isoelectronic sequences with electron number $12leq Nleq 18$ using a multi-channel method. Target representations are obtained with the atomic structure code AUTOSTRUCTURE, and ground-state cross sections are computed with the Breit--Pauli $R$-matrix method (BPRM) in intermediate coupling, including damping (radiative and Auger) effects. The contributions from channels associated with the 2s-hole $[2{rm s}]mu$ target configurations and those containing 3d orbitals are studied in the Mg and Ar isoelectronic sequences. Cross sections for the latter ions are also calculated in the isolated-resonance approximation as implemented in AUTOSTRUCTURE and compared with BPRM to test their accuracy. It is confirmed that the collisional channels associated with the $[2{rm s}]mu$ target configurations must be taken into account owing to significant increases in the monotonic background cross section between the L and K edges. Target configurations with 3d orbitals give rise to fairly conspicuous unresolved transition arrays in the L-edge region, but to a much lesser extent in the K-edge which is our main concern; therefore, they have been neglected throughout owing to their computationally intractable channel inventory, thus allowing the computation of cross sections for all the ions with $12leq Nleq 18$ in intermediate coupling with BPRM. We find that the isolated-resonance approximations performs satisfactorily.
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