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The relative photoionization cross section for starting from a particular fine-structure level of the initial state of an atomic system and leading to a particular fine-structure level of the residual ion is presented for the case of atomic systems having one open subshell using a simple theoretical model in which emphasis is placed on the analysis of geometrical effects. This model parametrizes photoionization cross sections in terms of LS-dependent, single-configuration dynamical amplitudes, unlike previous treatments which assume LS-independent transition amplitudes from the start. In special cases our general formulas are shown to reduce to those of previous workers. We highlight photoionization of inner s subshells in open-shell atoms and show that when the total angular momenta for the initial atomic and final ionic fine-structure levels differ by more than 1/2 then such transitions are quasiforbidden. This prediction is tested in detail for the case of Cl 3s-subshell photoionization by comparison of our single-configuration results with the multiconfiguration, eigenchannel R-matrix results of Robicheaux and Greene [Phys. Rev. A (to be published)]. All of our results apply also to photoionization of open-shell positive ions or photodetachment of open-shell negative ions.