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The use of the random-phase approximation with exchange (RPAE) for calculating partial and total photoionization cross sections and photoelectron angular distributions for open-shell atoms is examined for atomic chlorine. Whereas the RPAE corrections in argon (Z=18) are large, we find those in chlorine (Z=17) to be much smaller due to geometric factors. Hartree-Fock calculations with and without core relaxation are also presented. Sizable deviations from the close-coupling results of Conneely are found.