The radial density profiles of the ions corresponding to 35, 45, 47, and 48 amu, inside the ionopause of comet Halley, obtained by the heavy ion analyzer (PICCA) on board the Giotto spacecraft are presented. A photochemical model of the outflowing atmosphere/ionosphere, which emphasizes the sulfur chemistry in an H2O-dominated atmosphere, is used to support the identification of the four ions as H3S+, HCS+, H3CS+, and SO+, respectively. Both the observed values as well as the radial profiles of the ion densities are in fair agreement with the observations in the inner portion of the ionosphere (where the densities are monotonically decreasing with radial distance) considering the uncertainties in the observations and the limitations of the photochemical model. While the observed increases in the ion densities just inside the ionopause, following the initial radial decreases, cannot be explained by this simple spherically symmetric flow model, it can nevertheless be shown that they are not a consequence of the photochemistry. We speculate that the increased ion densities may be associated with the existence of a thin "inner" shock layer just inside the ionopause, where both lateral flow and dissociative recombination play important roles in determining the ion densities. We propose to consider this in a future paper.