One of the surprises of the Herschel mission was the detection of ArH+ towards the Crab Nebula in emission and in absorption towards strong Galactic background sources. Although these detections were limited to the first quadrant of the Galaxy, the existing data suggest that ArH+ ubiquitously and exclusively probes the diffuse atomic regions of the ISM. In this study, we extend the coverage of ArH+ to other parts of the Galaxy with new observations of its J = 1-0 transition along seven Galactic sight lines towards bright sub-mm continuum sources. We aim to benchmark its efficiency as a tracer of purely atomic gas by evaluating its correlation (or lack there of) with other well-known atomic and molecular gas tracers. The observations of ArH+ near 617.5 GHz were made feasible with the new, sensitive SEPIA660 receiver on the APEX 12 m telescope. The two sidebands of this receiver allowed us to observe p-H2O+ transitions of at 607.227 GHz simultaneously with the ArH+ line. By analysing the steady state chemistry of OH+ and o-H2O+, we derive on average a cosmic-ray ionisation rate (CRIR), of 2.3e-16 s^-1 towards the sight lines studied in this work. Using the derived values of the CRIR and the observed ArH+ abundances we constrain the molecular fraction of the gas traced by ArH+ to lie below 2e-2 with a median value of 8.8e-4. Combined, our observations of ArH+, OH+, H2O+, and CH probe different regimes of the ISM, from diffuse atomic to diffuse and translucent molecular clouds. Over Galactic scales, we see that the distribution of N(ArH+) is associated with that of N(H), particularly in the inner Galaxy with potentially even contributions from the warm neutral medium phase of atomic gas at larger galactocentric distances. We derive an average o/p-ratio for H2O+ of 2.1, which corresponds to a nuclear spin temperature of 41 K, consistent with the typical gas temperatures of diffuse clouds.
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