The Australia Telescope Compact Array (ATCA) has been used to measure positions with subarcsec accuracy for more than 50 masers at the 6035-MHz transition of excited OH. Eleven of the masers are new discoveries; the remainder complete the detailed study of masers from an earlier single-dish survey of the southern Galactic plane using the Parkes telescope. All previously known masers in the region were strong enough to be studied in the present observations, despite the common occurrence of variability. Typically, the intensity varies by less than a factor of two over several years, but one of the new masers is, remarkably, 100 times stronger than the upper limit measured six years earlier. The precise positions confirm that most of the masers coincide with a 1665-MHz ground-state OH maser counterpart that is usually stronger. However, there are a few instances where any 1665-MHz counterpart is either much weaker or not detected. When surveyed with comparable sensitivity, we show that the 6035-MHz masers are approximately one-third as common as 1665-MHz masers. We also add to earlier evidence that 1720-MHz masers preferentially occur at the sites hosting 6035-MHz masers. These facts are discussed in the context of current maser pumping models. Towards most of the 6035-MHz maser sites we find a coincident 6668-MHz methanol maser, and towards some of the maser sites we report new detections of ultracompact H ii regions. Clusters of two or three sites, each showing one, or several, of the principal molecular masing transitions, are found to be common; future comparative studies of these sites within small clusters will elucidate the precise conditions favouring different maser species. Several instances of absorption occur at 6035 MHz, one of them especially striking since it extends over a broad velocity range adjacent to maser emission related to the ultracompact H ii region 5.885−0.392. The absorption provides new clues to understanding the geometry and excitation of 5.885−0.392. Three sources were observed at 6030 MHz, an OH transition from the same excited state (2Π3/2, J=5/2) as the 6035-MHz line; in one case, the matching velocity patterns at 6030 and 6035 MHz, their similar circular polarization characteristics, and their spatial coincidence, reveal Zeeman splitting in a magnetic field of −9 mG, a field strength close to the upper limit found for any such masers.
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