Methyl mercaptan (CH3SH) is a known interstellar molecule with abundances high enough that the detection of some of its minor isotopologues is promising. The present study aims at providing accurate spectroscopic parameters for the (13)CH3SH isotopologue to facilitate its identification in the interstellar medium at millimetre and submillimetre wavelengths. Through careful analysis of recent CH3SH spectra from 49-510 GHz and 1.1-1.5 THz recorded at natural isotopic composition, extensive assignments were possible not only for the ground torsional state of (13)CH3SH, but also in the first and second excited states. The torsion-rotation spectrum displays complex structure due to the large-amplitude internal rotation of the (13)CH3 group, similar to the main and other minor isotopic species of methyl mercaptan. The assigned transition frequencies have been fitted to within experimental error with a 52-parameter model employing the RAM36 programme. With predictions based on this fit, (13)CH3SH was searched for in spectra from the Atacama Large Millimetre/submillimetre Array (ALMA) towards the Galactic centre source Sgr B2(N2). Several transitions were expected to be observable, but all of them turned out to be severely blended with emission from other species, which prevents us from identifying (13)CH3SH in this source.
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