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The nature and evolution of high-redshift dusty star-forming galaxies (high-zDSFGs) remain an open question. Their massive gas reservoirs play an importantrole in driving the intense star-formation rates hosted in these galaxies. Weaim to estimate the molecular gas content of high-z DSFGs by using various gasmass tracers such as the [CI], CO, [CII] emission lines and the dust content.These tracers need to be well calibrated as they are all limited byuncertainties on factors such as aCO, XCI, aCII and GDR, thereby affecting thedetermination of the gas mass accurately. The main goal of our work is to checkthe consistency between the gas mass tracers and cross-calibrate the uncertainfactors. We observe the two [CI] line transitions for 29 SPT-SMGs with theALMA-ACA. Additionally, we also present new APEX observations of [CII] line for9 of these galaxies. We find a nearly linear relation between the infraredluminosity and [CI] luminosity if we fit the starbursts and main-sequencegalaxies separately. We measure a median [CI]-derived excitation temperature of34.5+/-2.1 K. We probe the properties of the interstellar medium (ISM) such asdensity and radiation field intensity using [CI] to mid- or high-J CO lines and[CI] to infrared luminosity ratio, and find similar values to the SMGpopulations in literature. Finally, the gas masses estimated from [CI], CO,dust, and [CII] do not exhibit any significant trend with the infraredluminosity or the dust temperature. We provide the various cross-calibrationsbetween these tracers. Our study confirms that [CI] is a suitable tracer of themolecular gas content, and shows an overall agreement between all the classicalgas tracers used at high redshift. However, their absolute calibration and thusthe gas depletion timescale measurements remain uncertain.

Observations of neutral carbon in 29 high-z lensed dusty star forming galaxies and the comparison of gas mass tracers