Almost 200 different species have been detected in the interstellar medium (ISM) during the last decades, revealing not only simple species but complex molecules with more than 6 atoms. Other exotic compounds, like the weakly-bound dimer (H2)2, have also been detected in astronomical sources like Jupiter. We aim at detecting for the first time the CO-H2 van der Waals complex in the ISM, which if detected can be a sensitive indicator for low temperatures. We use the IRAM30m telescope, located in Pico Veleta (Spain), to search for the CO-H2 complex in a cold, dense core in TMC-1C (with a temperature of 10 K). All the brightest CO-H2 transitions in the 3 mm (80-110 GHz) band have been observed with a spectral resolution of 0.5-0.7 km/s, reaching a rms noise level of 2 mK. The simultaneous observation of a broad frequency band, 16 GHz, has allowed us to conduct a serendipitous spectral line survey. No lines belonging to the CO-H2 complex have been detected. We have set up a new, more stringent upper limit for its abundance to be [CO-H2]/[CO] = 5x10^{-6}, while we expect the abundance of the complex to be in the range 10^{-8}-10^{-3}. The spectral line survey has allowed us to detect 75 lines associated with 41 different species (including isotopologues). We detect a number of complex organic species, e.g. methyl cyanide (CH3CN), methanol (CH3OH), propyne (CH3CCH) and ketene (CH2CO), associated with cold gas (excitation temperatures about 7 K), confirming the presence of these complex species not only in warm objects but also in cold regimes.
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