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We present our study of the realization of atom trap trace analysis for ³⁹Ar, an ultra-sensitive detection method for rare isotopes based on laser cooling. We report on the experimental determination of the hyperfine spectrum of the relevant cooling transition. A high-intensity, optically collimated beam of metastable argon atoms has been set up, and fluorescence detection of single ⁴⁰Ar atoms ina magneto-optical trap is realized. The deduced efficiencies of each stage lead to an expected ³⁹Ar count rate of six atoms per hour in the final setup.