Measurement of xenon radioisotopes from nuclear fission is a key element for monitoring underground nuclear weapon tests. $^{131m}Xe$, $^{133}Xe$, $^{133}mXe$ and $^{135}Xe$ in the air can be detected via low background systems such as a beta-gamma coincidence counting system. Radioxenon monitoring is performed through air sampling, xenon extraction, measurement and spectrum analysis. The minimum detectable concentration of $^{135}Xe$ can be significantly variable depending on the sampling time, extraction time and data acquisition time due to its short half-life. In order to optimize the acquisition time with respect to certain experimental parameters such as sampling and xenon extraction, theoretical approach and experiment using SAUNA system were performed to determine the time to minimize the minimum detectable concentration, which the results were discussed.
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