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Here we present a new method of irradiating 134 Xe capsules to produce 135 Xe gas standards which maximize the ratio of 135 Xe to 133 Xe production due to (n,g) and (n,2n) reactions, respectively. We performed "Spectral tuning" of the University of Utah TRIGA Reactor (UUTR) neutron spectrum to increase the length of time that 135 Xe dominates undesirable 135 Xe in the sample, so that the capsules - used for calibration and quality control testing of Xe gas detection equipment in support of the Comprehensive Test Ban Treaty (CTBT) - will remain viable for longer periods post-irradiation. Moreover, optimized methods of computation and analysis were developed yielding improved computational efficiency over standard Monte Carlo approaches. These methods provided valuable insight into the final design and manufacture of new, ex-core Teflon irradiation chambers tested in the UUTR. The methods of computation and analysis, as well as the physical irradiation chamber designs, were derived such that they could be readily applied to any reactor for spectral tuning of a specific reactor's flux profile. Results of the physical experiments employing the optimized irradiation chamber designs demonstrated sample viability time improvements of over 60% when compared to conventional, un-optimized methods of gas sample generation. Thus, use of these methods enhance both the CTBT-related calibrations and performance testing, and the continued stability of the CTBT monitoring network overall., (Copyright © 2022 Elsevier Ltd. All rights reserved.)