The FAST HI 21-cm Absorption Blind Survey. III. OH Absorption Search in the 21-cm Absorber Sample and Continued HI Absorption Search

We present the first blind search for OH 18-cm absorption with the Five-hundred-meter Aperture Spherical Telescope (FAST), conducted alongside the HI 21-cm absorption search. Our previous FAST blind HI absorption search identified 34 systems. In this work, we extend the search using 2024 and part of the 2025 CRAFTS and FASHI data (394.4 hr and 1622.1 deg squared) together with FATHOMER observations, yielding three known and four new HI absorbers, for a total of 41 HI absorption systems. We search for OH absorption in 19 HI absorption systems whose OH redshifted frequencies fall within the FAST band. The known OH absorber towards PKS 1413+135 was re-detected, making our survey the first blind survey to detect OH absorption. No new OH absorbers were identified. We examine the relationship between N and N, applying survival analysis to account for upper limits. The analysis does not provide statistically significant evidence for either an N - N correlation or redshift evolution of N / N. Finally, spectral stacking sets 3 sigma OH column density upper limits of 4.93, 1.64, and 1.72 T / c times 10 12 cm-2 K-1 for associated, intervening, and combined samples, corresponding to []/[] ratios of < 1.66 times 10-8, < 1.42 times 10-8, and < 0.90 times 10-8, assuming T =10K for OH and T =100K for HI. These results place the strongest constraints to date on the OH content in radio-selected HI absorbers and establish a blind-survey benchmark for future studies of molecular gas in HI-selected systems. They also demonstrate that known HI 21-cm absorbers provide an effective parent sample for systematic OH absorption searches, paving the way for future larger surveys.