Context. The age, evolution, and chemical properties of the Galactic disk can be effectively ascertained using open clusters. Within the large program Stellar Populations Astrophysics at the Telescopio Nazionale Galileo, we specifically focused on stars in open clusters, to investigate various astrophysical topics, from the chemical content of very young systems to the abundance patterns of lesser studied intermediate-age and old open clusters.

Aims. We investigate the astrophysically interesting element fluorine (F), which has an uncertain and intriguing cosmic origin. We also determine the abundance of cerium (Ce), as F abundance is expected to correlate with the s-process elements. We intend to determine the trend of F abundance across the Galactic disk as a function of metallicity and age. This will offer insights into Galactic chemical evolution models, potentially enhancing our comprehension of this element’s cosmic origin.

Methods. High-resolution near-infrared spectra were obtained using the GIANO-B spectrograph. The Python version of Spectroscopy Made Easy (PySME), was used to derive atmospheric parameters and abundances. The stellar parameters were determined using OH, CN, and CO molecular lines along with Fe I lines. The F and Ce abundances were inferred using two K-band HF lines (λλ 2.28, 2.33 µm) and two atomic H-band lines (λλ 1.66, and 1.71 µm), respectively.

Results. Of all the clusters in our sample, only King 11 had not been previously studied through medium- to high-resolution spectroscopy, and our stellar parameter and metallicity findings align well with those documented in the literature. We have successfully inferred F and Ce abundances in all seven open clusters and probed the radial and age distributions of abundance ratios. This paper presents the first F Galactic radial abundance gradient. Our results are also compared with literature estimates and with Galactic chemical evolution models that have been generated using different F production channels.

Conclusions. Our results indicate a constant, solar pattern in the [F/Fe] ratios across clusters of different ages, supporting the latest findings that fluorine levels do not exhibit any secondary behavior for stars with solar or above-solar metallicity. However, an exception to this trend is seen in NGC 6791, a metal-rich, ancient cluster whose chemical composition is distinct due to its enhanced fluorine abundance. This anomaly strengthens the hypothesis that NGC 6791 originated in the inner regions of the Galaxy before migrating to its present position. By comparing our sample stars with the predictions of Galactic chemical evolution models, we came to the conclusion that both asymptotic giant branch stars and massive stars, including a fraction of fast rotators that increase with decreasing metallicity, are needed to explain the cosmic origin of F.