Long-term monitoring of the ANTARES optical module efficiencies using $$^{40}\mathrm{{K}}$$ <math><mrow><msup><mrow></mrow><mn>40</mn></msup><mi>K</mi></mrow></math> decays in sea water

Cherenkov light induced by radioactive decay products is one of the major sources of background light for deep-sea neutrino telescopes such as ANTARES. These decays are at the same time a powerful calibration source. Using data collected by the ANTARES neutrino telescope from mid 2008 to 2017, the time evolution of the photon detection efficiency of optical modules is studied. A modest loss of only 20% in 9 years is observed. The relative time calibration between adjacent modules is derived as well.