Time modulations at per mil level have been reported to take place in the decay constant of several nuclei with period of one year (most cases) but also of about one month or one day. On the other hand, experiments with similar or better sensitivity have been unable to detect any modulation. In this letter we give the results of the activity study of two different sources: 40K and 226Ra. The two gamma spectrometry experiments have been performed underground at the Gran Sasso Laboratory, this way suppressing the time dependent cosmic ray background. Briefly, our measurements reached the sensitivity of 3.4 and 3.5 parts over 10^6 for 40K and 226Ra, respectively (1 sigma) and they do not show any statistically significant evidence of time dependence in the decay constant. We also give the results of the activity measurement at the time of the two strong X-class solar flares which took place in September 2017. Our data do not show any unexpected time dependence in the decay rate of 40K in correspondence with the two flares. To the best of our knowledge, these are the most precise and accurate results on the stability of the decay constant as function of time.
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