Results of a comparative analysis of the $^{214}$Po ($T_{1/2}= 163.47pm0.03$ $mu$s), $^{213}$Po ($T_{1/2}=3.705 pm 0.001$ $mu$s) and $^{212}$Po ($T_{1/2}=294.09pm0.07$ ns) half-life annular variation parameters are presented. It is shown that two ind
ependent sequential sets of the $^{214}$Po $tau$-values $(tauequiv T_{1/2})$ obtained in the spaced laboratories can be described by sinusoidal functions. The sinusoid curve with amplitude $A=(5.0 pm1.5) cdot 10^{-4}$, period $omega=(365pm 8)$ days, and phase $phi=(170 pm 7)$ days approximates the set of $^{214}$Po $tau$ values obtained at BNO INR RAS during the $sim$973 days starting on January 4, 2012. The function approximates a set of $tau$-values with a time duration of $sim1460$ days obtained at the KhNU has an amplitude $A=(4.9pm1.8)cdot10^{-4}$, a period $omega= (377pm13)$ days and a phase $phi=(77pm10)$ days. The $^{213}$Po $tau$-value set with a time duration of $sim1700$ days can be described by a sinusoidal function with an amplitude $A=(3.9pm1.2)cdot10^{-4}$, a period $omega= (370pm13)$ days and a phase $phi=(130pm9)$ days. The $^{212}$Po $tau$-value set with a time duration of $sim670$ days can be described by a sinusoidal function with an amplitude $A=(7.5pm1.6)cdot10^{-4}$, a period $omega= (375pm13)$ days and a phase $phi=(40pm10)$ days.
Precise measurement of half-life of $^{212}$Po (one of the daughter nuclides in radioactive chain of $^{232}$Th) was realized by means of liquid scintillator based on toluene doped by complex of thorium and trioctylphosphine oxide with concentration
of Th $sim0.1$ mass %. Fast photomultiplier tube and high frequency oscilloscope were used to acquire the scintillation signals waveforms. The algorithms were developed to find pairs of $^{212}$Bi beta-decays and subsequent $^{212}$Po alpha-decays, to calculate time differences between the events in the pair, and to build $^{212}$Bi beta-decay and $^{212}$Po alpha-decay energy spectra. Preliminary the $^{212}$Po half-life is $T_{1/2} = (294.8 pm 1.9)$ ns. The experiment is in progress aiming at reduction of the statistical and systematic uncertainties.
A device with the parent $^{229}$Th source was constructed to search for variations of the daughter $^{213}$Po half-life ($T_{1/2} = 4.2$ $mu$s). A solar-daily variation with amplitude $A_{So}=(5.3 pm 1.1) times 10^{-4}$, a lunar-daily variation with
amplitude $A_L = (4.8 pm 2.1) times 10^{-4}$, and a sidereal-daily variation with amplitude $A_S = (4.2 pm 1.7) times 10^{-4}$ were found upon proceeding the data series over a 622-day interval (from July 2015 to March 2017). The $^{213}$Po half-life mean value is found to be $T_{1/2} = 3.705 pm 0.001$ $mu$s. The obtained half-life is in good agreement with some of the literature values obtained with great accuracy.
Rare event physics demands very detailed background control, high-performance detectors, and custom analysis strategies. Cryogenic calorimeters combine all these ingredients very effectively, representing a promising tool for next-generation experime
nts. CUPID-0 is one of the most advanced examples of such a technique, having demonstrated its potential with several results obtained with limited exposure. In this paper, we present a further application. Exploiting the analysis of delayed coincidence, we can identify the signals caused by the $^{220}$Rn-$^{216}$Po decay sequence on an event-by-event basis. The analysis of these events allows us to extract the time differences between the two decays, leading to a new evaluation of $^{216}$ half-life, estimated as (143.3 $pm$ 2.8) ms.
Description of the TAU-4 installation intended for long-term monitoring of the half-life value $T_{1/2}$ of the $^{212}$Po is presented. Natural thorium used as a source of the mothers chain. The methods of measurement and data processing are describ
ed. The comparative results of short test measurements carried out in the ground (680 h) and underground (564 h) laboratories are given. Averaged value $T_{1/2}$ =$294.09pm 0.07$ ns of the $^{212}$Po half-life has been found for the ground level data set similar one for the underground data set. The solar-daily variations with amplitudes $A_{So}=(11.7pm 5.2)times10^{-4}$ for the ground data and $A_{So}=(7.5pm 4.1)times10^{-4}$ for the underground one were found in a series of $tau$ values.