Maximizing Accuracy in Half Life Measurements, by Minimizing Error, with Application to BISMUTH-212 and POLONIUM-218

Radon and short-lived progeny existing in all three primordial series, namely uranium, thorium and actinium, are of most significance for human exposure, since their inhalation is implicated in bronchogenic carcinoma. Because the dosimetric calculations utilize half-life, it is important to know this parameter with the maximum possible accuracy. The half-lives of Po-218 and Bi-212, radon-222 and radon-220 progeny, were measured as 3.078 +/- 0.01 min and 59.81 +/- 0.23 min respectively. Experimental data collected by alpha-counting included background from both the counter and the intrinsic radioactivity. A comparison of all mathematical methods presently employed in the analysis of experimental radioactivity decay is presented. The most commonly used methods are, the least squares, the weighted least squares with different weighting factors and the maximum likelihood (Peierls) method. Artificial data corresponding to three different nuclides, different total experimental duration, and different counting time intervals were generated. Testing these data showed that the WLSQ with the correct weighting factor gives the higher accuracy and precision. Without spectrometry, it is impossible to measure the quantity or half-life of Po-218 unless correction is made for the Po-214 daughter. For the measurement of Po-218, samples containing the short-lived radon-222 daughters were collected electrostatically. A method used to estimate the initial radon daughters concentration in air based on regression analysis is proposed. The comparison of this with the well known Thomas method using artificial data showed that the regression analysis method leads to more accurate results. The Bi-212 samples were prepared from a Th-228 solution by spontaneous electrodeposition on platinum and nickel disks. Corrections for the curve stripping have been applied. The methods developed here have general application to the measurement of any radioactive nuclides. A review of the measured half-lives of the uranium series isotopes is presented in a summary table. All the reported values in the literature are included. Mean values were calculated and suggested as today's "best" available data.