Radiation Measurements without Posing theInversion Problem

Purpose: Radiation measurement is an exponential analysis, which is an “illposed” problem, where the solution is not unique. Therefore, the accuracy of data points is critical. If the radiation detector is sensitive during the dead time, usually an extended dead time signal processing method is necessary and the calculation of the dead time and pile up rate invoke the inversion problem, which is difficult to solve, and only approximated. We have used two new approaches, where the inversion problem is not posed, and there is no need to assume the Poisson distribution or constant source strength. It goes beyond all previous techniques by handling the presence of discriminators. The preamplifier-signal processing chain has dead times and applies discriminators, as a consequence disturbs the randomness, and other distributions may also contribute. Although an undisturbed nuclear decay should be Poisson in nature, the measured spectrum usually does not have a Poisson distribution. The robustness of the two methods was investigated, focusing on the traceable derivation of statistical uncertainty. The two new methods were applied in gamma spectra measurements of 152Eu calibration sources, and nuclear half-life of 68Ga PET isotope, and compared with measurements using previous techniques. Methods: CSX (Cambridge Scientific) digital signal processors were used with five HPGe detectors in two operation modes in two measurement series. In quality assurance mode, the CSX processes all events, both the accepted and rejected ones, placing each event into one or more spectra based on the applied discriminators. Based on the accepted spectrum, the rejected spectra were analyzed to determine the single, double and triple events, the rate of unrelated, and noise events all to obtain the true input counts. The second and independent approach was a time interval histogram analysis for the measurement of the gamma ray intensities. In time interval histogram mode, the CSX creates an energy spectrum as well as an interval histogram of arrival times between successive events. This operation mode does not apply discriminators and has no dead time. The CSX signal processor was selected, as it offers a dead time free and less than 1% pile up rate up to about a million counts per second input rate, as well as quality assurance at the signal processing level. Results: The CSX processors employ a non-extended dead time approach and in quality assurance mode the true input rate is readily determined. As a consequence, the inversion problem was avoided. The uncertainties and uncertainty propagation are clearly justified. For the half-life measurement of 68Ga, the time interval histogram analysis gave six times smaller standard uncertainty than the square root of the counts. The inter-arrival time histogram was sensitive to non-deterministic behaviour of the detectors, and electronic disturbances, discrediting several measurement series. This additional ability is significant for quality measurements. Conclusion: Spectroscopy with HPGe detectors has lacked a method to credibly determine the uncertainties when discrimination is applied. In addition, a calibration procedure was required to establish the output rate versus input rate relations for each input rate preferably with a similar spectral distribution as the spectrum of interest. The preamplifier signal shape varied as a function of the input rate for each of the HPGe detectors studied. In such cases both the accepted and rejected event spectra are necessary for a proper evaluation. Accounting for all the events allows the determination of the uncertainties. The time interval histogram analysis is simple and straightforward, and offers an elegant way to determine the true input rate and uncertainty. The measurement can be applied over large input counting ranges, and does not require calibration.