Pile-up corrections for high-precision superallowed β decay half-life measurements via γ-ray photopeak counting

Abstract A general technique that corrects γ -ray gated β decay-curve data for detector pulse pile-up is presented. The method includes corrections for non-zero time-resolution and energy-threshold effects in addition to a special treatment of saturating events due to cosmic rays. This technique is verified through a Monte Carlo simulation and experimental data using radioactive beams of Na 26 implanted at the center of the 8 π γ -ray spectrometer at the ISAC facility at TRIUMF in Vancouver, Canada. The β -decay half-life of Na 26 obtained from counting 1809-keV γ -ray photopeaks emitted by the daughter Mg 26 was determined to be T 1 / 2 = 1.07167 ± 0.00055 s following a 27 σ correction for detector pulse pile-up. This result is in excellent agreement with the result of a previous measurement that employed direct β counting and demonstrates the feasibility of high-precision β -decay half-life measurements through the use of high-purity germanium γ -ray detectors. The technique presented here, while motivated by superallowed-Fermi β decay studies, is general and can be used for all half-life determinations (e.g. α -, β -, X-ray, fission) in which a γ -ray photopeak is used to select the decays of a particular isotope.