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

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 Na26 implanted at the center of the 8πγ-ray spectrometer at the ISAC facility at TRIUMF in Vancouver, Canada. The β-decay half-life of Na26 obtained from counting 1809-keV γ-ray photopeaks emitted by the daughter Mg26 was determined to be T1/2=1.07167±0.00055s following a 27σ 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.