The study of the origin of asymmetries in mirror $\beta$ decay is extremely important to understand the fundamental nuclear force and the nuclear structure. The experiment was performed at the National Laboratory of Heavy Ion Research Facility in Lanzhou (HIRFL) to measure the $\beta$-delayed $\gamma$ rays of ${}^{26}$P by silicon array and Clover-type high-purity Germanium (HPGe) detectors. Combining with results from the $\beta$ decay of ${}^{26}$P and its mirror nucleus ${}^{26}$Na, the mirror asymmetry parameter $\delta$ ( ≡$f{t}^{+}$/$f{t}^{-}$− 1) was determined to be 46(13)% for the transition feeding the first excited state in the daughter nucleus. Our independent results support the conclusion that the large mirror asymmetry is close to the proton halo structure in ${}^{26}$P.

Precise time synchronization among multiple electronic channels is essential for nuclear physics experiments. In digital data acquisition systems based on XIA Pixie-16 modules, the relative timing between channels is not necessarily preserved when a new data acquisition run is started. A run-dependent timing offset — typically on the order of 10 ns — can occur independently in each channel, which cannot be corrected through offline data analysis alone. To address this issue, a dedicated external electronic circuit is developed. This circuit operates as a programmable double-throw switch that routs a common reference clock signal to all channels at the start of each run, before switching to normal physics data acquisition. This procedure enables direct measurement and thus correction of relative timing offsets for all channels on a run-by-run basis without manual intervention. The method has been successfully applied in a nuclear reaction experiment using multiple Pixie-16 modules, where it effectively corrects the run-dependent timing offset and thus significantly improves the accuracy of timing-dependent observables such as Parallel Plate Avalanche Counter(PPAC) position reconstruction and beam tracking.