Recoil decay tagging (RDT) is a very powerful method for the spectroscopy of exotic nuclei. RDT is a delayed coincidence technique between detectors usually at the target position and at the focal plane of a spectrometer. Such measurements are often limited by dead time. This paper describes a novel triggerless data acquisition method, which is being developed for the Gamma Recoil Electron Alpha Tagging (GREAT) spectrometer, that overcomes this limitation by virtually eliminating dead time. Our solution is a total data readout (TDR) method where all channels run independently and are associated in software to reconstruct events. The TDR method allows all the data from both target position and focal plane to be collected with practically no dead-time losses. Each data word is associated with a timestamp generated from a global 100-MHz clock. Events are then reconstructed in real time in the event builder using temporal and spatial associations defined by the physics of the experimen
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