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Monitoring radioactive xenon in the atmosphere is one of several methods used to detect nuclear weapons testing. To increase sensitivity, monitoring stations use a complex system of separate beta and gamma detectors to detect beta-gamma coincidences from the Xe isotopes of interest, which is effective, but requires such careful gain matching and calibration that it is difficult to operate in the field. To simplify the system, a phoswich detector has been designed, consisting of optically coupled plastic and CsI scintillators to absorb beta particles and gamma rays, respectively. Digital pulse shape analysis of the detector signal is used to determine if radiation interacted in either or both parts of the detector and to measure the energy deposited in each part, thus using only a single channel of readout electronics to detect beta-gamma coincidences and to measure both energies. Experiments with a prototype detector show that the technique can clearly separate event types, does not degrade the energy resolution, and has an error rate for detecting coincidences of less than 0.1%. Monte Carlo simulations of radiation transport and light collection in the proposed detector were performed to obtain optimum values for its design parameters and an estimate of the coincidence detection efficiency (82-92%) and the background rejection rate (better than 99%).