We present a coupled quasiparticle random phase approximation and Hauser-Feshbach (QRPA+HF) model for calculating delayed particle emission. This approach uses microscopic nuclear structure information, which starts with Gamow-Teller strength distributions in the daughter nucleus and then follows the statistical decay until the initial available excitation energy is exhausted. Explicitly included at each particle emission stage is gamma-ray competition. We explore this model in the context of neutron emission of neutron-rich nuclei and find that neutron gamma competition can lead to both increases and decreases in neutron emission probabilities, depending on the system considered. A second consequence of this formalism is a prediction of more neutrons on average being emitted after beta decay for nuclei near the neutron drip line compared to models that do not consider the statistical decay.
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