This paper addresses a detection problem where a network of radiation sensors has to decide, at the end of a fixed time interval, if a moving target is a carrier of nuclear material. The problem entails determining whether or not a time-inhomogeneous Poisson process due to the moving target is buried in the recorded background radiation. In the proposed method, each of the sensors transmits once to a fusion center a locally processed summary of its information in the form of a likelihood ratio. The fusion center then combines these messages to arrive at an optimal decision in the Neyman-Pearson framework. The approach offers a pathway toward the development of novel fixed-interval detection algorithms that combine decentralized processing with optimal centralized decision making.