We have previously shown that the first stage scheme is effective in the detection of physical capture attacks in wireless sensor networks. Like most existing detection schemes, our scheme relies upon message passing. Regular message passing consumes considerable energy. In this paper the first stage scheme is integrated with a novel sleep/wakeup mechanism, which is completely pre-scheduled based upon a node's internal clock. The scheduling tolerates minor clock alignment errors, so no frequent synchronization is needed. In addition, a sink-based dissemination technique is adopted, which replaces frequent and overlapped flooding of many regular nodes with sparse sink-triggered flooding. The adoption further saves energy expense. A LDCFSD protocol has been implemented in simulation. Simulation results have confirmed above conclusion.