A spectrum of massive graviton states is present in several recent theoretical models that include extra space dimensions. In some such models the graviton states are well separated in mass, and can be detected as resonances in collider experiments. The ability of the ATLAS detector at the Large Hadron Collider to identify such states and measure their properties is considered, in the case that the resonances are narrow compared to the experimental resolution. The discovery limits for the detection of the decay mode G->e+e- are derived. The angular distribution of the lepton pair is used to determine the spin of the intermediate state. In one specific model, the resonance can be detected up to a graviton resonance mass of 2080 GeV, while the angular distribution favours a spin-2 hypothesis over a spin-1 hypothesis at 90% confidence for resonance masses up to 1720 GeV.
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