The normalized differential cross section for top-quark pair production in association with at least one jet is studied as a function of the inverse of the invariant mass of the tt\uaf + 1-jet system. This distribution can be used for a precise determination of the top-quark mass since gluon radiation depends on the mass of the quarks. The experimental analysis is based on proton-proton collision data collected by the ATLAS detector at the LHC with a centre-of-mass energy of 7 TeV corresponding to an integrated luminosity of 4.6 fb^( 121). The selected events were identified using the lepton+jets top-quark-pair decay channel, where lepton refers to either an electron or a muon. The observed distribution is compared to a theoretical predicti...