  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 $t \bar{t}+1$-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$^{-1}$. 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 prediction at
next-to-leading-order accuracy in quantum chromodynamics using the pole-mass
scheme. With this method, the measured value of the top-quark pole mass,
$m_t^{\rm pole}$, is: $m_t^{\rm pole}$ =173.7 $\pm$ 1.5 (stat.) $\pm$ 1.4
(syst.) $^{+ 1.0}_{-0.5}$ (theory) GeV. This result represents the most precise
measurement of the top-quark pole mass to date.
