CERN-LHC. The distributions of event-by-event harmonic flow coefficients vn for n = 2-4 are measured in sqrt(sNN) = 2.76 TeV Pb+Pb collisions using the ATLAS detector at the LHC. The measurements are performed using charged particles with transverse momentum pT > 0.5 GeV and in the pseudorapidity range |eta| < 2.5 in a dataset of approximately 7 mub^-1 recorded in 2010. The shapes of the vn distributions suggest that the associated flow vectors are described by a two-dimensional Gaussian function in central collisions for v2 and over most of the measured centrality range for v3 and v4. Significant deviations from this function are observed for v2 in mid-central and peripheral collisions, and a small deviation is observed for v3 in mid-central collisions. In order to be sensitive to these deviations, it is shown that the commonly used multi-particle cumulants, involving four particles or more, need to be measured with a precision better than a few percent. The vn distributions are also measured independently for charged particles with 0.5 < pT < 1 GeV and pT > 1 GeV. When these distributions are rescaled to the same mean values, the adjusted shapes are found to be nearly the same for these two pT ranges. The vn distributions are compared with the eccentricity distributions from two models for the initial collision geometry: a Glauber model and a model that includes corrections to the initial geometry due to gluon saturation effects. Both models fail to describe the experimental data consistently over most of the measured centrality range.

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