The paper presents studies of Bose-Einstein Correlations (BEC) for pairs of like-sign charged particles measured in the kinematic range $p_{\rm T}>$ 100 MeV and $|\eta|<$ 2.5 in proton--proton collisions at centre-of-mass energies of 0.9 and 7 TeV with the ATLAS detector at the CERN Large Hadron Collider. The integrated luminosities are approximately 7 $\mu$b$^{-1}$, 190 $\mu$b$^{-1}$ and 12.4 nb$^{-1}$ for 0.9 TeV, 7 TeV minimum-bias and 7 TeV high-multiplicity data samples, respectively. The multiplicity dependence of the BEC parameters characterizing the correlation strength and the correlation source size are investigated for charged-particle multiplicities of up to 240. A saturation effect in the multiplicity dependence of the correlation source size is observed using the high-multiplicity 7 TeV data sample. The dependence of the BEC parameters on the average transverse momentum of the particle pair is also investigated.
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