The production of two prompt $J/\psi $ mesons, each with transverse momenta $p_{\mathrm {T}}>8.5$ ?GeV and rapidity $|y| < 2.1$ , is studied using a sample of proton-proton collisions at $\sqrt{s} = 8$ ?TeV, corresponding to an integrated luminosity of 11.4?fb$^{-1}$ collected in 2012 with the ATLAS detector at the LHC. The differential cross-section, assuming unpolarised $J/\psi $ production, is measured as a function of the transverse momentum of the lower- $p_{\mathrm {T}}$ $J/\psi $ meson, di- $J/\psi $ $p_{\mathrm {T}}$ and mass, the difference in rapidity between the two $J/\psi $ mesons, and the azimuthal angle between the two $J/\psi $ mesons. The fraction of prompt pair events due to double parton scattering is determined by studying kinematic correlations between the two $J/\psi $ mesons. The total and double parton scattering cross-sections are compared with predictions. The effective cross-section of double parton scattering is measured to be $\sigma _{\mathrm {eff}} = 6.3 \pm 1.6 \mathrm {(stat)} \pm 1.0 \mathrm {(syst)}$
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