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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 ofproton-proton collisions at $\sqrt{s} = 8$ TeV, corresponding to an integratedluminosity of 11.4 fb$^{-1}$ collected in 2012 with the ATLAS detector at theLHC. The differential cross-section, assuming unpolarised $J/\psi$ production,is measured as a function of the transverse momentum of thelower-$p_{\mathrm{T}}$ $J/\psi$ meson, di-$J/\psi$ $p_{\mathrm{T}}$ and mass,the difference in rapidity between the two $J/\psi$ mesons, and the azimuthalangle between the two $J/\psi$ mesons. The fraction of prompt pair events dueto double parton scattering is determined by studying kinematic correlationsbetween the two $J/\psi$ mesons. The total and double parton scatteringcross-sections are compared with predictions. The effective cross-section ofdouble parton scattering is measured to be $\sigma_{\mathrm{eff}} = 6.3 \pm 1.6\mathrm{(stat)} \pm 1.0 \mathrm{(syst)}$ mb.

Measurement of the prompt $J/\psi$ pair production cross-section in $pp$ collisions at $\sqrt{s} = 8$ TeV with the ATLAS detector