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The measurement is performed using the neutron Zero Degree Calorimeters of the ALICE experiment, which detect neutral particles close to beam rapidity. The measured cross sections of single and mutual electromagnetic dissociation of Pb nuclei at $\\sqrt{s_{\\rm NN}}$ = 2.76 TeV with neutron emission are $\\sigma_{\\rm single\\ EMD} = 187.4\\pm0.2$ (stat.) $^{+13.2} _{-11.2}$ (syst.) b and $\\sigma_{\\rm mutual\\ EMD} = 5.7\\pm0.1$ (stat.) $\\pm$0.4 (syst.) b, respectively. 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