  We study mutual dissociation of heavy nuclei in peripheral collisions at
ultrarelativistic energies. Earlier this process was proposed for beam
luminosity monitoring via simultaneous registration of forward and backward
neutrons in zero degree calorimeters at Relativistic Heavy Ion Collider.
Electromagnetic dissociation of heavy ions is considered in the framework of
the Weizsacker-Williams method and simulated by the RELDIS code. Photoneutron
cross sections measured in different experiments and calculated by the GNASH
code are used as input for the calculations of dissociation cross sections. The
difference in results obtained with different inputs provides a realistic
estimation for the systematic uncertainty of the luminosity monitoring method.
Contribution to simultaneous neutron emission due to grazing nuclear
interactions is calculated within the abrasion model. Good description of CERN
SPS experimental data on Au and Pb dissociation gives confidence in predictive
power of the model for AuAu and PbPb collisions at RHIC and LHC.
