Challenge of lepton pair production in peripheral collisions of relativistic ions

The new approach to the lepton pair production in the Coulomb field of two highly relativistic nuclei was developed.Solving the operator equation for lepton scattering in arbitrary Coulomb field, we obtain the amplitudes for lepton scattering in the Coulomb potential in terms of light cone variables. Using the Watson expansion for the amplitude of lepton scattering on two centers we propose prescription which allows one to construct the amplitude for lepton pair production in the Coulomb field of two highly relativistic ions. We show that for the certain sums of finite terms of the Watson series numerous cancellations lead to infrared stability of amplitude.