  A new system used for monitoring energetic Coulomb-scattered electrons as the
main diagnostic for accurately aligning the electron and ion beams in the new
Relativistic Heavy Ion Collider (RHIC) electron lenses is described in detail.
The theory of electron scattering from relativistic ions is developed and
applied to the design and implementation of the system used to achieve and
maintain the alignment. Commissioning with gold and 3He beams is then described
as well as the successful utilization of the new system during the 2015 RHIC
polarized proton run. Systematic errors of the new method are then estimated.
Finally, some possible future applications of Coulomb-scattered electrons for
beam diagnostics are briefly discussed.
