The first-order cross section for Compton scattering is expressed in t
erms of the cross section for scattering by fast charged particles in
the plane-wave Born approximation as a function of the momentum, Q, tr
ansferred by the projectile to the atomic electron(s). As an example o
f this relationship, the high-energy photon limit for the ratio of dou
ble to single ionization by Compton scattering, R(C)(Q), is expressed
in terms of the ratio, R(Z)(Q), for scattering by charged particles at
large Q. Results for R(C)(Q) are presented.