We consider electron-atom scattering in a circularly polarized laser field
at sufficiently high electron energies, permitting us to describe the scatt
ering process by a first-order Born approximation. Assuming the radiation f
ield has sufficiently moderate intensities, the laser dressing of the hydro
gen target atom in its ground state will be treated in second-order perturb
ation theory. Within this approximation scheme, it is shown that the nonlin
ear differential cross sections of free-free transitions do not depend on t
he dynamical phase phi of the radiative process nor on the helicity of the
circularly polarized laser light. Relations to the corresponding results fo
r linear laser polarization are established.