Abstract
For pt.I see ibid., vol.14, no.6, p.1469-82 (1981). The Dirac equation of a relativistic free charged particle interacting with one quantised mode of the electromagnetic field is solved exactly. Stationary eigenstates and the corresponding eigenvalues (the spectrum) are obtained in closed analytical form for linear and circular polarisation. The states are parametrised by two quantum numbers, one of which, corresponding to the four-momentum, is continuous and the other, roughly corresponding to the photon content, discrete. Based on these results, the cross section of nonlinear Compton scattering is calculated. It is shown explicitly that the results reduce to the semiclassical one in the limit of high intensity and small depletion, while in the large (complete) depletion limit they contain a depletion factor which ensures convergence of the highly nonlinear processes.
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