  Using the semi-classical method of Nikishov-Ritus (NR), the derivation of the
transition rate of the beamstrahlung process is reviewed. This method uses the
Bound Interaction Picture and the exact solutions of the Dirac equation in the
external field potential. For future linear colliders, the nominal machine
parameters are such that this external field can be considered to be a constant
crossed electromagnetic field. The Dirac equation solutions can be Fourier
transformed such that they are functions of Dirac gamma matrices, Airy
functions and the usual non-external field solution. The resultant analytic
form for the transition rate is the same as that obtained by the Quasiclassical
Operator (QO) method of Baier-Katkov which sets a limit of ultra-relativistic
electron and vanishingly small radiation angle. The NR calculation however also
exhibits a pole in the radiation angle for back-radiated photons. The removal
of this pole requires a further study of IR divergences within the Bound
Interaction Picture.
