Resonant potential scattering in an intense low-frequency laser field
The total T matrix for the potential scattering in a laser field is decomposed into resonant and non-resonant parts using the projection operator formalism. The general case of several resonances is considered. It is shown that the resonant contribution to the total T matrix can be written as the sum over resonant states of the product of three factors: initial and final laser-modified vertex functions and a factor which contains the level shift matrix. A new method is used for deriving the low-frequency expansion for these three factors. The zeroth-order term gives the generalisation of the non-resonant Kroll-Watson (1973) result to the case of several resonances. Finally, the corrections in the laser electric field amplitude, to these nearly on-shell terms, are also obtained.