Approximate Perturbation Theory for High-Order Electromagnetic Transitions

An approximation method is developed which yields very simple and general analytical results for electromagnetic bound-bound or bound-free transitions for any arbitrarily high order of interaction with the electromagnetic field. The approximation is perturbative in the sense that transition probabilities are proportional to the field intensity raised to the power $N$, where $N$ is the order of the interaction. Limiting values of electromagnetic field strength are given within which the approximation is valid. These limits depend upon the binding potential which produces the bound states. A feature of the results is that they show the onset of high-order dominance effects which can occur at high-field intensities.