Formal theory of multiphoton double ionization: Sequential and direct

The rate parameters for double multiphoton ionization are obtained as functions of T matrices, which are derived from the S matrix by a generalization of the Fermi Golden Rule. The different T's appear, and are distinguished from each other as coefficients of different energy singularities, principal parts as well as delta functions, in S. These are connected to the rate parameters, which appear in three coupled-rate equations. New terms are shown to contribute to the direct ionization process and new interference terms are also found to contribute to the direct ionization rate. A new interpretation of the shake-off term is given, and it is found to be a sequential process.