Diagrammatic many-body theory for atoms in high-intensity laser fields Part I

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Abstract
Diagrammatic many-body theory has been used extensively in the treatment of electron–electron correlations in atomic photoionization at low intensities. We discuss how it can be used at high intensities also. The standard diagrammatic formalism is derived for time-independent interactions by using adiabatic switching. This formalism can be formally derived for harmonic fields also but leads to unphysical results for strong fields. If the amplitude function of the laser field is an exponential function, however, the standard derivation still applies. If the adiabatic limit is not taken, this time-dependent formalism can be used for any intensity. In practice one is still limited to slow turn-on, but, assuming slow turn-on, we show that for a discrete system the linked expansion, when summed to infinite order, gives the Floquet state that is adiabatically connected to the ground state. When continua are included, we find that qualitatively correct results are obtained only if one uses an expansion of the time derivative of the wave function instead of an expansion of the wave function itself. We also show that the imaginary part of the self-energies must be excluded from the energy denominators, since they otherwise lead to unphysical results. These results are found by treating model systems for which the exact solutions are known and for which the diagrams can be evaluated to any order.