Non-Hermitian Dynamics of Multiphoton Ionization

The construction of physical transition probabilities in non-Hermitian, effective-Hamiltonian models of multiphoton ionization is analyzed. Eigenstates of the effective Hamiltonians, $\hat{H}$ and ${\hat{H}}^{†}$, are respectively determined to be projected incoming and outgoing states. These models are found to be intrinsically $S$-matrix models, and the adiabatic eigenstates are used to construct appropriate transition amplitudes. The intermediate-time bound-electron population differs quantitatively from customary norm-of-state constructions.