Photoionization involves the removal of an electron and requires a careful treatment of both bound and continuum states. Here we describe a new approach that follows the time-dependent wavefunction across Fock space, allowing the system to evolve naturally between n- and (n−1)-electron Hilbert spaces. This picture captures the essential superposition of bound and ionized components as ionization unfolds.

Standard methods such as complex absorbing potentials (CAP) treat the continuum by introducing an artificial imaginary potential that reduces the norm of the wavefunction from unity. While this effectively mimics electron escape, it does not explicitly track the charge-state transition of the system.

To address this, we introduce a Modified Absorption Potential (MAP) framework, which builds continuum coupling directly into a non-Hermitian Hamiltonian. In MAP, creation and annihilation operators connect Fock subspaces, ensuring that the transition from a neutral n-electron system to its (n−1)-electron cation is explicitly represented. This approach provides a transparent description of ionization dynamics and accommodates non-orthogonal orbital bases.

Applications to simple systems such as H anion and N2 highlight how orbital character and coupling strengths dictate ionization pathways. For instance, diffuse 2p orbitals couple more strongly than compact 1s orbitals, leading to distinct timescales and final-state populations. Time propagation shows that the velocity of electron ejection strongly influences state mixing: slower ionization favors admixture of states, directly impacting the remnant wavefunction. These evolving populations can be tied to observables by reconstructing photoionization spectra from the final superposition.

Overall, MAP provides a rigorous but accessible alternative to absorbing boundary techniques, offering state-resolved insights into continuum–valence interactions. By directly linking quantum dynamics to spectral outcomes, this approach advances predictive modeling of ionization processes with relevance for spectroscopy, strong-field dynamics, and quantum information science.

Lee M Thompson

University of Louisville

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