Characterization of high-energy photoionization in terms of the singularities of the atomic potential. I. Photoionization of the ground state of a two-electron atom

Abstract

We describe single and double photoionization of two-electron atoms by photoabsorption at high incident photon energies $\ensuremath{\omega}$ (but still $\ensuremath{\omega}\ensuremath{\ll}{\mathrm{mc}}^{2})$ using a unified approach based on asymptotic Fourier transform (AFT) theory modified by Coulombic interactions. Within this approach the matrix elements for photoabsorption processes at high energies can be understood in terms of the singularities of the many-body Coulomb potential. These singularities $(e\ensuremath{-}e$ and $e\ensuremath{-}N)$ result in the singularities of the wave functions and the singularities of the $e\ensuremath{-}\ensuremath{\gamma}$ interaction, which determine the asymptotic behavior of the matrix element. Within our unified approach we explain the dominant contributions, including both the dominant contributions to the total cross section for single ionization and for ionization with excitation, and the dominant contributions to the double ionization spectrum, as a Fourier transform asymptotic in a single large momentum (dependent on the process and the region of the spectrum). These dominant contributions are connected, through AFT, with either the $e\ensuremath{-}N$ singularity or the $e\ensuremath{-}e$ singularity. The AFT results are modified by Coulombic interactions. We include these modifications, for the cases of single ionization and of double ionization in the shake-off region at high energies, and extract a slowly convergent factor (Stobbe factor). In this way we obtain rapid convergence of the cross sections to their high-energy behaviors. This also allows us to discuss the convergence of ratios of cross sections.