Time-dependent close-coupling calculations of correlated photoionization processes in helium

Abstract

Various correlated photoionization processes in helium are calculated by direct solution of the time- dependent Schrodinger equation. An inhomogeneous set of time-dependent close-coupled partial differential equations are partitioned on a numerical lattice for easy implementation on massively parallel computers. Projection of the time evolved wave function onto lattice eigenstates for He 1 yields cross sections for photo- ionization with excitation and double photoionization. The computational results are compared with recent experimental measurements. @S1050-2947~98!07701-4# PACS number~s!: 32.80.Fb I. INTRODUCTION An accurate description of the correlation between two electrons moving in the long-range Coulomb field of a third body, as found in the double photoionization of helium, re- mains a challenging theoretical problem. However, the diffi- culties are somewhat mitigated if examined in the time do- main. As pointed out by Bottcher @1#, the time evolution of a wave function localized in space, as found in the ground state of helium, obviates the need for answers to questions about the asymptotic form of the wave function in coordinate space or its singularities in momentum space. In this paper a time-dependent close-coupling method @2,3# developed to study the electron-impact ionization of atomic ions @4# has been extended to include radiative dipole coupling. This larger set of coupled partial differential equations may then be time propagated on a lattice to yield accurate cross sec- tions for a variety of correlated photoionization processes in two-electron atomic systems. We begin with test calculations for the photoionization of ground-state helium above the complete fragmentation threshold. Recent synchrotron light experiments have nar- rowed the measurement uncertainties both for photoioniza- tion with excitation @5# and double photoionization @6-8# of ground-state helium so as to provide benchmarks for the de- velopment of new theoretical methods. Additional compari- sons may be made with the vast number of time-independent computational theories developed to understand correlated processes in the photoionization of helium. The most popular methods for photoionization with excitation are based on many-body perturbation theory @9,10# and standard R-matrix theory @11,12#. Recent calculations for double photoioniza-