A master equation approach to double ionization of helium

It is demonstrated how a numerical approach based on absorbing boundaries may be used to describe the process of non-sequential two-photon double ionization of helium. Contrary to any method based on solving the Schrödinger equation alone, this numerical scheme is able to reconstruct the remaining particles as one particle is absorbed. This may be used to distinguish between single and double ionization. A model of reduced dimensionality, which describes the process at a qualitative level, has been used. The results have been compared with a more conventional method in which the time-dependent Schrödinger equation is solved and the final wavefunction is analysed in terms of projection onto eigenstates of the uncorrelated Hamiltonian, i.e. with no electron–electron interaction included in the final states. It is found that the two methods indeed produce the same total cross sections for the process.