Simulation of a He resonance population and decay

We illustrate the use of multichannel single-ionization scattering states for the interpretation of time-resolved experiments in the case of the attosecond-XUV-pump IR-probe attosecond interferometric spectroscopy of the doubly 

This example incorporates several of those features that greatly benefit from a scattering-based analysis, namely the population of several doubly excited states with short as well as long lifetimes and a fully differential multichannel signal for extremely slow electrons. 

With few passages, it can be shown that this expression reduces to 

For the simulation, the time-dependent Schrodinger equation is integrated numerically with an exponential propagator 

As detailed in Section 5.1.2, the photoelectron distribution in a channel, identified by a parent ion a = Is, 2s, 2p is obtained by projecting the propagating wavefunction l (t) onto the helium scattering states, which satisfy incoming boundary conditions 

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