Transverse-electron-momentum distribution in pump-probe sequential double ionization

We study the transverse-electron-momentum distribution (TEMD) of the wave packets launched in a pumpprobe sequential double ionization from the valence shell of a noble gas atom. Our calculations, based on an accurate numerical solution of the time-dependent Schrödinger equation (TDSE), reproduce a characteristic cusp of the TEMD which is attributed to the Coulomb singularity. The evolution of the TEMD with the time delay between the pump and probe pulses is shown to be similar to the prediction of the standard tunneling formula (TF), as was observed experimentally for argon by Fechner et al. [Phys. Rev. Lett. 112, 213001 (2014)]. However, TDSE calculations show a clear deviation from the TF and predict a much more complicated structure which cannot be reproduced by the target orbital momentum profile filtered by the tunneling Gaussian. The accuracy of the TF can be improved if the target momentum profile is calculated with the Coulomb waves instead of the plane waves.