Optimized XFEL pulses for angle-resolved photoelectron spectroscopy: probing the role of the molecular potential in N2 double ionization

The attosecond core-hole wave packet dynamics can be probed through the angular correlation in two-site double core hole photoelectron angular distributions. The theoretical questions that remain unanswered are whether the core hole dynamics can be observed after taking into account the scattering phase shift with two photoelectron continuum states, and whether the present experimental capability at LCLS-II can observe such ultrafast dynamics. To address those questions, we have developed a range of approximations that uses a combination of time-dependent perturbation theory with variational scattering theory and the scattering phase shift by considering a plane wave and Coulomb wave continuum states with an optimized XFEL pulse. The phase information, which is encoded in the two photoelectron Coulomb continuum states shows the complex nature of the core hole oscillations due to coherent superposition from the multicenter potential. To address the second question, we introduce a dynamical parameter to optimize the FEL pulse. Our simulations predict a wide photon energy range where core hole dynamics can be observed experimentally that is consistent with the current capabilities of LCLS-II.