Reply to “Comment on ‘Test of the Stark-effect theory using photoionization microscopy’ ”

Abstract

The frame-transformation (FT) theory which describes the dynamics of nonhydrogenic atoms in an external uniform electric field was tested for the process of photoionization in a Stark field by Zhao et al. [Phys. Rev. A 86, 053413 (2012)]. Differential cross sections from the FT theory were found to be inconsistent with those from the fully quantum-mechanical coupled-channel theory. The discrepancy was attributed to the frame transformation of irregular wave functions. In a recent investigation, Giannakeas et al. [Phys. Rev. A xx, xxxxxx (2015)] draw a different conclusion. They show that the FT theory generates irregular wave functions in good agreement with exact solutions for low angular momenta, although an obvious disagreement is seen for high angular momenta. We performed test calculations for numerous Stark states, and found that our original conclusion remains valid, namely the Fano-Harmin frame-transformation for the irregular wave function is inaccurate.