The review article by W Nakel and C. T. Whelan you refer to do indeed tackle the relativistic regime but at the expense of a huge amount of numerical work. So, we think that presenting for the first time a work that incorporates fully analytical results and QED formalism is interesting to the scientific community. The work of W Nakel and C. T. Whelan is devoted to study heavy atoms but Our work is aimed to study analytically the hydrogen atom, we believe that such a comparison is impossible. Another difference that makes comparison difficult is that the work of W Nakel and C. T. Whelan uses coplanar asymmetric geometry while in our work we use coplanar symmetric geometry.
The authors did not mention this method for discussions in the manuscript. The RPWBA method in the manuscript should be compared with the previous rDWBA theory. At least the authors should mention the differences of the two methods and how far the RPWBA can be compared to rDWBA? In earlier publications [Physics Reports 315 (1999) 409 and related references], a fully relativistic distorted-wave Born approximation (rDWBA) has been developed to describe the relativistic ionization processes.