W. Heitler and Sow-Hsin Chen have introduced the derivation of photo-electric effect's cross section in the books of "The quantum theory of radiation: pp204" and "Interactions of Photons and Neutrons with Matter:pp246" respectively.

But I met some difficulties in the integral of  transition matrix element. I'd like to find another document (if possible) addressing the deravation of photo-electric effect's cross section with more details in the math.

Or, how the equation (8.122) changes to (8.123) in Sow-Hsin's book?