Q re a photon ionizing a hydrogen atom

[Buzz Bloom]

TL;DR

How is the size calculated of the area near a hydrogen atom that a photon must hit to ionize the atom?

This question is a followup to another thread.

https://www.physicsforums.com/threads/qs-re-the-behavior-of-atoms-after-decoupling-completed.994581/​

I would like to explore the issue raised by @kimbyd.

. . . after reionization the temperature of the intergalactic medium is dominated by interactions with photons from stars.​

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I have made an effort to find help on this topic from the Internet, but I have been unsuccessful. My search located three books that the local library system has available, and they superficially seemed to be promising, but when I tracked down the tables of contents it was quite disappointing.

1. Controlling the quantum world : the science of atoms, molecules, and photons / Committee on AMO 2010, Board on Physics and Astronomy, Division on Engineering and Physical Sciences​

2. Introduction to astrophysics / Professor Joshua N. Winn​

3. The new physics for the twenty-first century / edited by Gordon Fraser​

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I am hoping someone might know the answer to the question in the summary, or can cite what they recommend as a useful source.

 

[256bits]

Something like this, not that I know anything about the subject more than you do, but even less.
https://ned.ipac.caltech.edu/level5/Madau6/Madau1_2.html