How to calculate the Lamb Shift in Hydrogen?

[zincshow]

This recent article (https://www.quantamagazine.org/physicists-finally-nail-the-protons-size-and-hope-dies-20190911/) on the size of the proton left me with a couple of confusing questions:

1/ Is the amount of the lamb shift completely determined by Feynman diagrams or is "it spends part of its time inside the proton .. As a result, the amount of electrical attraction between the two decreases, reducing the energy that binds the atom together." calculated in some other manner?

2/ "By firing a laser into a cloud of hydrogen gas and exciting electrons to different levels", does most of the hydrogen stay electrically neutral or do you have a lot of H¯, H¯¯, and H⁺ flying around in addition to neutral hydrogen?

 

[vanhees71]

ad 1). The precision of the Lamb shift you need here unfortunately makes it necessary to not only consider QED Feynman diagrams but also to take into account the charge-distribution of the proton. After all you want to measure precisely one of its properties, namely the charge radius of the proton.

ad 2). The Lambshift is about tiny excitations of the hydrogen state, it's not about ionizing the hydrogen atom or looking at negatively charged ions (i.e., proton+2 or more electrons).