# How to calculate the Lamb Shift in Hydrogen?

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• zincshow
In summary, the article discusses the recent determination of the size of the proton and raises questions about the role of Feynman diagrams and the calculation of electrical attraction in the Lamb shift. It also clarifies that the Lamb shift is not related to ionization or the presence of negatively charged ions in the hydrogen gas.
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?

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).

MisterX

## 1. How is the Lamb Shift calculated in Hydrogen?

The Lamb Shift in Hydrogen is calculated by taking the difference between the measured energy levels of the 2S and 2P states in the Hydrogen atom. This shift is caused by the interaction between the electron and the vacuum fluctuations of the electromagnetic field.

## 2. What is the formula for calculating the Lamb Shift in Hydrogen?

The formula for calculating the Lamb Shift in Hydrogen is ΔE = (α/π) * (μ/2) * (ln(μ) - 1/2), where α is the fine structure constant and μ is the reduced mass of the electron-proton system.

## 3. How does the Lamb Shift in Hydrogen affect the energy levels?

The Lamb Shift in Hydrogen causes a splitting of the energy levels, resulting in a small difference between the measured and predicted energy levels. This shift is important for accurately predicting the energy levels and understanding the behavior of the Hydrogen atom.

## 4. What factors contribute to the Lamb Shift in Hydrogen?

The Lamb Shift in Hydrogen is primarily caused by the interaction between the electron and the vacuum fluctuations of the electromagnetic field. Other factors that can contribute to the shift include higher order quantum electrodynamic effects and the finite size of the proton.

## 5. How is the Lamb Shift experimentally measured in Hydrogen?

The Lamb Shift in Hydrogen can be experimentally measured by using spectroscopy techniques to measure the energy levels of the 2S and 2P states in the Hydrogen atom. The difference between these energy levels is then calculated to determine the Lamb Shift.

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