How, and in what atoms does the Lamb shift occur?

[Ali Lavasani]

The Uehling potential due to vacuum polarization by virtual electron-positron pairs is said to be the dominant contribution — 205.0073 meV — to the Lamb shift between the 2P1/22P1/2 and 2S1/22S1/2 states of muonic hydrogen. In the Wikipedia page (https://en.wikipedia.org/wiki/Lamb_shift), it is mentioned that the lamb shift is the difference in energy between two energy levels 2S1/2 and 2P1/2 of the hydrogen atom. Is what it says true, and the lamb shift also occurs in the regular (not muonic) hydrogen atom?

The Wikipedia page says that "the fluctuation in the electric and magnetic fields associated with the QED vacuum perturbs the electric potential due to the atomic nucleus. This perturbation causes a fluctuation in the position of the electron, which explains the energy shift". How is the change in the position of electrons related to an energy level shift? Is this concept the same as the Uehling potential? I ask this because as far as I know, the Uehling potential is effective only within a Compton wavelength of the particle producing the electric field. So how is it producing such a great force at a distance way larger than the Compton wavelength of the nucleus, that can dramatically deviate the electrons and cause an energy level shift?

 

[mfb]

It should occur in every hydrogen-like system, but it was first predicted for and measured with regular hydrogen.

How is the change in the position of electrons related to an energy level shift?

All this is a heuristic explanation only, but a smeared out distribution in an nonlinear potential has a different expectation value for the potential than a point-like distribution at its center.

Is this concept the same as the Uehling potential?

It looks like it but I'm not sure.

The Lamb shift is tiny for regular hydrogen.

 

[Ali Lavasani]

It should occur in every hydrogen-like system, but it was first predicted for and measured with regular hydrogen.All this is a heuristic explanation only, but a smeared out distribution in an nonlinear potential has a different expectation value for the potential than a point-like distribution at its center.It looks like it but I'm not sure.

The Lamb shift is tiny for regular hydrogen.

Thanks. Does the lamb shift occur in other atoms, like Helium, Calcium, Iron, Oxygen, etc too? I mean, the QED effects modifying the position of electrons are present everywhere, so why shouldn't they produce lamb shift in other atoms?

And, I'm also curious, how much do vacuum fluctuations smear the electrons? Suppose that the electron is a point within the atom, and gets smeared due to some vacuum fluctuations. I think the distribution should get more and more smeared after a while, and finally the initial point could be find anywhere within the atom, is this true?

 

[atyy]

As @mfb says, these are all hydrogen-like versions of helium, lithium, beryllium, boron, oyxgen etc

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.28.1609https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.28.1609https://journals.aps.org/pr/abstract/10.1103/PhysRev.123.1700https://arxiv.org/abs/1609.08019

 

[Ali Lavasani]

Thanks! How about non-Hydrogen like atoms or molecules (For example H2O, or Ca2+)? Does the electron smearing and lamb shift occur in the too? Why are all the lamb shift measurements on Hydrogen-like atoms?

 

[mfb]

There will still be a fine-structure, but things get much more complicated. Different states won't be degenerate even with nonrelativistic quantum mechanics.

 

[Ali Lavasani]

So you mean the only reason that hydrogen-like atoms are being tested for the lamb shift is that the calculations are simpler?

 

[atyy]

So you mean the only reason that hydrogen-like atoms are being tested for the lamb shift is that the calculations are simpler?

The Lamb shift is the deviation from the Dirac theory prediction for hydrogen-like atoms that two particular states have the same energy. While the physics underlying the deviation should be present in general for all atoms, it may not be the case that the Dirac theory predicts that the same two states also have the same energy when more complicated electronic configurations are present.

 

[Ali Lavasani]

The Lamb shift is the deviation from the Dirac theory prediction for hydrogen-like atoms that two particular states have the same energy. While the physics underlying the deviation should be present in general for all atoms, it may not be the case that the Dirac theory predicts that the same two states also have the same energy when more complicated electronic configurations are present.

The physics underlying the lamb shift are vacuum polarization and electron self-energy. What factor are these phenomena dependent on?

If they depend on the electric field, in may atoms the E field the electrons sense is equal or even more that the E field of an H atom's nucleus, because that atoms have stronger nuclei and not much bigger atomic radius.