M2L8b.txt

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We have discussed the Lamb shift,
but we have only discussed one contribution to the Lamb shift.
So this was the contribution that the Coulomb potential
is effectively smeared out.
And the result of this is that there
is a weaker binding energy.
However, there is a second contribution to the Lamb shift.

I've sometimes seen sources where
this is discussed as the main contribution to the Lamb shift.
But this is not correct.
This is only 3% of the total and contributes
only 27 megahertz.
This is what is called the vacuum polarization.
So if you have a proton positive charge,
and you have the electron.
And they scatter off each other.
And we use this kind of diagram to indicate that.
Now there is an additional diagram
which has this bubble, which is this production of e
minus, e plus pairs.
And you can see that if an electron and proton attract
each other, and you create, by virtual pair production,
because the vacuum is alive, things
can happen in the vacuum.
you do a virtual admixture of an electron positron pair,
that now you create a electron positron pairs, which
shield the Coulomb field.
And this is a second contribution
in addition to this shaking motion of the electron.
So I want you to just think about it for 10 seconds
before I tell you the answer.
Does this vacuum polarization strengthen or weaken
the binding energy?

Anybody wants to offer an opinion?

Whatever you say, you can't be wrong
because their are two aspects to the answer.

Well, the natural answer is to say,
if you create charges between the electron and the proton,
you have a shielding effect, and the shielding effect
should weaken the Coulomb field.
But the question is, what do we regard
as the elementary charge e in our Schrodinger equation.
And what we regard as the charge, what
is measured in a Millikan droplet
experiment is already the shielded charge.
So therefore, the fact that vacuum polarization exists
means we always measure the shielded charge.
But because vacuum polarization happens at a finite distance,
the electron in an s state can sort of penetrate the shield
and feel a somewhat stronger Coulomb potential.
So therefore, accounting for the fact
that we have these virtual electron positron
pairs, actually means that the binding energy is increased.
And the vacuum polarization has the opposite sign
as the dominant effect we've mentioned earlier.
So the summary is we observe the shielded charge,
and vacuum polarization implies that the s electron can
penetrate the shield and sees a higher charge.
So we normally observe the shielded charge,
but the electron can see the higher charge.
So therefore, that means now that we
have not an up-shift in energy but a downshift in energy,
which for the 2s one half state is 27 megahertz,
as I mentioned earlier.
Anyway I'm not really deriving it.
But I want to sort of uncover certain myth, so the vacuum
polarization, number one, is not dominant, and number two,
has the opposite sign as everybody would naively assume.

Questions?