M2L7k.txt

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Let me draw you sort of an energy level diagram,
put in a few numbers which then leads us
to the discussion of the lamb shift.
We have hydrogenic energy levels with n equals 1 and n equals 2.
We have s states and we have p states.
We just discussed the fine structure,
which shifts down the energy of all those levels in the ground.
I mentioned that the fine structure
is alpha to the 4 mc squared.
And for the ground state, the prefactor is minus 1/8.
And this is the one-- the term designation is 1S 1/2.
Here we get the 2S 1/2 level.
And the shift is minus 5 over 128 in the same unit,
alpha to 4 mc squared.
We have the exact degeneracy between the S 1/2
and the 2  P1/2 state whereas the P 3/2 state is only
shifted by minus 1 over 128.
To put in some numbers in electron volt,
the fine structure in the ground state
is on the order of 10 to the minus 4 electron volt.
The splitting here, which is the fine structure
splitting of the p 1/2 and the p 3/2 state is 4 times 10
to the minus 5 electron volt. So that means at the level of 10
to the minus 4 electron volt we understand atomic structure.

Well, but we want to go further.
And the next thing we want to discuss
is that what is the exact degeneracy between s 1/2
and p 1/2 is actually lifted when we introduce photons, when
we allow the electrons to couple to the electromagnetic.
That's QED, quantum electrodynamics.
And that introduced the Lamb shift, which, in the n
equals 2 state, is 10 to the minus 6
electron volt, which is approximately 1 gigahertz.
And that's what we want to derive next.
Since I have this nice level diagram,
I want to also indicate to you what we do next week.
And this is when we bring in the proton,
not just-- so far we have said there is a point charge.
But the proton is a real particle which has finite size,
but also it has finite angular momentum.
And then we have to bring in fine structure.
And we will learn that the 1S 1/2 ground state splits
into two hyperfine components.
And the hyperfine structure will be at a similar energy
scale as the Lamb shift.
And actually this fine structure splitting
is the famous 14-- it's about 1 gigahertz.
It's the famous 1420 megahertz line,
which everybody who does astrophysics knows about it.
It's also, in other units, the famous hydrogen maser,
which has an emission line at 21 centimeter.
Anyway, this is sort of our road map.
We have taken care of everything down to 10
to the minus 5 electron volts.
And now we want to proceed today
and in the next lecture to 10 to the minus 6.
First, the lamb shift where we are still
holding on, that the nucleus as a point charge
has no structure.
Then we have done everything we can do.
What happens in the coulomb field of point charge?
We have the spin of the electron, we have QED.
We have done everything.
And then what remains is to put in the structure of the proton which will lead us to hyperfine structure.