M2L8c.txt

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So what is next now in revealing the atomic structure
is we want to go beyond the Coulomb field created
by a point charge, and that means
we want to address the fact that we don't have a point charge,
but we have a nucleus.
And we are discussing now effects
of the nucleus, which also go by the name hyperfine structures.
So just to summarize, so far we have
treated in pretty much complete detail what
happens for an atom which consists of a point charge
and electrons, but now we want to bring
in that what creates a Coulomb field, the nucleus, has structure.

And there are actually four different ways
how the nucleus has structure and contributes
to observable effects on the atomic structure
and atomic energy levels.
The most important one is that the nucleus has
a magnetic moment associated with the angular
momentum of the nucleus I. The second contribution
is, in addition to magnetic moment,
there may be a quadrupole moment,
and since those effects can lead to a splitting,
this is actually usually called hyperfine structure,
but then there are two more effects.
One is the nucleus has finite mass,
and the nucleus has a finite volume.
Both the mass and volume effect lead to energy shifts,
but tiny energy shifts are hard to measure unless you have
two different shifts, and therefore those effects
go as isotope shifts because when you have an atom which
comes into different isotopes, you
find that due to those two effects
the energy levels are not the same.
So this goes by the name of isotope shifts.

By far the most important phenomenon
is the first one, the fact that, if a nucleus has angular
momentum, we have hyperfine structure,
and for the hydrogen atom, that
means that the ground state, the singlet S 1/2 state,
actually splits into two states with total angular momentum
quantum number F. So the relevance
of hyperfine splitting is-- it's actually of huge relevance--
one is you don't have a single ground state of many atoms.
You have several ground states.
So the lowest electronic state has several ground states, so
several hyperfine states.
Due to angular momentum selection rule
you can actually talk to them individually.
You can prepare them individually,
and many of you who do magnetic trapping know
that when you do magnetic trapping
you better prepare the atom in a single hyperfine state,
otherwise you are in trouble.
So you can prepare individual states.
In the old days, this was done by optical pumping,
and you can use several hyperfine states
to great advantage for the manipulation of atoms.
For instance, if you want to, you
can put atoms into a hyperfine state
where they don't absorb light, and then you
can have resonant light for the other ones.
Blast those away so you can play your tricks
because you have two states between which
you can juggle the atoms.
What else is the relevance of hyperfine structure?

If you have two levels-- F equals 1,
F equals 0-- you can observe a transition,
and the famous 21 centimeter line
is used for astronomical observations.

Hydrogen is the most abundant element in the universe,
and how do you see hydrogen out there?
Well, it is due to hyperfine transition, the 21 centimeter
line.
And finally, another aspect why hyperfine structure is relevant
where people use it is for the determination
of nuclear properties.
How do you know what the properties of nuclei are?
Well, there are techniques in nuclear physics,
but a lot about the knowledge of nuclei
comes from atomic spectroscopy.
If you measure atomic energy levels with high accuracy,
you figure out what the properties of the nucleus is.
And one of the most outstanding examples
we will discuss later on, and some
of which is also on your homework assignment,
is you can use atomic spectroscopy of hydrogen
to obtain the most accurate measurement-- how
big is the proton?
And the big surprise is that there was a surprise
that people figured out that, until now, even in 2014,
we do not fully understand how big the proton is,
but we'll talk about that later.
So for at the level of this introduction,
we can use it for determination of nuclear
properties, and actually you cannot only determine nuclear
properties of stable nuclei.
You can also determine properties of unstable nuclei.
At various accelerators, they have a
facility when by high energy collisions
they create unstable nuclei.
Maybe helium six.
Helium with four neutrons.
It exists, and you can take helium six, extract it,
neutralize it, and then have a neutral helium atom,
which looks like your everyday helium atom,
but it has two more neutrons in the nucleus,
and by performing atomic spectroscopy,
you can figure out what is the deformation, what
is the structure of this-- I want to say alpha particle,
but it's an alpha particle plus two neutrons.
So people have really learned to do those atomic physics
measurement within a few seconds after the element has been
produced, and thus determined nuclear properties even
of unstable nuclei.