Why Do g Factors Vary Among Different Atoms?

[mimocs]

Hi, last week I read Rabi's paper "The Molcular Beam Resonance Method".

This paper contains the basic idea of the oscillation which we call "Rabi Oscillation" as many of you guys know.

However, at the end of this paper, Rabi calculates nuclear magnetic moments of Li (atomic mass 6), Li (atomic mass 7), F (atomic mass 19) by measuring the g factor of the atoms above.

Here's my Question.
g factor for Li (atomic mass 6) is 0.820,
Li (atomic mass 7) is 2.167
F (atomic mass 19) is 5.243
These values differ greatly. Are there any logical reasons to explain the differences of g factor?
Or is it just an intrinsic property of each atoms (just like the spin of electron is 1/2)?

Have a nice day

 

[ChrisVer]

The g factor will depend on the energy differences of each state...so why not?

 

[mimocs]

The g factor will depend on the energy differences of each state...so why not?

I don't get it...
Isn't the g factor something very similar to gyromagnetic ratio?
And, I would like to know what you mean by 'energy differences of each state'.
Are you talking about the electric potential energy? Or is it something else?

 

[ChrisVer]

It's part of a definition. In general the g-factor is given by the energy difference between the transitions and also the angular momenta: So because of that it also depends on the angular momenta, something that the gyromagnetic ratio doesn't...

Suppose that your atom has a total angular momentum $F=I+J$ where $I$ and $J$ the nuclear and electronic angular momenta respectively. The Hamiltonian is given by:
$H= g~ I \cdot J = \frac{g}{2} [ F^2 - I^2 - J^2 ]$
passing into energies ($\hbar=1$):
$E= \frac{g}{2} [ F(F+1) - I (I+1) - J (J+1) ]$

That's the energy for a given state. Now it depends... after some transition, the energy difference will be:: $\Delta E$
and the $g$ will be that energy difference divided by some factor that comes from the angular momenta of those states...

 

[mimocs]

geeeee...

Never knew something like that
Thanks a lot for your help

It's part of a definition. In general the g-factor is given by the energy difference between the transitions and also the angular momenta: So because of that it also depends on the angular momenta, something that the gyromagnetic ratio doesn't...

Suppose that your atom has a total angular momentum $F=I+J$ where $I$ and $J$ the nuclear and electronic angular momenta respectively. The Hamiltonian is given by:
$H= g~ I \cdot J = \frac{g}{2} [ F^2 - I^2 - J^2 ]$
passing into energies ($\hbar=1$):
$E= \frac{g}{2} [ F(F+1) - I (I+1) - J (J+1) ]$

That's the energy for a given state. Now it depends... after some transition, the energy difference will be:: $\Delta E$
and the $g$ will be that energy difference divided by some factor that comes from the angular momenta of those states...