Lande' g-Factor: Is a Reduced Mass Correction Needed?

[Khashishi]

Ok. The Lande' g-factor is given as
$g = g_L \frac{J(J+1)-S(S+1)+L(L+1)}{2J(J+1)} + g_s\frac{J(J+1)+S(S+1)-L(L+1)}{2J(J+1)}$

Most sources say that $g_L = 1$ exactly, but Bethe and Salpeter p214 seems to indicate that there should be a correction for reduced mass. $g_L = 1- \frac{m_e}{m_i}$

Is that right? I think so, but I wanted to make sure, since nowhere else do I see it.

I assume g_s doesn't need any correction for reduced mass, since it's just the electron acting alone. Is that right?

 

[Hypersphere]

I haven't seen it outside that book or the article by Lamb they cite, but then again, it does seem like the kind of detail any book except for Bethe & Salpeter would hide under the rug. Except for the case of Hydrogen and possibly Helium, it really is a small effect.

Did you read the following paragraph, by the way? There is a reasonable argument to why that effective g_L factor should appear. Basically, some of the angular momentum of the atom is contributed by the nucleus, so if we separate the two contributions we get this term and one from the nucleus, which is negligible. And yeah, the g_S must be a different matter, as it couples the electron's magnetic moment to a magnetic field. The nucleus could have a magnetic moment of its own though, something Bethe and Salpeter do treat in the next section.

 

[DrDu]

Is that right? I think so, but I wanted to make sure, since nowhere else do I see it.

It sounds highly plausible. Why don't you try to proove it yourself?