# G-factor in BMT equation

1. Nov 25, 2012

### pomaranca

in Bargmann–Michel–Telegdi equation
$${\;\,dS^\alpha\over d\tau}={e\over m}\bigg[{g\over2}F^{\alpha\beta}S_\beta+\left({g\over2}-1\right)U^\alpha\left(S_\lambda F^{\lambda\mu}U_\mu\right)\bigg]\;,$$
there is $g$-factor present. I'm a bit confused about its definition. If it is defined as
$$\boldsymbol{\mu}_S = \frac{g_{e,p}\mu_\mathrm{B}}{\hbar}\boldsymbol{S}\;,$$
where for electron it is $g_e=−2.0023193043622$ and for proton $g_p= 5.585694713$, then in BMT equation one should probably use its negative $g=-g_{e,p}$ and not the absolute value.
Is this correct?

2. Nov 25, 2012

### andrien

μ is always in opposite direction to spin for electron and in same direction for proton.one always use the magnitude of g while dealing with it.

3. Nov 26, 2012

### pomaranca

So in BMT g is the absolute value of g-factor?

4. Nov 26, 2012

### andrien

yes,it is always the absolute value.I hope it is same as the lande factor.However what is μB in your eqn.

5. Nov 26, 2012

### pomaranca

In my case $\mu_B$ is nuclear magneton $\mu_N={e\hbar\over2m_P}$ as I'm dealing with a proton. Thanks for your answer.