G-Factors for e, n & P - Get Answers & Explanation

[Reality_Patrol]

g-factors for e,n & P??

Can anyone provide the latest g-factors for e, n & p? I could also use some explanation as to how they are applied and derived. I've already downloaded the appropriate files from the particle data site, and it does provide the most recent values for the moment data, but not their related g-factors!..Thanks in advance.

 

[zefram_c]

Well, you can learn doing Feynman diagrams and go at it

Here's something to get you started: http://scienceworld.wolfram.com/physics/GyromagneticRatio.html
For the neutron and proton, the calculation is likely much more complicated due to the three-body structure and QCD effects. All I can say is: good luck.

 

[Reality_Patrol]

Perfect! That link was just the kind of thing I was looking for - it gave the most current value and explained the derivation/calculation for e- !

Is it too much to ask for something similar for the neutron & proton? At least I would like to find the latest g values for both. Obviously the derivation for the proton would look the same as for the electron. However, I'm clueless as to how the neutron's value is calculated/derived - it has no charge! So, I'd appreciate even a simple explanation of the method for the neutron.

Oh yeah, I have absolutely zero intention of doing any of these calculations myself - 15 years on a single problem is 15 years too many!

 

[selfAdjoint]

Well, you can learn doing Feynman diagrams and go at it

Here's something to get you started: http://scienceworld.wolfram.com/physics/GyromagneticRatio.html
For the neutron and proton, the calculation is likely much more complicated due to the three-body structure and QCD effects. All I can say is: good luck.

This raises the interesting question, is the gyromagnetic ratio of the electron a transcendental number? Certainly Wolfram's expessions (5) and (6), exact expressions for the second and third coefficients in the expansion of the ratio in powers of alpha are transcendental by inspection.

 

[Orion1]

Gyro Gyruss...


Equation (3) in Ref 1. is not correct, the corrected equation is listed:

Classical Quantum Mechanics - Gyromagnetic Ratio

$$\text{Electron Gyromagnetic Ratio}$$
$$\mu_e = \frac{q \hbar}{2m_e}$$

$$g_e = -2 \frac{\mu_e}{\hbar}$$

$$g_e = -2 \frac{q}{2m_e}$$

$$g_e = -2 \frac{q}{2m_e} = -2 \frac{\mu_e}{\hbar}$$

$$\text{Electron g-factor}$$
$$g_f = -2 \left(1 + \frac{\alpha}{2 \pi} + ... \right) = -2(1.001159652) = -2.0023193043737$$
$$g_e = g_f \frac{\mu_e}{\hbar}$$

$$\text{Proton g-factor}$$
$$g_f = 2 (1 + 1.792847338) = 2(2.792847338) = 5.585694675(57)$$
$$g_p = g_f \frac{\mu_p}{\hbar}$$

$$\text{Neutron g-factor}$$
$$g_f = 2 (0 - 1.91304273) = 2(-1.91304273) = -3.82608545(90)$$
$$g_n = g_f \frac{\mu_n}{\hbar}$$

The negative Neutron g-factor indicates that its magnetic moment is opposite its spin angular momentum.

There are no known theories of nuclear magnetism that explains the nuclear g-factors.

Orion1 Theory:
Nuclear g-factor is a measurement of nuclear magnetic susceptibility.

$$\text{Orion1 g-factor Theory:}$$
$$\chi - \text{magnetic susceptibility}$$
$$\text{Proton g-factor}$$
$$g_f = 2(1 + \chi_p) = 2(1 + 1.792847338)$$
$$\chi_p = 1.792847338 \; \text{Paramagnetic}$$

$$\text{Neutron g-factor}$$
$$g_f = 2(1 + \chi_n) = 2(-1.91304273)$$
$$(1 + \chi_n) = (-1.91304273)$$
$$\chi_n = -2.91304273 \; \text{Diamagnetic}$$

According to this Orion1 g-factor theory, unpaired Protons are paramagnetic substances, unpaired Neutrons are diamagnetic substances.


Reference:
http://scienceworld.wolfram.com/physics/GyromagneticRatio.html
http://www.phys.au.dk/~horsdal/InApSRMenu/Gyro.html
http://www.phys.au.dk/~horsdal/Graphics/Gyromag-ratio.gif
http://hep.ucsd.edu/~branson/130/130b/130b_notes_prod/node102.html
http://www.phys.uAlberta.ca/~gingrich/phys512/latex2html2/node46.html
http://www.fnrf.science.cmu.ac.th/tcaep/science/constant/pntoq.htm
http://web.mit.edu/3.091/www/constants.html

 

[Reality_Patrol]

Orion1:

Your answer was simply superb. I am most grateful. Your theory at the end sounds plausible though I am in no position to really critique it (yet). As I'm still educating myself to this area, and as clearly you have a good deal of expertise, I would like to ask you a few more questions to shore up my understanding:

1. So the gyromagnetic ratio is really just the charge to mass ratio. Strictly speaking then, it only "really" exists for the proton and electron but not the neutron. Is this correct?

2. The g-factor relates the particles magnetic moment to the gyromagnetic ratio. It is always defined as 2*(1+anomaly).
a. The (2) factor is a correction to a classical expression, which didn't take into account the particle's orbital angular momentum. Is this correct?
b. The (1+anomaly) factor is purely a quantum mechanical correction. I have no clue where it comes from or even why the "1" is a "0" for the neutron. I suppose this is the trick that allows the neutron to be assigned a gyromagnetic ratio even though it has no (net) charge. Any basic guidance here would be appreciated.
c. Where does the "anomaly" expression come from in standard explanations?

Overall, your theory is probably the simplest answer I've ever seen given, but of course it could also be incorrect. Is there a short version of the "standard" answer to this that you've found? Perhaps also why you were motivated to go and find your own? Finally, I'll say this: it appears to me we're thinking along the same lines, i.e. magnetism is the fundamental property.

 

[zefram_c]

Orion1: I have no idea what you are doing at the end; please explain?

Reality_Patrol: You seem to have a number of misconceptions; let me try to clear those up.

-The gyromagnetic ratio is the ratio of the measured magnetic moment to the angular momentum (here: spin) of the object in question.
-In classical QM, this ratio is uniquely determined from the charge and mass of the particle. However, for electrons and other elementary particles (protons and neutrons do NOT qualify as such), the observed result is slightly over twice the classical result.
-The Dirac theory accounts for the factor of two and attributes it to the relativistic wave equation that electrons satisfy.
-The slight correction (called the anomaly) is accounted by quantum electrodynamics through the interaction of the electron with the background EM field.
-Electric charge is the fundamental property, not magnetism. Neutrons can have a magnetic moment because they are composed of charged constituents (quarks).
-A first-order calculation for proton/neutron magnetic moments based on the quark model can be found in "Introduction to Elementary Particles" by D. Griffiths, p180-182.

 

[Hans de Vries]

A good place to look for some background of the anomaly for leptons
are the papers that came after a discrepency was found for the muon
anolmaly and the predictions from the Standard Model as of 2001.

2 x 1.0011 659 203 (8) experimental
2 x 1.0011 659 159 (6) theoretical

Muon status Overview:

http://nac21.uv.es/pdf/0208251
http://g2pc1.bu.edu/~leptonmom/talks/deRafael.pdf

So there has been more interest in the muon than in the electron lately.

The experiment: (Brookhaven E821)

http://www.npl.uiuc.edu/~hertzog/Erice/Erice_final.ps
http://www.npl.uiuc.edu/~hertzog/panic/panic_final.pdf

The machine: (click on the photo to proceed)

http://www-jcsu.jesus.cam.ac.uk/~jg307/work/muon.xml

Some recent theoretical work (2004)

http://arxiv.org/pdf/hep-ph/0402206

Gives 2 x 1.0011 658 471 9 (2) theoretical which differs more
instead of less. (edit: oops, This is the number with QED
contributions only, so without hadronic or electroweak vacuum
polarization contributions )


Some remarks:

The same value for the fine structure constant is used for both
the electron and the muon.

I did not see any mass dependent terms in the formula for the
electron (here)

http://scienceworld.wolfram.com/physics/GyromagneticRatio.html

but they play an important role in the calculation of the muon.
(otherwise the analomy for the electron and muon would be equal)

Mass dependent terms are mass ratio's and logarithms of mass ratios.
These are ad hoc values and not predicted.

I wonder if there is a theoretical estimate of the tau anomaly?
There's no experimental value because of the very short life time
of the tau lepton.

Regards, Hans

 

[Reality_Patrol]

Reality_Patrol: You seem to have a number of misconceptions; let me try to clear those up.

Yes I do, thank you.

-The gyromagnetic ratio is the ratio of the measured magnetic moment to the angular momentum (here: spin) of the object in question.

Got it - so any particle with a magnetic moment (charged or not) can have one.

-In classical QM, this ratio is uniquely determined from the charge and mass of the particle. However, for electrons and other elementary particles (protons and neutrons do NOT qualify as such), the observed result is slightly over twice the classical result.
-The Dirac theory accounts for the factor of two and attributes it to the relativistic wave equation that electrons satisfy.

OK, thanks, but is the factor of (2) just an artifact of the mathematical formalism, or does/can it be given some intuitive physical interpretation?

-The slight correction (called the anomaly) is accounted by quantum electrodynamics through the interaction of the electron with the background EM field.

Ahh, here's where I'm really weak. I probably just need to study up on QED - though that's NOT very appealing.

-Electric charge is the fundamental property, not magnetism. Neutrons can have a magnetic moment because they are composed of charged constituents (quarks).

Yes, of course that's the standard explanation. My personal research involves looking into the possibility that magnetism is fundamental. By this I don't mean magnetic monopoles, I accept the evidence against their existence. I mean the obvious: the fundamental magnetic charge sources a magnetic field in a dipole configuration. I've never seen anything on this possibility. A corollary I also plan to investigate is: a magnetic charge in motion (spinning) appears to be an electrical charge to a stationary (non-spinning) observer! All of this is pure conjecture on my part, and most likely wrong - but fun to look into!

-A first-order calculation for proton/neutron magnetic moments based on the quark model can be found in "Introduction to Elementary Particles" by D. Griffiths, p180-182.

Thanks for the reference, I'll look into getting it. I'd prefer an on-line version that's free of course!

 

[zefram_c]

OK, thanks, but is the factor of (2) just an artifact of the mathematical formalism, or does/can it be given some intuitive physical interpretation?

I cannot think of an intuitive physical explanation, but that doesn't mean there isn't one. It's certainly there, when we measure it, so we want a theory that can produce it. What I am sure of is that this effect is not limited to the hydrogen atom.

Ahh, here's where I'm really weak. I probably just need to study up on QED - though that's NOT very appealing.

I don't know your situation, but unless you need it for grad school or research, your time can be better spent than learning the math. intricacies of QED.

I have not been able to find an online reference for the proton/neutron; perhaps someone else can.

Yes, of course that's the standard explanation. My personal research involves looking into the possibility that magnetism is fundamental. By this I don't mean magnetic monopoles, I accept the evidence against their existence. I mean the obvious: the fundamental magnetic charge sources a magnetic field in a dipole configuration. I've never seen anything on this possibility. A corollary I also plan to investigate is: a magnetic charge in motion (spinning) appears to be an electrical charge to a stationary (non-spinning) observer!

Actually, it might surprise you to learn that it is not the standard explanation! In the electroweak model, electric charge is a linear combination of two other, more 'elementary' properties: weak isospin and weak hypercharge. To me it makes much more sense to say that electric charge is something intrinsic to the particles, rather than magnetic dipoles. If that were so, what are those magnetic dipoles? In classical EM theory, they are produced either by currents (ie moving electric charges), or alignment of atomic magnetic dipoles (which are produced by the spins of charged particles). If we assume those dipoles to be fundamental magnetic charges, you'd have a lot of explaining to do - how do you get a conservative electric field out of them, for one? How do they fit in with the point particle model? How do you fit that into the electroweak model? I'm not trying to discourage you from your research, just pointing out the task might be deeper than you think.

 

[Reality_Patrol]

A good place to look for some background of the anomaly for leptons...Regards, Hans

Much thanks for the many fine references. I've been studying them and will continue to do so for some time...then I'll have some questions if you'll indulge me!