Since, the g-factor is measured to be slightly greater that two, the helical path is more likely, as then, the electron is partly (half the time period) outside of the orbit of the positive particle. A greater orbital radius gives greater angular momentum and magnetic moment given the same orbital speed, \(c\). An orbital path strictly within the orbit of the positive particle will give an g-factor of less than two.
The radius of the helix, \(r_h\) gives one more variable to effect the total energy of the electron other than just the principal quantum number, \(n\). A lower helix radius bring the orbiting negative particle closer to the orbit of the positive particle and reduces the g-factor to closer to two. Such changes in \(r_h\) can explain the Lamb Shift. For \(2p\) orbits, more orbits pack around the nucleus than a \(2s\) configuration. The more tightly packed \(2p\) orbits have lower helix radii and so a g-factor closer to two than \(2s\) orbits. At the same orbital speed, a lower orbital radius has less angular momentum. Assuming that both \(2s\) and \(2p\) configurations are at about the same orbital distance (positive particle) from the nucleus.
Note: Any circle centered at the orbit's center, inside the orbit, has smaller radius than the orbit. A helical path will spent more time outside of the orbital path than inside, because the swing of the helical orbit in the plane of the helix is more outside the positive particle orbit.
A particle in a circular helical orbit (a torus) transcribes an orbit of effective radius larger than the value given by the radius of the orbit through the center of the helix.
This effective radius is the result of considering the time the particle spent inside and outside the actual orbit through the center of the helix.
Given \(r_{or}\), the planar radius of the orbit and \(r_h\), the rotating radius of the helix, this effective radius, \(r_e\) should be fixed.
\(r_{e}=r_{or}.\cfrac{2\pi(r_{or}+r_{h})}{2\pi r_{or}}\)
\(r_{e}=r_{or}(1+\cfrac{r_{h}}{r_{or}})\)
From which we might obtain the change in \(r_h\) producing a Lamb Shift by measuring the change in magnetic moment, g-factors and the orbital radius.
And my data quota is...too little. Have a nice day.
