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Triple-gyro model for deduction of proton radius and magnetic moment
Johan K. Fremerey
translated from German, June 22, 2017 (original draft ~1990)
More than 30 years ago W. Finkelnburg [1] already stated (probably others did as
well sooner and later) the proton radius rp ≈ 1.3 x 10-15 m as experimentally
determined in different ways to stay in agreement with what is known as the
Compton wavelength λp = 2πℏ/mpc of the proton at rest. Inspired by this idea we get,
on the basis of spin approach Iω = ℏ/2 (polar angular momenta of classical cylinder
and spin-1/2 particle) by introducing I = mr2/2 (moment of inertia of cylindrical
body) and ω = mc2/ ℏ (relativistic energy approach), in a first step, to r = ℏ/mc, a
similar term which, however, turns out small by a factor 2π for the proton radius.
The discrepancy may be readily resolved by assuming the proton to be made up of
three spin ½ components, instead of one, with one third of the proton mass, each,
and three times the radius obtained in the first step. By putting together three such
gyros we get an assembly with radius of the order 6ℏ/mpc in good agreement with
well known proton radius. When further assuming the resulting proton spin to be
attributed to only one of the above gyros we will get an effective magnetic moment
µp ≈ 3e0ℏ/2mp * for the proton in agreement, as well, with experimental data. Here, in
fact, we attribute the respective gyro an elementary electric charge e0. By the features
described the triple-gyro model of the proton appears reasonable in view of quark
theory and supporting scattering experiments.
[1] W. Finkelnburg, Einführung in die Atomphysik, 5. - 6. edition, p. 247, Springer-
Verlag 1958
* In view of the above model nuclear magneton µN = e0ℏ/2mp is augmented by a
factor 3 as associated mass of single gyro is mp/3.