The number 860 and the fine structure constant

The Urantia Papers p. 474: "The quantity of energy taken in or given out when electronic or other positions are shifted is always a "quantum" or some multiple thereof, but the vibratory or wavelike behavior of such units of energy is wholly determined by the dimensions of the material structures concerned. Such wavelike energy ripples are 860 times the diameters of the ultimatons, electrons, atoms, or other units thus performing. The never-ending confusion attending the observation of the wave mechanics of quantum behavior is due to the superimposition of energy waves: Two crests can combine to make a double-height crest, while a crest and a trough may combine, thus producing mutual cancellation."

Probably Sommerfeld introduced the very interesting constant "alpha" as the ratio of the speed of the electron in its ground state in the Bohr-atom relative to the speed of light. Modern particle physicists prefer to speak about the coupling constant of the electromagnetic field because it enters directly into the formulas for the force between charged particles. Pauli, the father of the neutrino concept together with Fermi, was highly enthralled by this number alpha (= 1 / 137) which was considered to be a pure invariable constant. Today it is known that the value of alpha is not absolutely constant but it has a value that changes a little with temperature. The value of alpha today, in a low temperature, is about 1 / 137.0359. It has also been suggested that the value of alpha, and hence the wavelength (color) of spectral lines, might change with the age of the universe.

The 860 "law" is true for quanta produced by the annihilation process of electrons and positrons. The same type of radiation observed from space, around octave 64, might also come from regions, where new electrons are forming? For other spectral lines the 860 law holds, when calculated as a difference. If we estimate the ultimaton size by this law (1E-18 / 860) , we arrive at a size which is close to the expected size of the electron core (about 1E-21m, see ref. 5 and UB p.477), which is not equal to the classical electron radius Re=2.81794E-15 m; this "Radius" is really the diameter of the integrated electric field around an electron! The wavelength of annihilation radiation of electrons and positrons (Compton wavelength) is equal to 860 *Re.

The number 860...861 results from dividing two pi by alpha (2*pi*137 = 860.8). Now all spectral lines can be easily derived in the following way. The wavelength (lam) or the energy difference of the photon which results when an electron jumps from an orbit with diameter d1 to diameter d2 is :

d = 2*a*n*n d1 = 2*a*n1*n1 d2 = 2*a*n2*n2
1 / lam = 1 / (860*d1) - 1 / (860*d2) = R (1 / (n1*n1) - 1 / (n2*n2) )
a =  0.529177E-10 m, or  the Bohr  radius of  the  atom
d, d1 and d2 = Sommerfeld’s  value  for the atomic  diameter
n  = an  integer  or quantum state number 
R =  Rydberg’s spectral constant = 1 / (860*2*a)

But there are fine structures and "fluctuations"in the spectra that are difficalt to explain. The Urantia Papers say on p.478:
"The interelectronic space of an atom is not empty. Throughout an atom this interelectronic space is activated by wavelike manifestations which are perfectly synchronized with electronic velocity and ultimatonic revolutions. This force is not wholly dominated by your recognized laws of positive and negative attraction; its behavior is therefore sometimes unpredictable. This unnamed influence seems to be a space-force reaction of the Unqualified Absolute."

One further comment on my electron model:
The Urantia Papers say that the Ultimatons should be mutually interassociated by attraction. This is the case in my model and I figure that spin is the source of this attraction. All ultimatons rotate as a rigid packet, i.e. they don’t describe orbits inside the electron. If this model is a minimum energy state the ultimatons probably would arrange into this configuration almost by them selves and give out gamma-quanta similar to the annihilation quanta ( UB p.475). Such radiation is actually observed from the universe and it might represent zones where new electrons are formed and not annihilation zones as many physicists expect.