Many thanks, I sent over Note 435(1), which gives a method of finding m(r) from the observed Lamb shift. This solves the problem of having to guess an m(r), and also finds the m(r) function that gives the Lamb shift precisely. I think that computational quantum chemistry packages must be used for the heavier atoms and molecules.

It has to be considered that we computed the Lamb shift as a correction to the spin orbit coupling. This was a different integral. The Lamb shift is larger by orders of magnitude than what comes out as the correction factor in this calculation. A deviation by 10 power -9 is probably not measurable by a spectroscope.

I computed the correction factor with the Einsteinian m(r) = 1 – r0 / r for curiosity. The results are nearly identical to the last curve of UFT 434 (rational function). The power of r0/r seems to be important,

m(r) = 1 – (r0/r)^n

gives results similar to the exponential m(r) for n>=2. At least the characteristic of the splitting then is similar to that of the exponential m(r).

It has to be taken in mind that H is the worst system to study such effects. in heavy elements the deviations by m(r) will be much larger. However there are no analytical wave functions known for Z>1 as you know. We would need radial wave functions from quantum chemistry. What about the effect of spin? Will m(r) be spin-dependent in spin polarized atoms?

Horst

Am 23.03.2019 um 07:34 schrieb Myron Evans:

Exponential m Functions

These show precisely the behaviour seen in the Lamb shift, the 2S sub 1/2 orbital is affected by the 2P sub 1/2 orbital is not affected. In my opinion the next step would be to repeat these computations using the wavefunctions of the Dirac atom, which can be expressed in terms of the hydrogenic wavefunctions of the Schroedinger atom. That would introduce the spin angular momentum, missing from the Schroedinger atom. As a matter of curiosity it would be interesting to compute the effect of the Einsteinian m(r) = 1 – r0 / r on the H atom. That would give the effect of gravitation on the H atom spectrum. However, it is known that the Einstein theory is thoroughly obsolete, and has been superceded by ECE theory and m theory. The use of the time dependent Schroedinger equation is very powerful.

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