RESURRECTION OF THE BOHR/SOMMERFELD THEORY OF ATOMIC STRUCTURE THE ADDITION OF SMALL RELATIVISTIC ENERGY CORRECTION TERMS LEADING TO THE LAMB SHIFT. The links below are to the Sections of the paper on the development of small relativistic energy correction terms, that incorporate the lamb shift into the electron fine structure obital energy levels. These correction terms are shown to be due to essentially two causes. The first is the distributed nature of the electron charge on its outer surface, and the second is the effect of the dynamic distance of the nucleus from the central point of orbital rotation. |
| Introduction - The first section contains a title page, a brief abstract, and the main introduction.
The Energy Correction Term Source Components. - The second section provides derivations of the two component causes of this effect. The first is the effect on the central coulomb force of the electron charge being distributed uniformly on its outer surface. The second is the development of the effect on the central coulomb force of the dynamic distance of the nucleus from the central point of electron/nucleus orbital rotation. Determination of the Orbital Energy Correction Terms. - In this Section the results from the previous are developed into electron orbital energy correction terms. The effect of the electron spin matter wave radius is shown to be central in this development. Addition of the Energy Correction Terms to the Fine Structure Energy Levels, and Discussion of Results. - The fourth Section contains two subjects. The first is simply the addition of the energy correction terms to the fine structure energy level equation. This produces the final relationship for this stage of development. The second subject is a detailed discussion of all results, largely in comparison with data in the published literature. Topics covered are (i) the vacuum spectral wavelength results (ii) the air spectral wavelength results, (iii) the orbital energy levels, (iv) the orbital energy intervals, particularly the Lamb Shift, (v) the electron spin matter wave radius and the manner in which it, (a) contributes to the electron spin angular momentum quantum criteria and, (b) the manner in which it is instrumental in initiating orbital transitions, and finally, (vi) the principle quantum numbers at ionisation. A summary of all discussed results is also included in this Section. Conclusions - The final remarks deal largely with the veracity of the overall development of this resurrected theory to date. The most prominent subject being the reason for, and the manner in which, the electron spin matter wave radius has been treated in this paper. Appendix A - The first Appendix provides calculated emission spectra for hydrogen for the first seven orbitals down to the first three, using the electron enhanced orbital energy relationship developed in the fourth Section. These results may be directly compared with those in the literature by downloading, from the link provided, the spreadsheet within which they were computed. Appendix B - The second Appendix provides a simple derivation of the surface area of a sphere rotating at an angular rate such that its circumferential velocity reaches the velocity of light. Appendix C - The final Appendix provides a derivation of the Lorentz-Fitzgerald contraction of two dimensions, pertinent in the mathematical development in the second Section, due to the high angular rate of spin of the electron. |
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