RESURRECTION OF THE BOHR/SOMMERFELD THEORY OF ATOMIC STRUCTURE - [3] - MAGNETIC DIPOLE COUPLING.

The links below are to the Sections of the paper on the effects of magnetic couplings produced by the orbital and spin motions of both the orbiting electron and the nucleus. These effects produce small additions to the orbital energy of the electron which split the fine structure into doublets.

Introduction - The first section contains a title page, a brief abstract, the main introduction and the first Section detailing the magnetic characteristics of the electron and the nucleus, pertinent to magnetic dipole coupling. This includes a classical explanation for the effective doubling of the electron spin magnetic dipole over that of the orbital, quantum number differences aside.

Total Electron Orbital Energy - The second section provides derivations of the electron enhanced orbital energy in two ways. The first is via a re-evaluation of the principle quantum number criterion with spin - orbit coupling included. From this the isolated spin - orbit energy term is determined by the subtraction of the orbital energy without spin - orbit coupling incorporated from that with. This is followed by the derivation of this same isolated energy term from first principles from consideration of the basic electrostatic, magnetic and mechanical concepts involved. In addition all other magnetic coupling energy terms involving the nucleus are also derived in this section. A further electron enhanced orbital energy relationship is then produced and discussed in some detail.

Orbital Spin Reversals and Comparison with Quantum Mechanics Theory - This Section incorporates two Sections of the paper. The first deals with the effects of spin reversals within the four quadrants and dead zones of an elliptic orbital. A detailed example is provided to show how the electron undergoes intra-shell orbital transitions as its spin reverses around the four quadrants of the complete orbital path.
The second part of this Section provides a detailed comparison of this resurrected theory with that of the modern quantum mechanics version. A detailed discussion highlights the mathematical and physical differences and the reason for their existence.

Conclusions - Concluding remarks on the whole paper including further commentary on the comparision with the modern quantum mechanics theory of atomic structure.

Appendix A - The first Appendix provides a mathematical derivation of the median value of the radius vector magnitude from a focal point in an elliptic orbit. This parameter being a constituent part of the development in the main text.

Appendix B - The second Appendix provides a detailed derivation of the generation of the magnetic dipoles due to both the orbital and spin motions of the electron.

Appendix C - The final 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 second Section. These may be compared with those in the literature by ignoring the effects of the Lamb Shift in the latter.

References

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