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Theory of atomic structure, electron--atom and atom--atom scattering with application to communications and lasers. Final report, 1 Jun 1970--31 Mar 1975

V. W. Hughes, Charles M. Sommerfield

Published Jan 1, 1975• 0 citations
OpenAlex

Abstract

Very briefly described is research conducted on the following topics: fine structure and Zeeman effect of helium; Zeeman and Stark effects of positronium; hyperfine structure of the muonic helium atom; Lamb shifts of hydrogenic ions of high Z; nonadiabatic effects in slow atomic collisions; quenching of the metastable 2S state of muonic hydrogen and the muonic helium ion; two photon absorption; and quantization of electrodynamics hyperboloids and generalization of the effective action for electrodynamics. (GRA)

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The Astrophysical Journal•Mar 1, 1940•337 citations
Very briefly described is research conducted on the following topics: fine structure and Zeeman effect of helium; Zeeman and Stark effects of positronium; hyperfine structure of the muonic helium atom; Lamb shifts of hydrogenic ions of high Z; nonadiabatic effects in slow atomic collisions; quenching of the metastable 2S state of muonic hydrogen and the muonic helium ion; two photon absorption; and quantization of electrodynamics hyperboloids and generalization of the effective action for electrodynamics. (GRA)
Very briefly described is research conducted on the following topics: Fine structure and Zeeman effect of helium; Zeeman and Stark effect of positronium; hyperfine structure of the muonic helium atom; Lamb shifts of hydrogenic ions of high Z; nonadiabatic effects in slow atomic collisions; quenching of the metastable 2S state of muonic hydrogen and the muonic helium ion; two photon absorption; and quantization of electrodynamics hyperboloids and generalization of the effective action for electrodynamics.
1. The origin of the quantum theory Planck's radiation formula 2. The nuclear theory of the atom Bohr's theory of the hydrogen spectrum 3. The correspondence principle the photo-electric effect Einstein's deduction of Planck's formula 4. The adiabatic principle of Ehrenfest the stationary states of a periodic system 5. General dynamical theory 6. Contact transformations the Hamilton-Jacobi differential equation 7. The use of angle variables multiply periodic systems 8. The relativity theory of the fine structure of the hydrogen lines electron in a central field 9. The Stark effect 10. The Zeeman effect 11. The series spectra of the elements 12. The multiple structure of series lines theory of the Ritz formula 13. Arc and spark spectra excitation of lines by electrons or radiation 14. X-ray spectra 15. Absorption spectra and absorption edges Bohr's table of the atomic structures of the elements 17. Band spectra in the infra-red 18. Band spectra in the optical region molecular rotation and specific heat 19. The Keplerian orbit the Delaunay elements 20. The astronomical theory of perturbations and atom mechanics 21. General perturbation theory 22. The effect of electric and magnetic fields on the spectra of elements of higher atomic number. Recent developments of the quantum theory: the doublet theories of Sommerfield and Lande the dispersion theory of Kramers the quantum-kinematics of Heisenberg Index of authors.
A comprehensive set of lecture and study notes covering fundamental atomic and molecular physics. The text systematically works through the breakdown of the classical Rutherford atom and the Bohr-Sommerfeld model, followed by a full 3D Schrödinger treatment of the hydrogen atom using spherical harmonics and Laguerre polynomials. It details relativistic corrections, spin-orbit coupling, and fine structure via Clebsch-Gordan addition and Kramers' recursion relations. The notes further explore magnetic field interactions (normal and anomalous Zeeman effect, Paschen-Back effect), time-dependent perturbation theory for light-matter transitions, electric dipole selection rules, the 21-cm hyperfine splitting of hydrogen, and two-electron systems (Helium, exchange integrals, and Slater determinants). Includes extensive reference tables and angular momentum formulas.
The Bohr formulation—the original one—is now largely a matter of history. The usual career of a theory was its fate. It explained much, but it failed at the first signs of complication, even for the simplest molecules as hydrogen and helium. Some results were either only approximate in a loose or incomplete fashion, e.g. in the application of the correspondence principle to intensities, the only reliable predictions being only for an absence of certain lines, or they quite disagreed with experiment, e.g. in the case of the hydrogen molecule and the hydrogen molecule ion, the normal and excited states of helium, the anomalous Zeeman effect, the Ramsauer effect (the phenomenon of the deflection of electrons at low speeds being less than at higher speeds in atomic collisions), and in the treatment of problems where more than one electron was involved. In the last mentioned cases the perturbation method, so successful in solving “many-body” problems in celestial mechanics, failed completely because systems of several electrons, possessing frequencies of the order of light waves, cannot interact classically. A bit of much forced pragmatism was practiced in treating the many electron atom as a variation of the hydrogen atom. Besides, there were technical oddities, like ½ quantum numbers, and impenetrated anologies between visible and X-ray spectra.
The mean life of the 2S state of hydrogen in the absence of collisions is primarily determined by the simultaneous emission of two photons. Owing to this cause the mean life is `-*4 sec. It is expected that the mean life of is 2S `S of He i is of the same order of magnitude and is much shorter than that of is 2S 3S of He i. The non-adiabatic collisions with electrons are found to be more important than the static effects at small electron densities, leading to a transition probability `-*-`~h sec ` for an electron temper- ature `-.--`io,ooo° C and an electron density 30 cm3. The effect of static electric fields on the 2S state of hydrogen is worked out in more detail than previously by taking into account the hyperfine structure. The mean life in static electric fields which are strong enough to make double emission of little importance and yet weak enough to give a mean life > io7 sec is found to be the sum of two lives: (i) the mean life calculated neglecting hyperfine structure and (2) the mean life calculated neglecting radiation coupling. In both (i) and (2) the mixing of 2~ into 2S by the Stark effect is taken into account. Radiations due to quadrupole and magnetic dipole effects are considered qualita- tively for is 2S 3S of helium and quantitatively for 2S of hydrogen. For the latter there exists a small radiative magnetic dipole effect on Dirac's theory of the electron which is absent in the ordinary spin model