#### Title

The effect of closed classical orbits on quantum spectra: Ionization of atoms in a magnetic field

#### Date Awarded

1987

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (Ph.D.)

#### Department

Physics

#### Abstract

A quantitative theory of oscillatory spectra for atoms in a magnetic field is developed. When an atom is placed in a magnetic field, and absorption spectrum into states close to the ionization threshold is measured, it is found that the absorption as a function of energy is a superposition of many sinusoidal oscillations. Such interesting and surprising phenomenon are fully explained and described by the theory.;The theory is based on three approximations: (1) Near the atomic nucleus, the diamagnetic field is negligible. (2) Far from the nucleus, the wave propagates semiclassically. (3) Waves returning to the nucleus are similar to (cylindrically-modified) Coulomb-Scattering waves. Using these approximations, together with the simple physical picture of absorption process, formula is derived for the transition rate as a function of final states energy.;The main result is that the transition rate is equal to the sum of two very different kinds of contributions. The first is the averaged transition rate in the absence of the magnetic field, which is a smooth function of energy; the second is itself a sum over many oscillations. Each oscillation is closely associated with a band of wave, initially going out from the nucleus, propagating along a family of trajectories, and finally returning to the vicinity of the nucleus. Because in the center of the family of trajectories is a closed orbit going from the nucleus and returning to the nucleus, we say "a closed orbit makes an oscillatory contribution to the absorption spectrum".;Formulas and algorithms are derived and specified for the calculations of the spectrum from the initial quantum state, dipole polarization, and the properties of the closed classical orbits. Good agreements with experiments were found. Very detailed interpretations are obtained.

#### DOI

https://dx.doi.org/doi:10.21220/s2-khfp-vh38

#### Rights

© The Author

#### Recommended Citation

Du, Meng Li, "The effect of closed classical orbits on quantum spectra: Ionization of atoms in a magnetic field" (1987). *Dissertations, Theses, and Masters Projects.* Paper 1539623773.

https://dx.doi.org/doi:10.21220/s2-khfp-vh38