The Dynamics of an Excited Hydrogen Atom in a Parallel Low Frequency Microwave and Static Field

Kelly, Nicholas Christopher (2011). The Dynamics of an Excited Hydrogen Atom in a Parallel Low Frequency Microwave and Static Field. PhD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000f206

Abstract

This thesis examines the effect of parallel static and low frequency microwave fields on excited hydrogen atoms. By low frequency we mean, Ω0 = Ω/ωκ << 1, where Ω is the field frequency and ωκ is the Kepler frequency of the unperturbed excited electron. Experiments and calculations have shown that for certain field strengths, resonances arise, sometimes leading to enhanced ionisation.

Approximate time-dependent one-dimensional Hamiltonians describing the classical dynamics were derived previously by Richards [51]. Here we derive a number of properties from these Hamiltonians and use these to predict and explain ionisation behaviour.

Because the separatrix is a construct of classical dynamics affecting a relatively small area of phase space, it is unclear how it will affect the quantum mechanics of the system or how large the quantum numbers must be for measurable effects. For this reason, we derive a new quantal method to compute the ionisation probability for the system. The method is tested where possible and shown to accurately describe the general behaviour of the system. The method is applied to slowly switched fields and is computationally efficient, allowing calculations for high principal quantum numbers, n ≥ 800.

We compare classical and quantum ionisation behaviour. Significant qualitative differences exist for low quantum numbers, n ~ 10, but quantitative differences exist, for higher quantum numbers, even for n ≥ 100.

For slowly switched fields, the separatrix can considerably affect the ionisation structure. These effects are also manifest in the quantum mechanics for sufficiently high n, but even for n = 39, the influence of the separatrix is seen.

Ionisation times are calculated for systems prepared in a single initial state and for mi- crocanonical distributions of initial states. Classically, motion near the separatrix is shown to lead to longer ionisation times at resonance. This is also seen in quantal calculations, even for quantum numbers as low as n =39, that is, those accessible by experiment.