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This chapter explains the excitation of atoms by polarized resonance radiation and their interaction with static and radio-frequency fields, known as optical double-resonance. The Brossel-Bitter experiment on mercury vapour is discussed and classical and quantum mechanical theories of the effect are developed. The phenomena of radiation trapping and coherence narrowing are explained, and the effect of collision broadening is examined. Experiments involving intensity-modulated light are reported, and the density matrix formulation of optical double-resonance experiments is developed.

This chapter develops the theory of the hyperfine structure of atoms involving nuclear magnetic dipole and electric quadrupole moments. The Zeeman effect in weak, intermediate, and strong magnetic fields is considered. The experimental measurement of the hyperfine structure of ground state atoms by the techniques of optical pumping, atomic beam magnetic resonance, and optical double resonance is explained. The caesium beam atomic clock, the importance of hyperfine structure experiments in hydrogen, and the investigation of hyperfine structure of excited states are discussed.

This chapter assesses the choice of cohomology and Aubry-Mather type at the double resonance. It begins by choosing cohomology classes for the (unperturbed) slow mechanical system. As in the case of single-resonance, the strategy is to choose a continuous curve in the cohomology space and prove forcing equivalence up to a residual perturbation. To do this, one needs to use the duality between homology and cohomology. The chapter then proves Aubry-Mather type for the perturbed slow mechanical system and reverts to the original coordinates. As the system has been perturbed, one needs to modify the choice of cohomology classes to connect the single and double resonances. Finally, the chapter proves Theorem 2.2, proving the main theorem.

This chapter discusses the single-resonance non-degeneracy conditions and normal forms. It then formulates Theorem 3.3, which covers the forcing equivalence in the single-resonance regime. The classical partial averaging theory indicates that after a coordinate change, the system has the normal form away from punctures. In order to state the normal form, one needs an anisotropic norm adapted to the perturbative nature of the system. The chapter also uses the idea of Lochak to cover the action space with double resonances. A double resonance corresponds to a periodic orbit of the unperturbed system. Finally, the chapter looks at a lemma which is an easy consequence of the Dirichlet theorem.

This chapter examines the geometrical structure for the system at double resonance. After describing the normal form near a double resonance, it reduces the system to the slow mechanical system with perturbation. The system is conjugate to a perturbation of a two degrees of freedom mechanical system after a coordinate change and an energy reduction. The chapter then formulates the non-degeneracy conditions and theorems about their genericity. It also considers the normally hyperbolic invariant cylinders, and sketches the proof using local and global maps. The periodic orbits obtained in Theorem 4.4 correspond to the fixed points of compositions of local and global maps, when restricted to the suitable energy surfaces.

This chapter proves Aubry-Mather type for the double resonance regime. It begins by considering the “non-critical energy case” and showing that the cohomologies as chosen are of Aubry-Mather type. The proof consists of two cases. In the first case, the chapter uses the almost verticality of the cylinder, and the idea is similar to the proof of Theorem 9.3. It applies the a priori Lipschitz estimates for the Aubry sets. In the second case, the chapter uses the strong Lipschitz estimate for the energy, and the idea is similar to the proof of Theorem 11.1. It then looks at the construction of the local coordinates. This is done separately near the hyperbolic fixed point (local) and away from it (global).

This chapter proves various normal form results and formulates the coordinate changes that are used to derive the slow system at the double resonance. The discussions here apply to arbitrary degrees of freedom. The results also apply to the proof of the main theorem by restricting to the case n = 2. First, the chapter reduces the system near an n-resonance to a normal form. After that, it performs a coordinate change on the extended phase space, and an energy reduction to reveal the slow system. The chapter then describes a resonant normal form, before explaining the affine coordinate change and the rescaling, revealing the slow system. Finally, it discusses variational properties of these coordinate changes.

The first step in a unimolecular reaction involves energizing the reactant molecule above its decomposition threshold. An accurate description of the ensuing unimolecular reaction requires an understanding of the state prepared by this energization process. In the first part of this chapter experimental procedures for energizing a reactant molecule are reviewed. This is followed by a description of the vibrational/rotational states prepared for both small and large molecules. For many experimental situations a superposition state is prepared, so that intramolecular vibrational energy redistribution (IVR) may occur (Parmenter, 1982). IVR is first discussed quantum mechanically from both time-dependent and time-independent perspectives. The chapter ends with a discussion of classical trajectory studies of IVR. A number of different experimental methods have been used to energize a unimolecular reactant. Energization can take place by transfer of energy in a bimolecular collision, as in . . . C2H6 + Ar → C2H6* + Ar . . . . . . (4.1) . . . Another method which involves molecular collisions is chemical activation. Here the excited unimolecular reactant is prepared by the potential energy released in a reactive collision such as . . . F + C2H4 → C2H4F* . . . . . . (4.2) . . . The excited C2H4F molecule can redissociate to the reactants F + C2H4 or form the new products H + C2H3F. Vibrationally excited molecules can also be prepared by absorption of electromagnetic radiation. A widely used method involves initial electronic excitation by absorption of one photon of visible or ultraviolet radiation. After this excitation, many molecules undergo rapid radiationless transitions (i.e., intersystem crossing or internal conversion) to the ground electronic state, which converts the energy of the absorbed photon into vibrational energy. Such an energization scheme is depicted in figure 4.1 for formaldehyde, where the complete excitation/decomposition mechanism is . . . H2CO(S0) + hν → H2CO(S1) → H2CO*(S0) → H2 + CO . . . . . . (4.3) . . . Here, S0 and S1 represent the ground and first excited singlet states.

Jean Kibble and the author were married on 1^st September 1962. They honeymooned in Inverness, Scotland. Later they sailed to America. A day before docking they heard on the ship’s radio of the ensuing political storm when President John Kennedy challenged Nika Kruschoff the Russian President, over plans to place Russian missiles on Cuban soil. On arrival in Urbana they found a state of panic with air raid sirens sounding and shelter drills being practiced. The panic subsided when Kruschoff turned back the boats carrying the missiles. Doug and Pat Cutler had already arrived in Urbana and had acquired a Triumph sports car. While on a tour in Wyoming in 1965, Pat had a fatal accident. She was cremated at a Chicago Crematorium. Meanwhile he got immersed in a project in Charlie’s laboratory and Jean was employed in the University’s Health Centre. The research students in Charlie’s laboratory seemed far more experienced than he in Physics. Charlie was interested in the NMR of metals and metal alloys. His task was to grow a single crystal of copper doped with a few percent of zinc. In addition he was required to build a double resonance spectrometer to observe the Cu 63 and Cu 65 magnetic resonances. The equipment and copper sample were completed in one year and the experiment tried many times during the second year, but without success. During the last month or so in Urbana he wrote a paper on solid echoes extending the paper by Powles and Strange. While in the states they made two long summer tours of the Southern states visiting Nassau during their second year. Their return to Britain on the USS United States of America was uneventful. He had been offered a Lectureship in the University of Nottingham by Professor Raymond Andrew. He started at Nottingham in mid September 1964.

During the past decade, the study of photoinitiated reactive and inelastic processes within weakly bound gaseous complexes has evolved into an active area of research in the field of chemical physics. Such specialized microscopic environments offer a number of unique opportunities which enable scientists to examine regiospecific interactions at a level of detail and precision that invites rigorous comparisons between experiment and theory. Specifically, many issues that lie at the heart of physical chemistry, such as reaction probabilities, chemical branching ratios, rates and dynamics of elementary chemical processes, curve crossings, caging, recombination, vibrational redistribution and predissociation, etc., can be studied at the state-to-state level and in real time. Inevitably, understanding the photophysics and photochemistry of weakly bound complexes lends insight into corresponding processes in less rarefied surroundings, for example, molecules physisorbed on crystalline insulator and metal surfaces, molecules residing on the surfaces of various ices, and molecules weakly solvated in liquids. However, such ties to the real world are not the main driving force behind studies of photoinitiated reactions in complexed gaseous media. Rather, it is the lure of going a step beyond the more common molecular environments. Theoretical modeling, which in many areas purports to challenge experiment, must rise to the occasion here if it is to offer predictive capability for even the simplest of such microcosms. Subtleties abound. Roughly speaking, two disparate regimes can be identified which are accessible experimentally and which correspond to qualitatively different kinds of chemical transformations. These are distinguished by their reactants: electronically excited versus ground state. For example, it is possible to study the chemical selectivity that derives from the alignment and orientation of excited electronic orbitals, albeit at restricted sets of nuclear coordinates. This is achieved by electronically exciting a complexed moiety, such as a metal atom, which then undergoes chemical transformations that depend on the geometric properties of the electronic orbitals such as their alignments and orientations relative to the other moiety (or moieties) in the complex.