Transition state in atomic physics

The transition state is fundamental to modern theories of reaction dynamics: essentially, the transition state is a structure in phase space that all reactive trajectories must cross. While transition-state theory (TST) has been used mainly in chemical physics, it is possible to apply the theory to considerable advantage in any collision problem that involves some form of reaction. Of special interest are systems in which chaotic scattering or half-scattering occurs such as the ionization of Rydberg atoms in external fields. In this paper the ionization dynamics of a hydrogen atom in crossed electric and magnetic fields are shown to possess a transition state: We compute the periodic orbit dividing surface (PODS) which is found not to be a dividing surface when projected into configuration space. Although the possibility of a PODS occurring in phase space rather than configuration space has been recognized before, to our knowledge this is the first actual example: its origin is traced directly to the presence of velocity-dependent terms in the Hamiltonian. Our findings establish TST as the method of choice for understanding ionization of Rydberg atoms in the presence of velocity-dependent forces. To demonstrate this TST is used to (i) uncover a multiple-scattering mechanism for ionization and (ii) compute ionization rates. In the process we also develop a method of computing surfaces of section that uses periodic orbits to define the surface, and examine the fractal nature of the dynamics

Statistical Theory of Asteroid Escape Rates

Transition states in phase space are identified and shown to regulate the rate of escape of asteroids temporarily captured in circumplanetary orbits. The transition states, similar to those occurring in chemical reaction dynamics, are then used to develop a statistical semianalytical theory for the rate of escape of asteroids temporarily captured by Mars. Theory and numerical simulations are found to agree to better than 1%. These calculations suggest that further development of transition state theory in celestial mechanics, as an alternative to large-scale numerical simulations, will be a fruitful approach to mass transport calculations

Quantum Manifestations of Bifurcations of Classical Orbits: An Exactly Solvable Mode

We examine photodetachment of H− in parallel electric and magnetic fields, hν+H−→H+e− using semiclassical approximations. The fields cause the electron to return to the atom, producing recurrences that are visible as interference oscillations in the photodetachment cross section. As the energy is varied, new returning orbits are created through bifurcations. Each such new recurrence increases the complexity of the absorption spectrum, and each bifurcation causes a local failure of the semiclassical approximation. The failure is repaired by a Fresnel diffraction integral

Closed-orbit Theory and the Photodetachment Cross Section of H- in Parallel Electric and Magnetic Fields

In this paper we obtain a simple analytic formula for the photodetachment cross section of H− in parallel electric and magnetic fields. The three-dimensional semiclassical approximation predicts oscillations in the spectrum and correlates these oscillations with closed classical orbits. The cylindrical symmetry of the Hamiltonian produces some interesting effects. In particular, at boundary energies the semiclassical approximation fails as a focused cusp approaches the origin

Quantum Manifestations of Bifurcations of Closed Orbits in the Photodetachment Cross Section of H- in Parallel Fields

In the preceding paper, we showed that the semiclassical approximation diverges at a bifurcation, and that this divergence coincides with the passage of a focused cusp through the origin. Here we obtain a wave function in the vicinity of this cusp, and we use that wave function to eliminate the divergences in the photodetachment cross section. To describe the focused cusp, we first discuss the wave function of an ordinary two-dimensional (nonfocused) cusp. This wave function is known as a Pearcey function, and it has been studied extensively. Then we show how the formulas that lead to the Pearcey function have to be modified to describe a cylindrically focused cusp. The resulting wave function turns out to be given by an integral of Fresnel type containing within it a cylindrical Bessel function. This wave function is used to derive a formula for the photodetachment cross section near a bifurcation. That formula is a simple closed-form expression containing a Fresnel integral. Comparison with exact quantum calculations shows that this corrected-semiclassical formula is quite accurate

Transition State Theory For Laser-Driven Reactions

Recent developments in transition state theory brought about by dynamical systems theory are extended to time-dependent systems such as laser-driven reactions. Using time-dependent normal form theory, the authors construct a reaction coordinate with regular dynamics inside the transition region. The conservation of the associated action enables one to extract time-dependent invariant manifolds that act as separatrices between reactive and nonreactive trajectories and thus make it possible to predict the ultimate fate of a trajectory. They illustrate the power of our approach on a driven Henon-Heiles system, which serves as a simple example of a reactive system with several open channels. The present generalization of transition state theory to driven systems will allow one to study processes such as the control of chemical reactions through laser pulses

Classical Singularities In Chaotic Atom-Surface Scattering

In this paper we show that the diffraction condition for the scattering of atoms from surfaces leads to the appearance of a distinct type of classical singularity. Moreover, it is also shown that the onset of classical trapping or classical chaos is closely related to the bifurcation set of the diffraction-order function around the surface points presenting the rainbow effect. As an illustration of this dynamic, application to the scattering of He atoms by the stepped Cu(115) surface is presented using both a hard corrugated one-dimensional wall and a soft corrugated Morse potential

Detection and Management of Early Glucose Abnormalities in Cystic Fibrosis

With advances in technology, it is now possible to detect the emergence of glucose abnormalities in cystic fibrosis with improved sensitivity, and from a very early age. These abnormalities are increasingly recognized as predictors of clinical decline, raising the possibility that early intervention may slow or prevent this deterioration. In this chapter, we will review the available literature on methods of detecting glucose abnormalities in cystic fibrosis (random and fasting glucose, HbA1c, oral glucose tolerance testing, and continuous glucose monitoring), and detail their advantages and possible limitations in the interpretation of glycemic data. We will also discuss treatment outcomes of early intervention, prior to the diagnosis of diabetes as currently defined

Transition state theory for laser-driven reactions

This is a pre-print.Recent developments in Transition State Theory brought about by dynamical systems theory are extended to time-dependent systems such as laser-driven reactions. Using time-dependent normal form theory, we construct a reaction coordinate with regular dynamics inside the transition region. The conservation of the associated action enables one to extract time-dependent invariant manifolds that act as separatrices between reactive and non-reactive trajectories and thus make it possible to predict the ultimate fate of a trajectory. We illustrate the power of our approach on a driven H´enon-Heiles system, which serves as a simple example of a reactive system with several open channels. The present generalization of Transition State Theory to driven systems will allow one to study processes such as the control of chemical reactions through laser pulses