Nonlocal complex potential theory of dissociative electron attachment: Inclusion of two vibrational modes

The process of dissociative electron attachment (DEA) to molecules with several vibrational degrees of freedom is usually treated in the approximation of the local potential for the description of the nuclear motion. We develop the nonlocal complex potential theory to treat the dissociation dynamics when there is more than one vibrational mode in the neutral molecule. We demonstrate the application of the multimode nonlocal theory to a generic molecule of the type CY3X, where Y denotes the H or F atom and X denotes the halogen atom, with the inclusion of symmetric C–X stretch and CY3 deform (“umbrella”) vibrational modes. We present results for the dependence of DEA cross sections on the electron energy and vibrational energy for the CF3Cl molecule in the two-mode approximation. The 1.5 eV peak in the DEA cross section is well described in the one-mode approximation. However, inclusion of additional modes is required to explain the experimentally observed low-energy peak in the DEA cross section at the vibrational temperature Tv = 800 K

Semiclassical theory of laser-assisted radiative recombination

We study the process of laser-assisted radiative recombination of an electron with a proton by using a semiclassical approach involving calculation of classical trajectories in combined laser and Coulomb fields. Due to chaotic scattering in the combined fields, the radiation probability as a function of the impact parameter and the constant phase of the laser field exhibits chaotic behavior and fractal structures. We obtain a strong enhancement of the recombination cross section as compared to the laser-free case due to the Coulomb focusing effect. For sufficiently low incident electron velocities the cross section becomes infinite, and we limit it by assuming a finite laser pulse duration. With the pulse duration tp = 5 ps we obtain the gain factor for capture into the ground state of the hydrogen atom of about 220 for infrared fields in the intensity range 109–1012 W/cm2. The gain factor grows with tp but slower than linearly

Classical theory of laser-assisted spontaneous bremsstrahlung

We study the process of laser-assisted spontaneous electron bremsstrahlung by running classical trajectories in a combined Coulomb and laser (ac) fields. Due to chaotic scattering in the combined Coulomb and ac fields, the radiation probability as a function of the impact parameter and the constant phase of the laser field exhibits fractal structures. However, these structures are smeared out when the cross section is integrated over the impact parameter and averaged over the phase. We analyze the role of different types of orbits, including the trapped orbits, and the dependence of the radiation probability on the impact parameter and the initial phase of the ac field.We show that, at low incident electron kinetic energy, the Coulomb focusing leads to a substantial extension of the range of impact parameters contributing to the bremsstrahlung cross section and results in a substantial increase (by one to two orders of magnitude) of the cross section as compared with the pure Coulomb case. As examples, we discuss the case of relatively high ponderomotive energy Ep when we obtain an efficient production of photons with frequencies up to 2Ep, and the case of low Ep when only infrared photons are produced. Overall accuracy of the classical approach is estimated to be very good, although it does not describe resonant processes studied previously by quantum-mechanical methods

Semiclassical theory of laser-assisted dissociative recombination

We study the process of laser-assisted dissociative recombination of an electron with a molecular cation using a semiclassical approach. In the region outside a reaction sphere the electron motion in the combined laser and Coulomb fields is treated classically. Within the sphere the laser-field effects are neglected, and the recombination probability is obtained from quantum-mechanical cross sections calculated for the laser-free process. Specific calculations are performed for dissociative recombination of H2+ in the field of the intensity 2.09 GW/cm2 and the wavelength 22.8 μm. In the energy region above 1 meV the cross section is significantly enhanced compared with the field-free case due to the Coulomb focusing effect. The influence of the indirect process due to electron capture into Rydberg states is also investigated. Although the Rydberg resonances are washed out due to the field effects, they influence significantly the magnitude of the dissociative recombination cross section

Scale Invariance in Road Networks

We study the topological and geographic structure of the national road networks of the United States, England and Denmark. By transforming these networks into their dual representation, where roads are vertices and an edge connects two vertices if the corresponding roads ever intersect, we show that they exhibit both topological and geographic scale invariance. That is, we show that for sufficiently large geographic areas, the dual degree distribution follows a power law with exponent 2.2 < alpha < 2.4, and that journeys, regardless of their length, have a largely identical structure. To explain these properties, we introduce and analyze a simple fractal model of road placement that reproduces the observed structure, and suggests a testable connection between the scaling exponent alpha and the fractal dimensions governing the placement of roads and intersections.Comment: 6 pages, 10 figures; revision incorporates more rigorous statistical analyses; matches journal versio

Coupled-Channel Theory of Photoionization Microscopy

We develop a quantum-mechanical coupled-channel theory to simulate spatial distributions of electron current densities, produced in photoionization for nonhydrogenic atoms in the presence of a uniform external electric field. The coupled Schrodinger equations are numerically solved using the renormalized Numerov method. The expression for the outgoing wave function for photoelectrons ejected from the nonhydrogenic atomic source is derived. The theory is applied to investigations of photoionization for ground-state Li atoms. The distributions of electron current densities are computed and compared to the corresponding experimental images. Excellent agreement is obtained. It is, furthermore, found that the presence of the nonhydrogenic residual ion significantly changes the differential cross sections and/or electron current densities with respect to the hydrogenic case. Finally, the implications of the presence of the atomic core for quantum resonance tunneling are also analyzed

Modifying the photodetachment near a metal surface by a weak electric field

We show the photodetachment cross sections of H near a metal surface can be modified using a weak static electric field. The modification is possible because the oscillatory part of the cross section near a metal surface is directly connected with the transit-time and the action of the detached-electron closed-orbit which can be changed systematically by varying the static electric field strength. Photodetachment cross sections for various photon energies and electric field values are calculated and displayed.Comment: 16 pages, 7 figure

Ballistic matter waves with angular momentum: Exact solutions and applications

An alternative description of quantum scattering processes rests on inhomogeneous terms amended to the Schroedinger equation. We detail the structure of sources that give rise to multipole scattering waves of definite angular momentum, and introduce pointlike multipole sources as their limiting case. Partial wave theory is recovered for freely propagating particles. We obtain novel results for ballistic scattering in an external uniform force field, where we provide analytical solutions for both the scattering waves and the integrated particle flux. Our theory directly applies to p-wave photodetachment in an electric field. Furthermore, illustrating the effects of extended sources, we predict some properties of vortex-bearing atom laser beams outcoupled from a rotating Bose-Einstein condensate under the influence of gravity.Comment: 42 pages, 8 figures, extended version including photodetachment and semiclassical theor

Highly optimized tolerance and power laws in dense and sparse resource regimes

Power law cumulative frequency $(P)$ vs. event size $(l)$ distributions $P(\geq l)\sim l^{-\alpha}$ are frequently cited as evidence for complexity and serve as a starting point for linking theoretical models and mechanisms with observed data. Systems exhibiting this behavior present fundamental mathematical challenges in probability and statistics. The broad span of length and time scales associated with heavy tailed processes often require special sensitivity to distinctions between discrete and continuous phenomena. A discrete Highly Optimized Tolerance (HOT) model, referred to as the Probability, Loss, Resource (PLR) model, gives the exponent $\alpha=1/d$ as a function of the dimension $d$ of the underlying substrate in the sparse resource regime. This agrees well with data for wildfires, web file sizes, and electric power outages. However, another HOT model, based on a continuous (dense) distribution of resources, predicts $\alpha= 1+ 1/d$. In this paper we describe and analyze a third model, the cuts model, which exhibits both behaviors but in different regimes. We use the cuts model to show all three models agree in the dense resource limit. In the sparse resource regime, the continuum model breaks down, but in this case, the cuts and PLR models are described by the same exponent.Comment: 19 pages, 13 figure