Electron Swarm

Quantum chemical methods, exemplified by CASSCF and other MCSCF methods, have now evolved to an extent where it is possible to routinely treat accurately the excited electronic states of molecules containing a number of atoms. Mixed nuclear dynamics, such as swarm of trajectory based surface hopping or Ehrenfest dynamics, or the Gaussian wavepacket based multiple spawning method, use an approximate representation of the nuclear wavepacket based on classical trajectories. They are thus able to use the infoiination from quantum chemistry calculations required for the propagation of the nuclei in the form of forces. These methods seem able to reproduce, at least qualitatively, the dynamics of non-adiabatic systems. Test calculations have now been run using duect dynamics, and these show that even a small number of trajectories is able to produce useful mechanistic infomiation about the photochemistry of a system. In some cases it is even possible to extract some quantitative information. 

The electrons have a range of kinetic energies and are therefore at different temperatures. Depending on the strength of the applied electric field, some electrons in the swarm will have... 

The increase in the electron energy may have several consequences. It may lead to dissociative or nondissociative electron attachment (54, 61). This would give rise to a step enhancement as in N20 (8). The most important possibility is electronic excitation of the molecular species, which should manifest itself by an increased yield of all products arising from excited intermediates as the mean energy of the electron swarm rises with field strength. 

Top typical saturation curve and variation of mean electron energy with applied field. Middle fraction of the electron swarm exceeding the specific energy at each field strength. Calculated assuming constant collision cross-section and Maxwell-Boltzman distribution. Bottom variation of products typical of involvement of ionic precursors (methane) and excited intermediates (ethane) with applied field strength... 

For larger atomic aggregates, another possibility is that a stable and dense plasma forms, consisting of a swarm of relatively free electrons moving in a background of an equal number of positively charged ions (metallic bonding). 

The thermalization time for an electron swarm starting with an initial energy Eg is then given by... 

This compound also possesses a comparatively large ionisation potential (15.3 eV)163,164, and one of the largest known cross-sections for the capture of thermal electrons. The latter process has been studied in considerable detail by beam, swarm and microwave techniques104 165-170. The initial attachment gives rise to a vibrationally excited ion169,17°, viz. 

As Fig. 2.4 illustrates, a cation can associate with a surface as an inner sphere, or outer-sphere complex depending on whether a chemical, i.e., a largely covalent bond, between the metal and the electron donating oxygen ions, is formed (as in an inner-sphere type solute complex) or if a cation of opposite charge approaches the surface groups within a critical distance as with solute ion pairs the cation and the base are separated by one (or more) water molecules. Furthermore, ions may be in the diffuse swarm of the double layer. 

Years ago, people thought that electrons travel around the nucleus in definite circular patterns, or orbits. You may have seen pictures like this. Now we know that electrons don t follow a perfect circle around the nucleus but are more likely to go around in certain places. A famous physicist named Erwin Schrbding-er said the electron is like a vibrating string. If you took a picture of all of the places that electrons go, it would look like a cloud, like the drawing below. The electrons do orbit in shells, which are regions of space around the nucleus. If you think of the nucleus as a beehive, then the electrons would be the bees swarming around it. 

Approximately 75% of all elements found on and in the Earth are metals. They are crystalline solids that at room temperature range from hard to butter-like soft to liquid (mercury). They are generally good conductors of heat and electricity as a result of the swarm of relatively free electrons in their outer shell that move without much resistance to other elements, particularly those with a dearth of electrons in their outer shells. In pure states, most metals have a shiny luster when cut. Those located at the far left of the table have only one electron in their outer shell. Therefore, they are very reactive and are not usually found in pure form. Instead, they are found in compounds, minerals, or ores that must be processed to extract the pure metal from the other elements in the compounds. 

Johnsen, R. Lee, H.S. Swarm Studies and Inelastic Electron-Molecule Collisions, Pitchford,... 

Elements are fundamental substances that cannot be broken down into smaller chemical components. The smallest unit of an element is an atom, a term based on the Greek word atomos, meaning indivisible. But atoms are divisible—they consist of a nucleus containing positively charged particles called protons and electrically neutral particles called neutrons, surrounded by a swarm of electrically negative particles called electrons. In chemical reactions, atoms interact and combine to form a molecule of a compound. (Chemical reactions also occur when the atoms in molecules interact and combine to form even bigger com-... 

In the simplest model of an atom, electrons swarm around a compact nucleus containing protons and neutrons. 

In Chapter 5, we discussed how electrons are arranged around an atomic nucleus. Rather than moving in neat orbits like planets around the sun, electrons are wavelike entities that swarm in various volumes of space called shells. 

Most of the work in solving the Boltzmann equation for electrons has been for the relatively simple conditions of electron swarm experiments. In these experiments, electrons are released from a cathode in low concentrations and drift under the influence of a uniform applied electric field in a low-pressure gas towards an anode at which the electrons are collected. If... 

Another point in favor of the simpler, but less accurate, fluid approach is that discharge diagnostics are still quite primitive. In studies of electron and ion swarms, experimentalists routinely measure mobilities and diffusiv-ities with a precision in the order of a few percent. A sophisticated model must be used to properly interpret such experiments. However, for discharges, even relative concentration profiles for a few of the dozens of important neutral and charged species are difficult to attain. Thus, an overly complex and expensive model is probably inappropriate, and the fluid model is a good compromise at present. 

Traditionally, experimental values of Zeff have been derived from measurements of the lifetime spectra of positrons that are diffusing, and eventually annihilating, in a gas. The lifetime of each positron is measured separately, and these individual pieces of data are accumulated to form the lifetime spectrum. (The positron-trap technique, to be described in subsection 6.2.2, uses a different approach.) An alternative but equivalent procedure, which is adopted in electron diffusion studies and also in the theoretical treatment of positron diffusion, is to consider the injection of a swarm of positrons into the gas at a given time and then to investigate the time dependence of the speed distribution, as the positrons thermalize and annihilate, by solving the appropriate diffusion equation. The experimentally measured Zeg, termed Z ), is the average over the speed distribution of the positrons, y(v,t), where y(v,t) dv is the number density of positrons with speeds in the interval v to v + dv at time t after the swarm is injected into the gas. The time-dependent speed-averaged Zef[ is therefore... 

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