Number density electron

Only the quantities the electron number density, and the coUision cross section, present any difficulty in their calculation. 

The actual electron density is —eP(r), but authors speak about / (r), which is strictly the electron number density, as if it were the same thing. I will follow this sloppy (but common) usage from time to time. 

The key papers in the field were written by physicists. They tend to write n(r) for the electron number density, i.e. P(r). I have kept to the original wording in the following abstract, but you should mentally switch to P r) for n(r). 

An important specific feature of the present experiment is worth noting. The X-ray photons have energies that are several orders of magnitude larger than those of optical photons. The pump and probe processes thus evolve on different time scales and can be treated separately. It is convenient to start with the X-ray probing processes, and treat them by Maxwellian electrodynamics. The pumping processes are studied next using statistical mechanics of nonlinear optical processes. The electron number density n(r,t), supposed to be known in the first step, is actually calculated in this second step. 

In the previous Maxwelhan description of X-ray diffraction, the electron number density n(r, t) was considered to be a known function of r,t. In reality, this density is modulated by the laser excitation and is not known a priori. However, it can be determined using methods of statistical mechanics of nonlinear optical processes, similar to those used in time-resolved optical spectroscopy [4]. The laser-generated electric field can be expressed as E(r, t) = Eoo(0 exp(/(qQr ot)), where flo is the optical frequency and q the corresponding wavevector. The calculation can be sketched as follows. 

If an atomic transition is optically pumped by a beam of laser radiation having the appropriate frequency, the population in the upper state can be considerably enhanced along the path of the beam. This causes an intensification of the spontaneous emission from this state, which contains information about the conditions within the pumped region, since the exponential decay time for the intensified emission depends upon both the electron number density and the electron temperature. The latter can be obtained from the intensity ratio of the fluorescence excited from two different lower levels, if local thermal equilibrium is assumed. This method has been dis-... 

The subscript 1 can be omitted. The basic quantity of DFT - the electron number density - is thus... 

The qualitative study of electronic structure through the electron (number) density p(r) relies heavily on linecut diagrams, contour plots, perspective plots, and other representations of the density and density differences. There is a review article by Smith and coworkers [302] devoted entirely to classifying and explaining the different techniques available for the pictorial representation of electron densities. Beautiful examples of this type of analysis can be seen in the work of Bader, Coppens, and others [303,304]. 

M. Grotti, C. Lagomarsino and J. M. Mermet, Effect of operating conditions on excitation temperature and electron number density in axially-viewed ICP-OES with introduction of vapors or aerosols, J. Anal. At. Spectrom., 21(9), 2006, 963-969. 

This expression has been superseded by the expression derived by Bethe and Bloch based on momentum transfer in a quantum mechanically correct formalism. Their expression with the expanded form of the electron number density is... 

Formulation of Equations. Discharge structure influences chemistry primarily through electron-impact dissociation and surface ion bombardment. To predict the rate of electron-impact dissociation, local electron number density and energy must be known. These quantities are obtained from equations for electron continuity and electron energy, respectively. 

For an electron number density of 1015 m 3 and a mobility of 0.022 (m2/V-s), calculate the time required to reach 99 percent of the saturation charge of an initially neutral particle by field charging. If the length of the charging chamber is 5 cm, what is the maximum particle velocity allowed to ensure 99 percent saturation charge ... 

To do the calculation in more detail, for the baryons (nuclei) and electrons, we define the ionization fraction X (t), the ratio of the density of ions to neutrals if we assume overall charge-neutrality, this is equal to the ratio of the free electron number density to that of neutrals. We also assume that the number density of any massive species (i) is large enough that it can be described by a Boltzmann distribution,... 

There is another approach which can be used in suitable circumstances. Developed by Kowalik and Kruger (31), it involves measuring the population of an excited atomic state by LIFS. If the ground state population is known to be uniform in the flow field, then information about temperature can be inferred. They have used the method to measure electron number density in MHD plasma flows. 

Free-space light wave vector Plasmon momentum Electron mass Electron number density Ambient refractive index... 

Figure 8 Influence of multiphoton and avalanche ionizations on electron number density at different pulse durations [13] for A = 1053 nm and k =10 TW/cm [13]...

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