Free electron kinetic energy

To take these factors into account, one must incorporate aspects of the electron hopping model. For this purpose, it has been proposed to modify the kinetic energy e of each free electron by introducing a universal scaling law = 4>( 7)ei, 0 < (77) < 1. The idea is to preserve the one-particle aspect of electron motion, by setting the free-electron kinetic energy at... 

Fig. 11. "Universal curve" of inelastic mean free path, X, as a function of electron kinetic energy. Solid line is universal curve, points are experimental data...

Ri,R2,. ..,Rk denotes the nuclear coordinates. The first two terms in equation (1) describe, respectively, the electronic kinetic energy and electron-nuclear attraction and the third term is a two-electron operator that represents the electron-electron repulsion. These three operators comprise the electronic Hamiltonian in free space. The term V(r) is a generic operator for an external potential. One of the common ways to express V(f), when it is affecting electrons only, is to expand it as a sum of one-electron contributions... 

Fig, 4.1. The universal curve for the electron mean free path as a function of electron kinetic energy. Dots show individual measurements... 

For a free electron this energy is purely kinetic, so that E = p2/2m. Hence p = hk = h/X, as we have already found experimentally for free particles, namely eqs (18) and (2.14). 

Figure 2. Electrons photoejected from a surface (a). Idealized graph of the mean free path length as a function of electron kinetic energy (b).

Figure 3. Electron mean free path as a function of electron kinetic energy through organic materials. Key V, PMMA , poly(p-xylene) O, plasma polymerized fluorocarbon , barium stearate 0, cadmium arachidate and A, carbon. (Reproduced, with permission from Ref. 35.)...

Photoelectron spectroscopy is a highly surface sensitive technique because of the inelastic mean free path of the photoelectrons Ae, which depends on the electron kinetic energy Ekin and has typical values of 0.2-3nm [31,37,38]. Determination of Schottky barrier heights b, or valence band discontinuities AEyB, can be performed by following the evolution of the position of the valence band maxima with respect to the Fermi level of substrate and overlayer with increasing thickness of the overlayer. For layer-by-layer growth the attenuation of the substrate intensities is given by the inelastic... 

Equations (48) and (50) show that the formation of a stable diatomic molecule from the free atoms is characterized by an increase of the mean electronic kinetic energy and a relatively more important decrease of the mean electronic potential energy. According to the above discussion, the chemical bond would result from the diminution of the mean potential energy of the electrons at the equilibrium distance, this effect would prevail over the augmentation of T and V ... 

The interaction of a free electron with a molecular ion is likely to lead to dissociation of the molecular ion, but the time scale of the dissociation process can, in principle, range from tens of femtoseconds to billions of years or even longer depending on the energy of the electron. The interaction of a low-energy electron (kinetic energy, e, 1 eV) with a molecular ion results in dissociative recombination (DR), a process which has a very large cross section and can be described as... 

Two especially important variants of REMPI (Johnson, et al., 1975) spectroscopy are ionization-dip (Cooper, et al., 1981) and Zero Electron Kinetic Energy (ZEKE) (Miiller-Dethlefs and Schlag, 1991 Merkt, 1997 Signorell and Merkt, 1999) photoelectron spectroscopy. Ionization-dip REMPI spectroscopy is especially useful when one wants to record free<—bound spectra from a single, selectable v, J level. Without such v, J selection, most of the oscillatory structure in a free<—bound spectrum will be washed out. One potential problem with some ionization-dip schemes is that, if the ionization transition originates from the initial level of the free<—bound transition being studied, there is a possibility that the observed linewidths will be distorted by power broadening (especially when the free final state is a weakly predissociated state with linewidth < lcm-1). 

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