Elastic mean-free path /.?

In this section we give a proof of the Kawabata formula (52), following a method due to Kaveh (1984) and Mott and Kaveh (1985a, b). We assume that an electron undergoes a random walk, which determines an elastic mean free path l and diffusion coefficient D. If an electron starts at time t=0 at the point r0 then the probability per unit volume of finding it at a distance r, at time U denoted by n(r, t) obeys a diffusion equation... 

Fig. 5 dotted lines). The overall spectra shapes are qualitatively reproduced, except for the peak of the 50 nm spectra which is noticeably different from the experimental data. At large Ln, the predicted mini-gap is clearly smaller than in the experiment. Changing the s values or introducing a small interface resistance in the calculation did not improve the fit. We tried to take into account the dependence of the elastic mean free path with the normal metal thickness Ln, and hence the related variation of the characteristic length n... 

If d is smaller than the electron mean free path l (l l = It1 + l l, li is the elastic mean free path), the electrons flow through the contact ballistically. In opposite cases (d f>> l) they perform a diffusive motion, but if the energy relaxation length Ae remains larger than d,... 

The question may arise whether the self-energy effects are important in the normal state. These are known to be smaller than the inelastic backscattering nonlinearities in the ballistic regime [18]. If we decrease the contact size d or the elastic mean free path li in order to make the inelastic contribution negligible, the latter parameters become comparable to the Fermi wave length of charge carriers and the strong nonlinearities connected with localization occur, which masks the desired phonon structure [19]. 

The mean square variation in Rj is represented by the Debye-Waller factor, aj] X is the elastic mean-free path of the photoelectron and it is the damping term [exp(-2Rj/X)] that invariably limits back-scattering contributions to <4 A from a metal atom in a biological system. The jth. neighbor makes an angle d, with the polarization vector of the incident X ray and the term 3 cos dj averages to 1 for solutions and polycrystalline samples. 

NIST Standard Reference Database 71 NIST Electron In-elastic-Mean-Free-Path Database. Available online at http //www. nist.gov/srd/nist71. htm. 

Source Brightness (particles cm eV sr ) Elastic mean free path (A) Absorption length s (A) Minimum probe size (A)... 

Fig. 2. The geometry used in the XPS (6) data acquisition. Do is typically taken to be twice k, the elastic-mean-free-path. See text...

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