Electronic scattering length

The Critical Angle for total external reflection of X-rays is given by ac =(25)V2 = (4jrprf) j 2 , where ro is the electron scattering length, p is the electron density in the material (electrons per cubic A) and is the wavevector (see below). It is typically on the order of mrad. 

When an electron scatters from an atom, its phase is changed so that the reflected wave is not in phase with the incoming wave. This changes the interference pattern and hence the apparent distance between the two atoms. Knowledge of this phase shift is the key to getting precise bond lengths from SEXAFS. Phase shifts depend mainly on which atoms are involved, not on their detailed chemical environment, and should therefore be transferable from a known system to unknown systems. The phase shifts may be obtained ftom theoretical calculations, and there are published tabulations, but practically it is desirable to check the phase shifts using... 

Calibration to absolute intensity means that the scattered intensity is normalized with respect to both the photon flux in the primary beam and the irradiated volume V. Thereafter the scattering intensity is either expressed in terms of electron density or in terms of a scattering length density. Both definitions are related to each other by Compton s classical electron radius. 

In Eq. (7.21) the normalization to the scattering cross-section r2 leads to the definition of absolute intensity in electron units which is common in materials science. If omitted [90,91], the fundamental definition based on scattering length density is obtained (cf. Sect. 7.10.1). 

Figure 6.7 The principle of LEED is that a beam of monoenergetic electrons scatters elastically from a surface. Because of the periodic order of the surface atoms, electrons show constructive interference in directions for which the path lengths of the electrons differ by an integral number times the electron wavelength. Directions of constructive interference are made visible by collecting the scattered...

The spectral distribution of light scattered from a plasma depends on its wavelength Xq, the electron Debye length and the scattering... 

Implicit in such a dependence is the recognition that scattering lengths of thermal and epithermal electrons are similar. A least-squares fit of the data for compounds containing only hydrogen and carbon leads to the solid line shown in Fig. 1 for which a = 0.25 and X = 0.33, for in cm /Vs. 

When the optical length of the sample is much shorter than the other factors such as the length of the electron pulse, the response function takes on a Gaussian shape. As the optical length increases, the shape of the response function becomes trapezoidal. Furthermore, a thick sample causes the prolongation of the electron pulse by electron scattering, which leads to the degradation of time resolution. Therefore the experiment to observe ultrafast phenomena requires the use of a thin sample. 

However, for the resistivity of non-crystalline materials at low temperatures, the most important effect is on Lb the inelastic diffusion length. We have seen (Chapter 1, Section 10) that thisisgivenbyLi=(DTi)1/2 and that there is a term in the conductivity proportional to //Lj, so that electron-electron scattering gives a negative term in the resistivity proportional to T with v between 1 and J. 

The range of coherence follows naturally from the BCS theory, and we see now why it becomes short in alloys. The electron mean free path is much shorter in an alloy than in a pure metal, and electron scattering tends to break up the correlated pairs, so dial for very short mean free paths one would expect die coherence length to become comparable to the mean free path. Then the ratio k i/f (called the Ginzburg-Landau order parameter) becomes greater than unity, and the observed magnetic properties of alloy superconductors can be derived. The two kinds of superconductors, namely those with k < 1/-/(2T and those with k > l/,/(2j (the inequalities follow from the detailed theory) are called respectively type I and type II superconductors. 

---