Scattering length, electron

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). 

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. 

Pertinent information concerning the interaction of free electrons with rare gas atoms is obtained from low energy scattering data in the gas phase. Table I presents the scattering lengths, a, for the rare gas atoms, defined as... 

Table I. Scattering Lengths of Electrons by Rare Gas Atom...

From the gas phase scattering data we conclude that a plane wave state for the electron in liquid helium lies at positive energy relative to the vacuum level in agreement with Sommers electron injection experiment. We proceed now to a semiquantitative treatment of free electron states in liquids characterized by a positive scattering length, which will be used to estimate the energy of interaction of a free electron with liquid helium (18). 

To obtain a rough estimate of the multiple scattering effects a model proposed by M. H. Cohen is useful (18). This model is based on the application of the Wigner-Seitz scheme to an electron in a helium crystal. Each helium atom is represented as a hard sphere characterized by a radius equal to the scattering length. The electron wave function will then be... 

Pore masking is not always easy in an X-ray s.a.s. experiment because certain supports have such high electron densities that it is impossible to find a fluid which can match them.47 It is here that neutron s.a.s. can be particularly useful since it is relatively easy to find a suitable fluid with the same neutron scattering length density as a chosen catalyst support. 

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