A Scattering Experiments

Figure Bl.24.3. Layout of a scattering experiment. Only primary particles that are scattered within the solid angle O spaimed by the solid state detector are counted.

A scattering experiment involves a source of monochromatic radiation that interacts with electrons of the sample and a detector that measures the scattered radiation. Figure 17.1 shows a schematic of a scattering experiment. 

Fiber Symmetry Equator and Meridian. Figure 4.1 sketches a scattering experiment of a polymer sample under uniaxial load. Let us assume that the material... 

The measured intensity in a scattering experiment depends on the scattering length density contrasts of the different components i with respect to the matrix ... 

The observation of resonances in a scattering experiment requires high resolution of the collision energy, which, however, is rather difficult to achieve in a conventional molecular beam machine. In a photodissociation experiment, on the other hand, the frequency of the light beam determines the collision energy in the upper state and hence the necessary energy resolution is much easier to accomplish. More crucial for the... 

The complete degree of specification of a scattering experiment is rarely realized in an actual experiment and, normally, we will just monitor the number of C molecules in the specified state, irrespective of the quantum state and velocity of D. In order to obtain that quantity, we integrate over j>d and sum over m in Eq. (2.4). Thus,... 

This result is that used by Rutherford in his original a-scattering experiments. Note that cosec(.x) = 1 /sin(.x), cosec-is the inverse function, and... 

However, it is important to realize that although the differential cross sections in the c.m. system at 0 and — 0 are identical, the same is not true of the corresponding lab quantities. The lab differential cross section, which is actually determined in a scattering experiment, is defined by an expression exactly analogous to that for /c.m (0), that is,... 

If the particles are small, this condition may never be met. It is still possible, however, to determine a fractal dimension for such particles in a scattering experiment. This method makes use of Guinier s law, which ap-... 

In a scattering experiment a beam of electrons of momentum k hits a target. We consider the target to be represented by a potential V(r). Electrons are observed by a detector placed at polar and azimuthal angles 9,(f) measured from the direction of the incident beam, which is the z direction in a system of spherical polar coordinates (fig. 4.2). For a central potential the problem is axially symmetric. Relevant quantities do not depend on (f). The detector subtends a solid angle... 

The isotropic nature of a liquid implies that any structure factor, S(k), obtained from a scattering experiment (typically X-ray or neutron) on that liquid will contain no angular dependence (of the molecules). Thus, the Fourier transform of any S(k) will yield a radial distribution function. Recently developed techniques of isotopic substitution [5-7] have been utilized in neutron diffraction experiments in order to extract site-site partial structure factors, and hence site-site radial distribution functions, gap(r). Unfortunately, because g p(r) represents integrals (convolutions) over the full pair distribution function, even a complete set of site-site radial distribution functions can not be used to reconstruct unambiguously the full molecular pair distribution function [2]. However, it should be mentioned at... 

An extensive discussion of the PB cell model has recently been presented by Deserno and coworkers [8] (see also preceding chapter by Vlachy et al). Hence, it suffices here to delineate the main features and how this model is compared to data deriving from a scattering experiment. The PB cell model treats the system as an assembly of N rods confined in cells of radius Rq. ... 

One also sees how the expansion coefficients jJk, or if one prefers, the squeezing parameter ((k), of the Bogoliubov ground state are experimentally accessible since as noted above S (k) can in principle be determined directly from a scattering experiment. 

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