Scattering length

Fig. XV-4. Schematic drawing of four streptavidin molecules bound to biotinylated lipid in a monolayer above heavy water. The scattering length density for neutron reflectivity is shown at the side. (From Ref. 30.)...

Sears V F 1999 Scattering lengths for neutrons International Tables for Crystallography 2n6 edn, vol C, ed A J C Wilson and E Prince (Dordrecht Kluwer) section 4.4.4... 

Let us take two polymers (one deuterated and one hydrogenated) and dissolve them in a solvent (or another polymer) having a scattering length b. The coherent scattered intensity can be derived from (B 1.9.117), which gives... 

Here is the position operator of atom j, or, if the correlation function is calculated classically as in an MD simulation, is a position vector N is the number of scatterers (i.e., H atoms) and the angular brackets denote an ensemble average. Note that in Eq. (3) we left out a factor equal to the square of the scattering length. This is convenient in the case of a single dominant scatterer because it gives 7(Q, 0) = 1 and 6 u,c(Q, CO) normalized to unity. 

Figure 2 Variations in the neutron scattering amplitude or scattering length as a function of the atomic weight. The irregularities arise from the superposition of resonance scattering on a slowly increasing potential scattering. For comparison the scattering amplitudes for X rays under two different conditions are shown. Unlike neutrons, the X-ray case exhibits a monotonic increase as a function of atomic weight.

In this list, p is the mass density, X b is the sum of scattering lengths of the atoms con rising the molecule, 8 is the real part of the refractive index, Gq is the critical angle, and is the critical neutron momentum. 

The data taken is normally presented as the total structure factor, F(Q). This is related to the neutron scattering lengths hi, the concentrations C , and the partial structure factor Sy(Q) for each pair of atoms i and j in the sample, by Equation 4.1-1 ... 

Po is the average scattering length density of the particle V is the volume of the particle Rg is the radius of gyration... 

Sears VF (1984) Thermal-neutron scattering lengths and cross-sections for condensed matter research. Chalk River Nuclear Laboratories, Chalk River... 

Considering only scattering at small momentum transfers, we may neglect the detailed atomic arrangements within e.g. a monomer or a solvent molecule and take into account only the scattering length densities pM or ps of such scattering units... 

Measurements of the self-correlation function with neutrons are normally performed on protonated materials since incoherent scattering is particularly strong there. This is a consequence of the spin-dependent scattering lengths of hydrogen. Due to spin-flip scattering, which leads to a loss of polarization, this... 

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). 

I(q) is the intensity at wave vector q, (bjjr-bp) is a contrast factor arising from the difference in scattering lengths of deuterated and protonated species, M is molecular weight of the deuterated polymer, c is concentration in gm/ml, S(q) is a particle scattering factor, and A contains machine constants, detector efficiency, and other fixed quantities. For the purpose of the current study, S(q) is the quantity of significance, and it is given by... 

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