Scattering length incoherent

Table 1 Coherent Scattering Lengths, Incoherent Scattering Cross Sections, and Absorption Cross Sections for Some Elements...

Incoherent scattering length Incoherent scattering length for the hydrogen atom unit of the neutron cross-section, in 10 atom Back-scattering... 

Nuclei Coherent scattering length Incoherent cross-section... 

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... 

In Eq. 6.1, p = b dJM, where is the scattering length of carbon, its mass density, and the molecular weight, q is the magnitude of the transfer wave vector, g=(47t/)i)sin( /2). An important difference between SAXS and SANS is the contribution in the latter case from incoherent scattering, I This originates... 

To recognize island formation one takes advantage of the difference between coherent and incoherent diffraction from a set of N identical scatterers. If the waves scattered off the individual scatterers are incoherent in their phases, the observed intensity will be proportional to N (addition of intensities). If, however, these scattered waves are coherent, the intensity will be proportional to N (addition of amplitudes). Incoherence occurs either when the incident wave arrives with incoherent phases at different scatterers, which occurs in practice for scatterers separated by at least the coherence length of the incident beam, or when the scatterers themselves are located incoherently, i.e. are disordered. 

Table 2 Bound scattering lengths, i>(fm) and cross section for selected isotopes and for selected naturally occurring isotopic mixtures of the elements u(hams, 1 bam = 100 fm ). Z, atomic number A, mass number I, spin of the nuclear groimd state i>coh> bine, coherent and incoherent scattering lengths ffa, ffeCh, coherent and incoherent cross sections ffa, absorption cross section for 2.2 km s neutrons ...

Some expansion and development of the incoherent term will help us cast it in a more usefiil form. It is important to note that it has been assumed that there is no correlation between the particular value of the neutron scattering length and the location of the scatterer within the sample. We can use this to write bjb = bj b for j so that in equation (8) above, only the terms where j = k survive leaving ... 

Element Coherent scattering length (cm X 10 ) Incoherent scattering cross section (cm x 10 ) Absorption cross section (cm X 1024)... 

The other terms account for an incoherent elastic background that comes about because of the different scattering length of atoms on different sites. 

To an incident beam of neutrons the atoms of chorine are a random mixture of Cl and Cl. We calculate the proportions of neutrons scattered coherently and incoherently from chlorine (75% Cl, 25% Cl) with coherent scattering lengths, icoh (m) from Appendix 1. The average scattering length, which provides the coherent signal, is... 

---