[18] Hubbell JH, Veigele WJ, Briggs EA, Brown RT, Cromer DT, Howerton RJ (1975) Atomic form factors,

incoherent scattering functions, and photon cross sections.

The

incoherent scattering function [S.sub.inc](Q, [omega]) in the elastic region is usually separated into an elastic "delta" component, [A.sub.0](Q)[delta]([omega]), and a quasi-elastic component, [A.sub.1](Q)L([omega]), where L([omega]) is a Lorentzian function, centered on [omega] = 0.

Normalized by the incident power, the total coherent and

incoherent scattering and transmission coefficients are obtained as follows, for TM polarization,

Further, the theoretical scattering cross sections were calculated by a numerical integration in intervals of 0.01[degrees] using form factor and

incoherent scattering functions along with the Thomson scattering cross section and Klein-Nishina cross sections in the integrand, respectively (see Hubbell et al.

Among specific topics are small-angle neutron scattering (SANS), neutron imaging, calculating real space parameters and ab initio models from isotropic elastic SANS patterns, the soft matter sample environment for SANS and neutron reflectometry, dynamics of polymers, protein dynamics studied by neutron

incoherent scattering, and pulsed neutron sources and facilities.

Fairly accurate cross section values for coherent and

incoherent scattering are available (Hubbell et.

For dry bulk samples, only

incoherent scattering background was observed, and there was no visible neutron contrast.

Note that the

incoherent scattering contributions from the hybrid components were subtracted from the SANS profiles prior to the following Porod Law analysis of the experimental data.

It is shown that with the increasing of the radius of the cylinder, the specular coherent scattering changes slightly, while the

incoherent scattering at non-specular region increases evidently, especially at the backward scattering direction, as the coupling scattering between the target and the rough surface increases simultaneously.

Finally, the q-independent background

incoherent scattering, primarily because of hydrogen atoms, was removed by scaling the scattering from a pure protonated polymer sample by the proton density in the scattering volume.

n is a low-Q Porod exponent, [[d[SIGMA](Q)/d[OMEGA]].sub.ellipsoids] was discussed above and B is a constant representing the Q-independent background mostly due to

incoherent scattering from hydrogen.