• displaystyle
  • where m and n are nonnegative integers with n ≥ m, φ is the azimuthal angle, ρ is the radial distance 0 ≤ ρ ≤ 1 {\displaystyle 0\leq \rho \leq 1} , and Rmn are the radial polynomials defined below. (wikipedia.org)
  • Ψ p ∘ ⟩ {\displaystyle \vert {\Psi _{\mathbf {p} }^{\circ }}\rangle } is the corresponding free scattering solution sometimes called the incident field. (wikipedia.org)
  • photons
  • In X-ray scattering, photons interact with the electronic cloud so the bigger the element, the bigger the effect is. (wikipedia.org)
  • Owing to the small illuminated sample volume and the wastefulness of the collimation process - only those photons are allowed to pass that happen to fly in the right direction - the scattered intensity is small and therefore the measurement time is in the order of hours or days in case of very weak scatterers. (wikipedia.org)
  • beam
  • The incident beam strikes the sample under a small angle close to the critical angle of total external x-ray reflection. (wikipedia.org)
  • The intense reflected beam as well as the intense scattering in the incident plane are attenuated by a rod-shaped beam stop. (wikipedia.org)
  • In this case, the reflected beam from the substrate has a similar strength as the incident beam and thus the scattering from the reflected beam from the film structure can give rise to a doubling of scattering features in the perpendicular direction. (wikipedia.org)
  • This as well as interference between the scattering from the direct and the reflected beam can be fully accounted for by the DWBA scattering theory. (wikipedia.org)
  • As the SAS measurements are performed very close to the primary beam ("small angles"), the technique needs a highly collimated or focused X-ray or neutron beam. (wikipedia.org)
  • SANS usually uses collimation of the neutron beam to determine the scattering angle of a neutron, which results in an ever lower signal-to-noise ratio for data that contains information on the properties of a sample at relatively long length scales, beyond ~1 μm. (wikipedia.org)
  • This is because the comparatively weak scattering signal from the sample has to be measured in the immediate vicinity of the direct beam. (panalytical.com)
  • Thus the scattering is centro-symmetrically distributed around the primary X-ray beam and the scattering pattern in the detection plane consists of circles around the primary beam. (wikipedia.org)
  • The beam can be either polaarized with supermirrors or with polarized 3He gaz The neutron precession in an induction field is rather small. (wikipedia.org)
  • Moreover, the angle of incidence that an ion beam makes with the sample must also be taken into account for correct analysis of the sample. (wikipedia.org)
  • incident
  • In the interpretation of GISAS images some complication arises in the scattering from low-Z films e.g. organic materials on silicon wafers, when the incident angle is in between the critical angles of the film and the substrate. (wikipedia.org)
  • Generally in scattering theory and in particular in quantum mechanics, the Born approximation consists of taking the incident field in place of the total field as the driving field at each point in the scatterer. (wikipedia.org)
  • It is accurate if the scattered field is small compared to the incident field on the scatterer. (wikipedia.org)
  • micelles
  • We study the structure and reorientation dynamics of nanometer-sized waterdroplets inside nonionic reverse micelles (water/Igepal-CO-520/cyclohexane) with time-resolved mid-infrared pump-probe spectroscopy and small angle x-ray scattering. (uva.nl)
  • We find that even small micelles contain a large fraction of water that reorients at the same rate as water in the bulk, which indicates that the polyethylene oxide chains of the surfactant do not penetrate into the water volume. (uva.nl)
  • electron
  • The Ewald sphere has a curvature ten times smaller than in the low energy case and allows whole regions to be mapped in a reciprocal lattice, similar to electron diffraction. (wikipedia.org)
  • geometry
  • It included Rfree cross-validation for model-to-data match, bond length and angle parameters for covalent geometry, and sidechain and backbone conformational criteria. (wikipedia.org)
  • vector
  • The refraction correction applies to the perpendicular component of the scattering vector with respect to the substrate while the parallel component is unaffected. (wikipedia.org)
  • One interpretation of the scattering vector is that it is the resolution or yardstick with which the sample is observed. (wikipedia.org)
  • sample
  • In biological systems hydrogen can be exchanged with deuterium which usually has minimal effect on the sample but has dramatic effects on the scattering. (wikipedia.org)
  • Forward scattering and penetration make sample environments easy and straight forward. (wikipedia.org)
  • Depth resolution is depended upon stopping power of heavy ions after interactions with sample, and the detection of scattered primary ions is reduced due to the narrow scattering cone of heavy ions scattering from light elements. (wikipedia.org)
  • interpretation
  • When observing a remote source through the Earth atmosphere the light scattering gives rise to a spurious signal which dims the source and compromises the measurement interpretation. (spie.org)
  • parameters
  • The P2VP molecules are either assumed to be Gaussian chains or they fill a shell of thickness L with possible water penetration.The fitting of the models to the experimental scattering cross sections leads to important structural parameters like the aggregation number, the core radius, the gyration radius and the thickness of the P2VP shell. (ac.be)
  • depend
  • Since the overall scatter of a molecule depends on the scatter of all its components, this will depend on the ratio of hydrogen to deuterium in the molecule. (wikipedia.org)
  • different
  • These features are persistent across many images and retain their direction and overall morphology when recorded at different scan angles. (epfl.ch)