• 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)
  • 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)
  • sensitivity
  • The sensitivity of this technique, primarily depending upon scattering cross-section area, and the method has almost equal sensitivity to all light elements. (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)
  • particle
  • Further, we show that Pd nanoparticles are significantly smaller and more uniform when formed on TMV1cys in solution as compared to Pd particle growth in the absence of TMV1cys. (tufts.edu)
  • 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)
  • 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)