Incoherent Scattering Cross Sections Research Articles

Fourth- and higher-order small-perturbation solution for scattering from dielectric rough surfaces

A recursive solution of the small-perturbation method for rough surface scattering is presented. These results permit fourth- and higher-order corrections to rough surface scattering coefficients to be determined in a form that explicitly separates surface and electromagnetic properties. Sample results are presented for the fourth-order correction to the specular reflection coefficient of a rough surface and the sixth-order correction to incoherent scattering cross sections.

A precise measurement of the spin-dependent neutron scattering length of 3He

The poor knowledge of the spin-dependent neutron scattering length of 3He has until now handicapped nuclear four body theory and the interpretation of excitations in the quantum liquid. We have measured, for the first time directly, the real part of the bound incoherent neutron scattering length, bi′ of 3He. A neutron spin echo spectrometer was used to detect pseudomagnetic precession of polarised neutrons passing through polarised 3He gas. Any absolute calibrations of sample and beam parameters were avoided using simple transmission measurements with non-polarised neutrons. The only a priory information required was the spin-dependent neutron absorption cross section of 3He. The result is bi′ = -2.365(20) fm, which reduces the prior uncertainty by a factor 30. The corresponding new value of the bound incoherent scattering cross section is σi = 1.532(12) barn. Including the known value of the coherent neutron scattering length, we obtain new values for the real parts of the free triplet and singlet neutron scattering lengths, a-′ = 7.370(58) fm and a+′ = 3.278(53) fm.

Inelastic scattering of [formula omitted] photons at small momentum transfers by Ti, Fe and Ni elements

Differential incoherent scattering cross sections of 59.54 keV photons were measured for Ti, Fe and Ni elements at scattering angles 40–135° employing a reflection geometry set up and a graded shielding arrangement. The measurements were performed using a point source of Am-241 radioisotope as photon source and a Si(Li) detector. Thin targets have been used to minimize the contribution of multiple scattered photons to the inelastic scattered peak. The product of the intensity of incident photons and geometrical factors was eliminated using the K X-ray yields from same elements. The comparison of the measured cross sections with Klein–Nishina theory shows electron-binding effects becoming significantly large at small scattering angles. Incoherent scattering functions S( x, Z), corresponding to momentum transfer values 1.644– 4.442 A ̊ −1 were extracted from the measured cross sections and were compared with theoretical predictions. The results are compared with the non-relativistic Hartree–Fock values.

Incoherent scattering of 59.54 keV gamma rays for some rare earth elements at low photon momentum transfers

Incoherent scattering functions S(x, Z) for six rare earth elements were evaluated from accurately measured whole atom differential incoherent scattering cross sections for 59.54 keV γ-rays scattered at 30°, 45°, 60° and 90° scattering angles corresponding to 1.24, 1.84, 2.40 and 3.39 Å −1 photon momentum transfers. Our results for S(x, Z) are the first for these rare earth elements.

Incoherent scattering of 59.54 keV γ-rays at small momentum transfers

Whole atom differential incoherent scattering cross sections for 59.54 keV γ-rays were measured for a number of elements in the region 29⩽ Z⩽82 at scattering angles 90, 60, 45 and 30° employing a reflection geometry set up and a graded shielding arrangement. A 6 cm 3 HPGe detector was used to detect the scattered γ-rays. All the 49 cross sections reported in this paper constitute the first experimental measurement and serve to fill the existing gaps in the cross-section data. The comparison of the measured cross sections with Klein–Nishina theory shows electron binding effects becoming significantly large at small scattering angles and for high Z elements. Incoherent scattering functions S( x, Z), corresponding to momentum transfer values 3.395, 2.4, 1.84 and 1.242 Å −1 were extracted from the measured cross sections and were compared with the theoretical predictions. The non-relativistic Hartree–Fock theory is found to be comparatively better than the Thomas–Fermi model. At small momentum transfer values and for high Z elements experimental values deviate more from Hartree–Fock theory also suggesting the need for a more rigorous second-order S-matrix calculations.

A new method for the determination of incoherent differential scattering cross sections

With the help of a Si(Li) detector, incoherent scattering cross sections of Ag, In and Sn were determined from 40°-135° in the case of 59.54 keV gamma rays of Am-241. A new method has been developed to determine differential incoherent scattering cross sections of elements. This method is based on simultaneous measurement of fluorescence radiation and scattered radiation, thus avoiding problems with measuring the source strength and source-to-detector solid angle. The results are compared with the non-relativistic Hartree-Fock values of Hubbell et al.

Assessment of detector calibration materials for SANS experiments

The properties of incoherent-scattering samples that are used as calibrants for small-angle neutron scattering (SANS) experiments have been investigated using time-of-flight analysis of the wavelengths of the scattered neutrons. Such samples are employed both as secondary intensity standards and to calibrate the relative efficiency of detectors. The data show that care must be taken to allow for wavelength dependence of the detector efficiency if the measured results are to be understood or compared with respect to different instruments. At ambient temperatures, glassy polymer sheets of poly(methyl methacrylate) or polycarbonate offer better performance as secondary standards than water. The results reveal the limits for the use of transmission measurements to estimate incoherent scattering cross sections. Use of uniform scattering as a basis for a measure of the effective cross section is, in practice, instrument dependent, owing to extensive inelastic multiple scattering.

Mass operator for wave scattering from a slightly random surface

This paper deals with the mass operator representing multiple-scattering effects in the theory of wave scattering from a slightly random surface. By means of the stochastic-functional approach, a recurrence equation for the mass operator is obtained in the form of an iterative integral. However, its solution oscillates in a non-physical manner against the number of iterations. Next, the recurrence equation may be regarded as a nonlinear integral equation, when the number of iterations goes to infinity. An analytical solution of the nonlinear integral equation is presented for a special case in which the roughness spectrum is the Dirac delta function. Then, the nonlinear integral equation is solved numerically for the Gaussian roughness spectrum by iteration, starting from such an analytical solution. It is shown that only a few iterations are required to obtain the mass operator, even when the correlation distance is small. Effects of the mass operators on the coherent reflection coefficient and the incoherent scattering cross section are calculated and shown in figures.

Whole-atom differential incoherent-scattering cross sections at 279.2 keV

The incoherent-scattering cross sections are determined at 279.2 keV γ-ray energy in the angular range 30° - 105° in Ni, Zn, Ag, Cd, In, Sn, and Pb. The measurements were carried out using an NaI (Tl) detector coupled to a single channel analyser. The scattering functions so determined experimentally have been compared with values evaluated on the basis of non relativistic SCF Hartree-Fock wave function. A reasonable agreement is observed between the theory and experiment within the limit of experimental errors. PACS Nos.: 52.25Nr and 32.80-t

Incoherent scattering of 59.54 keV gamma rays by selected elements in the atomic region 29⩽Z⩽74

Abstract Incoherent scattering cross-sections for 11 moderate to high atomic number elements have been experimentally determined using 59.54 keV gamma rays emitted by the radionuclide 241 Am. Measurements were performed using a standard back-scattering geometry set up to obtain scattering angles of 145°, 154° and 165°. Resulting photon momentum transfers were in the range 4.58⩽ x ⩽4.76 A −1 . High purity (better than 99.9%) foils of Cu, Zn, Zr, Nb, Mo, Ag, Cd, In, Sn, Ta and W were used as targets. Results of measurements, good to within a conservative experimental uncertainty of 10%, reveal no systematic trend in departure from agreement with tabulated theoretical incoherent-scattering cross-sections based upon non-relativistic wave functions.

Whole-atom differential incoherent-scattering cross sections at 279.2 keV

Whole-atom differential incoherent-scattering cross sections at 279.2 keV

Quasielastic neutron scattering study on rotational aromatic groups of a thermotropic copolyester (vectra)

The rotational motion of aromatic groups which constitute a thermotropic copolyester, vectra was investigated in terms of the quasielastic neutron scattering (QENS) originating from incoherent scattering of hydrogen. Vectra which is a random copolyester of p-hydroxybenzoic acid (HBA) and 2-hydroxy-6-naphthoic acid (HNA) with a faction of 73/27 (mol/mol), gives rise to the nematic phase transition at Tm=558 K from semicrystalline phase, i.e., a mixture of crystalline and amorphous phases (Tg=393 K). In the region above Tm, the elastic incoherent scattering cross section due to hydrogen, obtained for optical geometry in which q vector is normal to the molecular axis of vectra, was successfully decomposed into (i) the Debye–Waller factor due to vibrational hydrogen, (ii) the elastic incoherent structure factor (EISF) for the rotational aromatic groups with hydrogen and (iii) the QENS for the rotational aromatic groups with hydrogen. The QENS spectra and EISF thus obtained were well reproduced by a free rotational model for the aromatic groups, in which residing sites for hydrogen on the rotational circle is infinite. On the other hand, in the solid (semicrystalline) phase below Tm, the QENS spectra and EISF became less q dependent with decreasing temperature; these observations agree qualitatively with a more restricted motion, e.g., a jump rotation having finite residing sites for hydrogen.

Photon interaction cross-sections and anomalous scattering factors of Cu and Ag

Total attenuation cross sections of copper and silver have been measured in the energy range 5 to 85 keV in a narrow beam good geometry set up using X- andγ-rays emitted from radio isotopes, by employing a high resolution hyper pure germanium detector. From the measured values, the photoeffect cross-sections have been derived by subtracting a small contribution of the sum of the theoretical coherent and incoherent scattering cross sections. The photoeffect cross-sections so obtained are found to be in better agreement with the unrenormalized values of Scofield [10]. These photoeffect cross-sections have been used to evaluate the dispersion corrections (also called anomalous scattering factors)f + andf″ for the forward Rayleigh scattering amplitude by a numerical evaluation of the dispersion integral that relates them at the energies at which the cross-sections have been measured. To thef + values so obtained, the relativistic corrections proposed by different investigators are included separately and the valuesf′ so obtained are compared with the available data and discussed. Possible conclusions are drawn from the present study.

A microwave backscattering model for deformed first-year sea ice and comparisons with SAR data

Like-polarized backscattering from randomly tilted ice blocks in deformed first-year sea ice is modeled. An approximation for the coherent and incoherent scattering cross section of a single ice block is formulated and validated by comparison with moment method computations. It is found that the model is accurate for lossy ice blocks but underestimates the scattering when the loss is low, which is attributed to multiple scattering within the blocks. The backscattering coefficient is evaluated by averaging over an ensemble of blocks with a distribution of slopes and effects of shadowing are estimated. In situ measurements of ice ridge properties in the Baltic Sea are used as input when comparing the model results with coincident ERS-1 SAR data. The model is found to agree with the data to within 1.5 dB, where the discrepancies are mainly due to the uncertainty of the dielectric loss factor in the ice blocks. The model also shows good agreement with airborne 5.3 GHz SAR data of a first-year shear ridge in the Beaufort Sea for incidence angles between 25-50.

Rayleigh and Compton scattering cross sections for low, medium and high Z elements in the energy region 23.18 ⩽ E ⩽ 30.85 keV

Using nearly monoenergetic unpolarised Kα x-ray photons coherent (Rayleigh) and incoherent (atomic Compton) scattering cross sections in the atomic region 13 ⩽ Z ⩽ 82 have been measured at 23.18, 24.14, 25.19, 26.27 and 30.85 keV. Experimental scattering cross sections in the momentum transfer region 1.322 h Å−1 ⩽ q ⩽ 1.759 h Å−1 [q = sin (θ/2)λ(Å)] were obtained at an angle of 90°. Experimental coherent scattering cross sections are in good agreement with second order S-matrix calculations, compared to theoretical estimates based on form factor approximations. Experimental incoherent scattering cross sections are higher than the theoretical estimates calculated using non-relativistic incoherent scattering functions for low and medium Z elements and lower for heavy elements. The latter is due to the binding effects at low photon energies.

Elastic and compton scattering cross sections in the atomic region 12 ⩽ Z ⩽ 82

Coherent and Compton scattering cross sections for the elements Mg, Al, Mn, Ni, Cu, Y, Mod, Pd, Ag, Cd, In, Sn, Sb, Au and Pb have been measured at 32.06 keV (Ba Kα) and 33.29 keV (La Kα) x-ray energies. Measurements have been performed using an x-ray tube with a secondary excitor system as the excitation source instead of radioisotopes. In order to improve the efficiency of the detection system the excitation source detector and the sample assembly were placed in a vacuum chamber and a pressure of 10 −2 mbar was maintained throughout the measurements. The present system reduced the scattering and background effects considerably and improved the monochromaticity. Experimental coherent scattering cross sections are compared with the normalised integrated coherent scattering cross sections. Experimental results are higher around the edges indicating the oscillatory nature of coherent intensity, resonance behaviour and fine structure effects. Experimental incoherent scattering cross sections are higher than the theoretical estimates for low medium Z elements and lower for heavy elements. The latter is due to the effect of electron binding at low photon energies for heavy elements.

Coherent and incoherent scattering of low-energy X-ray photons in the atomic region 13 ≤ Z ≤ 82

Coherent- and incoherent-scattering cross sections for the elements Al, Cu, Y, In, Au, and Pb were measured using nearly monoenergetic unpolarized 35.86 and 39.96 keV X-ray beams with high-resolution Si (Li) detectors. Bremsstrahlung radiation from an X-ray tube was used to excite nearly monoenergetic X-rays in secondary targets. To improve the efficiency of the detection system the excitation source, detector, and the target assembly were placed in a vacuum chamber and a pressure of 10−2 mbar was maintained throughout the measurements. This system considerably reduced the background and scattering effects and improved the monochromacy. Experimental coherent-scattering cross sections are compared with the normalized integrated coherent-scattering cross sections calculated using the relativistic, nonrelativistic, and relativistic-modified form factors. Experimental incoherent-scattering cross sections are compared with the theoretical values, calculated using the nonrelativistic incoherent-scattering function. Good correspondence is observed between experimental and theoretical values in the given energy region.

Coherent and incoherent scattering of 14.93, 17.44 and 21.12 keV photons from Al, Cu, Sr, Cd, Ce, Pr, Sm, Pt, Au and Pb

Coherent and incoherent scattering cross sections for the elements Al, Cu, Sr, Cd, Pr, Ce, Sm, Pt, Au and Pb have been measured at 14.93, 17.44 and 21.12 keV Kα x-ray energies. Measurements have been performed using an x-ray tube with a secondary exciter system as the excitation source instead of radioisotopes. Bremsstrahlung radiation from the x-ray tube has been used to excite nearly monoenergetic x-rays in secondary targets. In order to improve the efficiency of the detection system the excitation source detector and the target assembly were placed in a vacuum chamber and a pressure of 10−2 mbar is maintained throughout the measurements. The coherently and incoherently scattered intensity by the sample into the detector has been detected at an angle of 90° using low energy HP Ge and Si (Li) photon detectors. The present system considerably reduced the scattering and background effects and improved the monochromacy. Experimental scattering cross sections are compared with the normalised integrated cross section based on form factor and incoherent scattering approximations. The present experimental results do not strongly support any set of theoretical values. More accurate experimental results and extended exact calculations of atomic form factors at more closely spaced values of incident x-ray energies and scattering angles are clearly needed if more meaningful comparison between experiment and theory are to be possible.

Whole-atom integral incoherent scattering cross sections of elements Na, Cl, K, Cu, Br, Rb, Ag, Cd, I, and Hg at 661.6 keV.

The whole-atom integral incoherent-scattering cross sections of elements Na, Cl, K, Cu, Br, Rb, Ag, Cd, I, and Hg have been derived with the aid of the mixture rule from the incoherent-scattering cross sections of their simple halides. The cross sections of the halides are extracted from their total attenuation cross sections measured by performing transmission experiments in a modified narrow-beam setup. The results are found to be in good agreement with the values assembled by Hubbell et al. [J. Phys. Chem. Ref. Data 4, 471 (1975)] that are interpolated to 661.6 keV.

Verification of incoherent scattering functions at intermediate photon momentum transfer

Experimental whole atom differential incoherent scattering cross sections were measured for Cu, Mo, Ag, Cd, Sn, Pr, Sm, Gd, Dy, Ho, Yb, Ta, W, Th and U for the 90 degrees scattering of 145.4 and 84.3 keV gamma rays. The scattering experiments were conducted in a reflection geometry set up with a graded shielding arrangement. A 133 cm3 HpGe detector was used to detect the scattered gamma rays. The cross sections were measured using Al as standard. From the measured cross sections the incoherent scattering functions were extracted. The results are compared with theory and with the experimental values reported in literature for available cases. The electron binding effects and the validity of the incoherent scattering functions at intermediate momentum transfer are discussed.