Neutron scattering from Au,Hg, and Tl

The elastic and the inelastic scattering of fast neutrons from Au, Hg, and Tl was studied at incident neutron energy intervals of ~50 keV from 0.3 to 1.5 MeV. The differential elastic scattering cross sections were determined approximately every fifteen degrees from 20 to 145 degrees. The cross sections for the inelastic excitation of states in Au at 77, 270, 409, 520, 540, 740, 830, 940, 1120, and 1220 keV; in Hg at 160, 208, 440, 610, 980, and 1120 keV; and in Tl at 205, 279, 615, 680, 930, and 1080 keV were determined. The measured elastic scattering cross sections were compared with the results of optical model calculations and evidence for a decrease in the imaginary part of the potential near the doubly closed shell atA=208 was observed. The results of Hauser-Feshbach calculations, utilizing known spin and parity assignments together with those estimated from nuclear systematics, were in qualitative agreement with the measured inelastic excitation functions. The effect of resonance width fluctuations was considered in the context of the experimental results.     

Neutron scattering from Bismuth,Strontium and Sodium at 14.8 MeV

Differential cross sections for the elastic and inelastic scattering of 14.8 MeV neutrons from Bi, Sr and Na have been measured with four neutron detectors participating in a time-of-flight system which had an energy resolution of 900 keV for the incident neutrons. The whole procedure was checked by scattering from carbon. For the elastic scattering of Bi, Sr and Na satisfactory optical-model fits were obtained. The absolute cross sections for excitation of collective states are compared to the distorted-wave theory for direct reactions, and a reasonable agreement has been found. The nuclear deformation parameters are extracted and compared to the values from other experiments.     

Neutron elastic and inelastic scattering from 28Si, 32S and 34S

Differential cross sections for the elastic and inelastic scattering of neutrons from the sd-shell nuclei ²⁸Si, ³²S and ³⁴S have been measured in the 20–26 MeV region. The data are analyzed in terms of the rotation-vibration (²⁸Si) and anharmonic vibration (^{32, 34}S) collective models. Isoscalar E2, E3 and E4 transition matrix elements are obtained from the normalized multipole moments of the real potential and the results are compared with those obtained from electromagnetic probes and from nuclear structure theoretical calculations.     

Neutron scattering studies of the structure and dynamics of nanobundles of single-wall carbon nanotubes

Elastic and inelastic neutron scattering are used to study the structure and dynamics of single-wall carbon nanotubes (SWNT) self-assembled into nanobundles (NBSWNT). Suspensions of NBSWNT are characterized by small-angle neutron scattering. Neutron diffraction is used as a useful tool to study the structure of both the SWNT and NBSWNT. Calculations on finite-size bundles are compared to the data in order to estimate the distribution of tube diameters. Finally, we present time of flight inelastic scattering measurements of the phonon density of states and discuss the main features of the spectra in comparison with calculations. Received: 9 June 1999 / Accepted: 3 August 1999 / Published online: 27 October 1999     

Neutron scattering length of terbium structure refinement and magnetic moments of terbium iron garnet

The neutron scattering length of terbium was redetermined from powder data on terbium iron garnet (TbIG) and TbO₂ by the profile analysis technique. The mean value obtained is b (Tb) = 0.735(10) x 10^?12cm. Furthermore the positional and thermal parameters of TbIG have been refined from single crystal X-ray and neutron powder data. The results from both experiments agree well. The X-ray data from a sphere of diameter φ = 282μm were collected by MoKα radiation. The refinement was carried out including an extinction parameter which was also applied to correct for anomalous transmission. The powder data were treated by the profile analysis technique where the structural parameters and the magnetic moments were refined simultaneously. Two slightly different form factor curves were applied for Fe³⁺ in the crystallographic sites. The magnetic moments for the iron ions were found to be μ = 3.69(10)μ_B for the octahedral and 3.65(10)μ_B for the tetrahedral site at room temperature. The moment for terbium is μ = 1.15(09)μ_B and the whole magnetisation for one formula unit is 0.12(0.40)μ_B. The observed moments of Fe³⁺ are considerably reduced as compared to the free ion spin only value which was calculated from a Brillouin function for $\text{S =}\text{5}\text{2}$ to be 4.34μ_Bat 300 K.     

Neutron scattering study of the structure and dynamics of butane adsorbed on graphite2

Inelastic and elastic neutron scattering have been used to study the dynamics and structure of monolayer films of butane (CH₃(CH₂)₂CH₃) adsorbed on a graphitized carbon powder at 77 K. In addition to the intramolecular torsional modes found in the bulk solid, the inelastic spectra of the films contain new excitations associated with coupling of the molecular motion to the substrate. Model calculations are described which show the monolayer excitation spectrum to be sensitive to the orientation of the adsorbed butane molecule and the location and strength of the bonds to the substrate. For butane we infer that the molecule is adsorbed with the plane of the carbon skeleton parallel to the graphite layers. We have also used elastic neutron diffraction to investigate the possibility of long-range order in the butane films. Although we have not found Bragg peaks indicative of an ordered two-dimensional structure in a 1.5 layer film at 81 K, a large modulation of the graphite 002 Bragg reflection is observed. The experimental approach discussed here would seem to be applicable to the study of the dynamics, molecular orientation, and bonding of other hydrogenous adsorbates as a function of film thickness and temperature. Measurements are presently being extended to propane (CH₃CH₂CH₃) and ethane (CH₃CH₃) adsorbed on graphite.     

The structure factor for liquid nitrogen and liquid oxygen from neutron scattering studies

The structure factor, S(Q), has been measured for liquid nitrogen at 77 K and liquid oxygen at 84 K by neutron diffraction over a range of momentum transfer, Q, from 0·3 to 7·3 Å^-1. In the case of oxygen a correction for magnetic scattering has been included.

The liquid structure factor for nitrogen compares well with that obtained from X-ray diffraction measurements but there are significant discrepancies in the case of oxygen. These may be partially attributed to uncertainty in the form factor for paramagnetic scattering.

The data have been analysed in terms of several different models for the orientational correlation between neighbouring molecules. The results are particularly sensitive to uncertainties in the absolute normalization of the data, the inter-nuclear distance for the molecular structure and Placzek corrections; the effect of these errors is considered in detail. It is shown that some form of orientation correlation must exist but its precise nature could not be obtained from the present data.     

Acoustic scattering from density and sound speed gradients: modeling of oceanic pycnoclines

A weak-scattering model that allows prediction of acoustic scattering from oceanic pycnoclines (and the accompanying sound speed gradients) based on hydrographic profiles is described. Model predictions, based on profiles from four locations, indicate that scattering from oceanic pycnoclines is measurable using standard scientific sonars operating at frequencies up to 200 kHz but generally only for pycnocline thicknesses less than 10 m. Accurate scattering models are key to assessing whether acoustic remote sensing can be used to map oceanic pycnoclines and for determining whether scattering from pycnoclines needs to be taken into account when estimating, for instance, zooplankton abundance from acoustic data.     

Acoustic beam scattering and excitation of sphere resonance: Bessel beam example

The exact partial wave series for the scattering by a sphere centered on an ideal Bessel beam was recently given by Marston ["Scattering of a Bessel beam by a sphere," J. Acoust. Soc. Am. 121, 753-758 (2007)]. That series is applied here to solid elastic spheres in water and to an empty spherical shell in water. The examples are selected to illustrate the effect of varying the beam's conical angle so as to modify the coupling to specific resonances in the response of each type of sphere considered. The backscattering may be reduced or increased depending on properties of the resonance and of the specular contribution. Changing the conical angle is equivalent to changing the beamwidth. Some applications of the Van de Hulst localization principle to the interpretation of the partial wave series and to the interpretation of the scattering dependence on the beam's conical angle are discussed. Some potential applications to the analysis of the scattering by spheres of more general axisymmetric beams are noted.     

Neutron scattering lengths of the isotopes of thulium,ytterbium and lutetium

Coherent neutron scattering lengths and total cross sections have been measured on samples of ordinary Tm, Yb and Lu and on isotopically enriched compounds. From the experimental data for 0.57 meV neutron energy the following data were obtained: the coherent scattering lengths (in fm) of the bound atoms¹⁶⁹Tm (7.07+0.03);¹⁷⁰Yb (6.8±0.1);¹⁷¹Yb (9.7±0.1);¹⁷²Yb (9.5±0.1);¹⁷³Yb (9.56±0.10);¹⁷⁴Yb (19.2±0.1);¹⁷⁶Yb (8.7± 0.1); Yb (12.41±0.03);¹⁷⁵Lu (7.28±0.09);¹⁷⁶Lu (6.3±0.2) and Lu (7.21±0.03); the thermal absorption cross sections (in barn) for¹⁶⁹Tm (100±2); Yb (34.8±0.8) and Lu (74±2). In combination with the resonance parameters the measured coherent scattering lengths allowed the determination of potential scattering radii R′ which are of particular interest for the permanently deformed and deformable nuclei in the rare-earth region.     

On the influence of the scattering particle concentration on the probe beam coherence, signal quality, and measuring accuracy of interferometric systems

Experimental data on the influence of the scattering particle concentration in a turbid medium on the probe beam coherence, statistic characteristics of responses, and measuring accuracy of interferometric systems are reported. It is shown that even if the power of probe beams is low (on the order of 10 mW) and the concentration of scattering particles is so high that they attenuate the input power by several hundred times, light beams almost completely retain time and spatial coherences and their respective interference pattern is highly contrast. The spectral characteristics of the signal, signal-to-noise ratio, and measuring accuracy remain nearly unchanged.     

Numerical simulation of Gaussian beam scattering by complex particles of arbitrary shape and structure

An efficient numerical method based on the surface integral equations is introduced to simulate the scattering of Gaussian beam by complex particles that consist of an arbitrarily shaped host particle and multiple internal inclusions of arbitrary shape. In particular, the incident focused Gaussian beam is described by the Davis fifth-order approximate expressions in combination with rotation defined by Euler angles. The established surface integral equations are discretized with the method of moments, where the unknown equivalent electric and magnetic currents induced on the surfaces of the host particle and the internal inclusions are expanded using the Rao–Wilton–Glisson (RWG) basis functions. The resultant matrix equations are solved by using the parallel conjugate gradient method. The proposed numerical method is validated and its capability illustrated in several characteristic examples.     

Dynamic structure factor of diamond and LiF measured using inelastic X-Ray scattering

The dynamic structure factors S(q-->,omega) of diamond and LiF have been measured using inelastic x-ray scattering. The experimental data are compared to results of ab initio calculations, which take into account the interaction of the excited electron with the remaining hole. In diamond, the vicinity of the indirect band gap and its momentum dependence are studied. In LiF, a larger energy range, which covers the fundamental exciton, the plasmon, and several interband transitions, is investigated. Calculations and measurements agree quite well and emphasize the need to properly include the interaction of the excited electron in the conduction band with the hole in the valence band.     

Computation and analysis of the Bessel beam scattering by a submerged elastic sphere

Taking an elastic sphere for example,the acoustic scattering of a submerged object illuminated by a Bessel beam is studied.The partial wave series representation for an elastic sphere has been extended to the case of Bessel beam scattering.Referring to the scattering of a plane wave,the peak to peak intervals in backscattering form function caused by the interference of the specular wave and the Franz wave have been analyzed in geometry.The influence of the characteristic parameterβof a Bessel beam on the peak to peak intervals has been indicated,and a predictive formula of the peak to peak intervals has been established for the first time.Meanwhile the elastic scattering of each partial wave has been separated based on the Resonance Scattering Theory.The influence ofβon the pure elastic resonance has been studied further.The results show that selecting specificβcan reduce the contribution of a certain partial wave.Therefore the resonance at the corresponding frequency and the nearby region in the backscattering is remarkably suppressed.The work of this paper could be helpful to the applications of Bessel beams on the acoustic detection of submerged objects.     

Neutron scattering studies of the solid tetramethyl compounds of silicon,germanium and tin

A study is presented of both quasi-elastic and inelastic neutron scattering on Si(CH₃)₄, Ge(CH₃)₄ and Sn(CH₃)₄. Within the applied resolution no quasi-elastic scattering was detected for the silicon compound and only a small broadening of the elastic line for the germanium compound at 149 and 178 K was determined, in agreement with NMR data. From the quasi-elastic scattering between 81 and 211 K of Sn(CH₃)₄ an activation energy for 3-fold jump reorientation of the methyl group, E_a = (3.4 ± 0.2) kJ/mol, was deduced.For all three compounds a very similar lattice vibration spectrum was found. The inelastic neutron spectrum between 10 and 24 meV of Ge(CH₃)₄ and Sn(CH₃)₄ and Sn(CH₃)₄, measured with a very good resolution, revealed some new peaks and made a more accurate determination of the torsiònal transitions of the methyl groups possible. It is shown that the barrier heights for methyl reorientation, determined from these transitions correspond very well with activation energies found in NMR experiments and from the quasi-elastic scattering in this investigation.