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Inelastic neutron scattering cross sections for vibrational transitions of molecules are calculated from a knowledge of the eigenvalues and eigenvectors of the vibrational motion which are, in turn, calculated from a knowledge of the molecular potential energy function. In this way, inelastic neutron scattering data may be used as a test of molecular potential energy functions, especially the small nonbonding terms which influence the low frequency motions. In this work the potential energy function of Lifson and Warshel is used in conjunction with the neutron scattering formalism of Zemach and Glauber to calculate neutron scattering spectra for several alkanes. A numerical procedure is used for the orientation averaging. The results are compared to the experiments of Strong and co-workers. It is demonstrated that reliable cross sections and frequencies can be obtained for the low frequency torsional modes of propane, n-butane, and cyclohexane without readjustment of the parameters of the potential functi...

Quasielasiic scattering experiments on nematic p-azoxyanisol have been performed at relatively small scattering vectors (K

The asymmetry of 15 MeV neutrons has been measured after successive scattering from two high-pressure helium gas scintillators. The experimental result is compared with predictions of variousn-4He phase shift sets. The phases of Hoop and Barschall, Niileret al. and of Satchleret al. agree with the present experiment.

The scattering process of neutrons by a crystal including the multiple scattering is simulated by a computer, assuming that the scattering has a rotational symmetry around the normal of a plate-like polycrystalline specimen. The calculated intensities agree well with experimental results, even for iron with a large multiple Bragg scattering. This method is useful in subtracting contributions from multiple scattering from the experimentally observed intensities of diffuse scattering.

Inelastic neutron scattering measurements on single-domain orthorhombic KNbO3 at room temperature show no evidence of overdamped scattering, in contrast with previous neutron results in the cubic phase. As in the case of KTaO3, the observed diffuse x-ray planes are shown to correspond to a highly anisotropic transverse acoustic branch with an unusually flat dispersion in the 'soft' plane. In addition, a well defined optic branch with a polarization related to the orthorhombic-rhombohedral phase transition is seen to become soft as q to 0 in the soft plane. A mode-eigenvector determination confirms the x-ray result that essentially only one atom (niobium) moves in the flat transverse acoustic mode. The connection with other experimental results and with the independent chain model is discussed.

Differential cross sections for elastic scattering of deuterons by $^{4}\mathrm{He}$ were measured at laboratory energies of 29.8, 32.3, 34.8, 37.3, and 39.8 MeV. The angular range extended from 15 to 160\ifmmode^\circ\else\textdegree\fi{} cm in steps of about 5\ifmmode^\circ\else\textdegree\fi{}. The average relative error was 2%, and the uncertainty in the absolute normalization was 2%.

The elastic scattering cross section of 7.9 MeV photons by U and Th was measured in the angular range 25°–140°. It is shown that at this energy the forward elastic scattering is due almost entirely to Delbruck scattering. The results are systematically lower by > 50% than the calculated values. A good agreement with theory was obtained only after excluding the contribution of the real part of the Delbruck scattering amplitude.

The integrated intensity of quasielastic neutron scattering by protons in polycrystalline NbH0.16 and in a single crystal of NbH0.045 was investigated as a function of the scattering vector Q. Strong deviations from a harmonic Debye-Waller factor behavior were observed at elevated temperatures. The results show a temperature dependent delocalization of the proton extending as far as the neighboring sites of the interstitial lattice. Experiments on the single crystal indicate a directional dependent mean-square amplitude of the proton even at room temperature.

The structure of the quasielastic incoherent neutron scattering from polydimethyl siloxane has been determined at low momentum transfer under conditions of high resolution. Within the limits of experimental error the quasielastic peak is a single component; a two component peak was not found. The findings are consistent with a previous tentative interpretation of the quasielastic peak being due to a Doppler broadening phenomenon attributed to the long range conformational changes of the polymer backbone.

Neutron diffraction experiments on small particles of lead in the pores of Vycor glass are described. The small particles have a coherence length of (107 ± 20) Å; there is only a slight increase in the lattice parameter as compared with bulk lead, but an analysis of the intensity of the diffraction peaks reveals that there is an increase in the average amplitude of vibration of 28%. At least 80% of the lead in the glass is present in the crystalline state and contributes to the coherent diffraction.

The use of neutron scattering spectroscopy for the study of the structure of disordered crystals is reviewed.

The temperature renormalization of magnons propagating in the hexagonal planes of FeCl2 is calculated using simple two-magnon scattering theory, and it is consistent with measurements by Birgeneau et al. (1972) for temperatures up to 89% of the Neel temperature. The renormalization of the large single-ion anisotropy energy dominates that of the exchange energy, and this feature together with the two-dimensional nature of the problem distinguish the calculation from previous studies of magnon renormalization. A magnon-phonon coupling linear in both the spin and phonon operators is expected in FeCl2, and is shown to have minimal effect on the temperature renormalization. Calculations of the hybridized excitations including an external field are presented and the neutron scattering cross section is estimated. In addition, neutron polarization analysis experiments are proposed that are a direct and sensitive measure of the magnetic character of the excitations in a magnetic field.

Ultracold neutron containment in closed vessels with pyrolytic graphite and copper walls was investigated at the FRM swimming-pool reactor. In the neutron energy range where containment is due to total reflection at any angle of incidence on the wall the measured mean containment times for various velocity intervals show a strong decrease for neutron velocities close to the upper limiting value ∼ 5.8 m/s for total reflection at normal incidence. Measurements with higher velocities in the range 10

Cross sections have been measured for the elastic scattering of 7.40-, 7.55-, 8.00-, 8.55-, 9.00-, and 9.50-MeV neutrons from nitrogen and oxygen in the angular range from 2.5 to 15 deg. The result...

The diffraction properties of curved silicon crystals, with curvature radii between ∞ and 25 m obtained by microscopic techniques, were investigated by means of a neutron diffractometer. The ratio of neutron reflectivity between plane and curved silicon crystals was measured as a function of the neutron wavelength using different reflecting planes in both Bragg and Laue cases in symmetrical and asymmetrical conditions. The experimental results were interpreted with the results of theoretical investigations on the dynamical theory of diffraction applied to the curved-crystal case. The implications of this work on neutron monochromator design are briefly discussed.

Differential cross sections of the scattering of3He-particles were measured from144, 148, 150, 152, 154Sm nuclei atE τ=40.9 MeV. The elastic scattering data were analysed with the simple optical model. The ambiguities of the real central potential and some trends depending on the target mass in the optical potential parameters are discussed.

The s-wave neutron scattering cross section for 40Ca is reconstructed from published resonance parameters. Averages over energy intervals of varying size reveal the presence of intermediate structure below 1.2 MeV. The same structure appears at all angles in the differential scattering cross section. Monte Carlo sampling of the Porter-Thomas and Wigner distributions favors the interpretation of the structure as non-statistical. A coupled-channels formalism is applied to investigate intermediate states in n + 40Ca using the particle-vibrator coupling model. All parameters of the calculation are fixed a priori using other, non-neutron, experimental data. Various particle-vibrator configurations leading to 12+ resonances are examined. About two-thirds of the s-wave strength below 1.3 MeV is accounted for.

A simple model for scattering from a deuteron is studied. Within this model exact coupled channel solutions, including all multiple scattering series terms, are obtained for a fixed separation of the two scattering potentials. These solutions are compared with approximations which involve a spherically averaged or non-overlapping potential. Our results indicate that the non-negligible contributions arising from the overlapping potential region can be adequately reproduced by a combination of simple approximations thereby facilitating calculations of scattering from a more physical deuteron model.

Groups that are a generalization of magnetic groups, and called 'spin groups', are defined. Among the spin groups those called 'spin translation groups' are tabulated and described in some detail. The possible magnetic reflexions of unpolarized neutrons elastically scattered from a single crystal whose spin arrangement is invariant under a spin translation group are also tabulated. It is shown how by using these tables and considering the indices of magnetic reflexions one can obtain information on the mutual orientation of non-collinear spins without making any assumptions on the rotational symmetry of the spin arrangement. As an example of this, the neutron diffraction data of the 'umbrella' spin arrangement of CrSe is reanalysed.

Presented here is a compilation, with bibliography, of optical-model parameters determined by fitting elastic-scattering angular distributions for various incident particles including heavy ions. Only parameters published in the period 1969–1972 are included.

The formulation of rigorous, dispersion relations for on-shell three-body amplitudes in a separable model is reported. The results of approximate N D calculations of s-wave n-d elastic scattering are compared with exact, numerical solutions of the Faddeev equations.

Neutron small‐angle scattering has been used to measure the distribution of voids in irradiated aluminum crystals. The scattering measurements were obtained with a spectrometer utilizing the focusing properties of nearly perfect germanium crystals. Direct inversion of the scattering data yields void distributions very close to those obtained with electron microscopes for similar aluminum samples.

A general method is described to take into account the multiple scattering effect in a small-angle light scattering from thin polymer films. It is seen that multiple scattering tends to make the scattering envelope more diffuse, reducing the intensity in the high intensity regions and increasing it in the low intensity regions. The method is applied here to a spherulitic system, but it is valid for any other system where the principal scattering is in the forward direction.

By neutron elastic and quasi-elastic scattering from K2CoF4, sublattice magnetization and spin correlations are examined quantitatively. The obtained critical exponents β, ν, γ, and η coincide precisely with those from Onsager's exact solution for the two-dimensional Ising model.

We present data on forward and backward scattering in CuCl at liquid N2 temperature. Peaks at 146 and 172 cm-1 which appear in both forward and backward scattering spectra are attributed to other than first order scattering by optical phonons. The data on polarition scattering indicate that the atomic displacement contribution to the scattering by TO phonons is rather small. From the experimentally determined polarition dispersion curve we obtain a value of 174 ±2.5 cm-1 for ωT and a value of 5.3 for ϵS.

The multiple-scattering corrections for neutron scattering at angles greater than 140° are presented. The total fraction of neutrons which are scattered once or twice in the target in the case of both elastic and inelastic (first excited level) scattering can be evaluated for any backward angle. Monte Carlo random-walk techniques are used. The program includes the effect due to energy loss by the neutrons following the scattering, together with the corresponding dependence on energy and angle of the cross sections for all types of collisions. The geometry considered is particularly suited for backscattering experiments where extended targets must be used. The illustrative example of the reaction 32S(n, n′)32S is presented.

A TOF (time-of-flight) type crystal spectrometer to measure the neutron incoherent scattering has been installed at the pulsed neutron source produced by the Tohoku electron linac. The monochromatized pulsed neutron beam has been obtained by Bragg reflection from a large quasi-bent pyrolytic graphite plate and the energy spectrum of the scattered neutrons has been determined by the conventional TOF method. The spectrometer has been used to detect the paramagnetic scattering from the powder specimens of various manganous oxides to determine the nearest-neighbour exchange integrals between Mn 2+ ions in the oxides. It has been found that several hours operation is sufficient to accumulate the data with reasonable resolution and good signal-to-noise ratio. The spectrometer has also been used to measure the paramagnetic scattering from a single crystal of a Heusler alloy of Pd 2 MnSn, and the difference in energy spectra between the scattering at the zone boundary and that at the zone c center could be detected at a temperature of T / T c = 1.5.

We elucidate the relative roles played by the accumulation space-charge region and by the skin depth in determining the magnitude of the wave vectors of the coupled LO-phonon---plasmon modes which take part in Raman scattering in $n$-InAs at the ${E}_{1}$ gap.

The polarization in neutron-proton scattering was studied using polarized neutron beams obtained from the 3 H(d, n) reaction, scattering these beams in monocrystalline anthracene scintillators and observing the asymmetry of the associated recoil protons. The technique used is a new one which utilizes the direction dependence of the scintillation properties in order to determine the left-right asymmetry of the proton recoils within the scintillation crystal. The measurements led to polarization values at neutron c.m. scattering angles from 90° to 150° at 16.4 MeV and from 50° to 170° at 21.6 MeV, in 20° steps in both cases. The Δ LS P and Δ LS D spin-orbit splitting phase parameters derived from the measurements are: 0.52°±0.06° and 0.02°±0.05° respectively at 16.4 MeV; and 0.93°±0.04° and 0.11°±0.02° respectively at 21.6 MeV. The data are compared with the predictions of the Yale-Buffalo and Livermore phase parameter fits.

Single crystals of argon were grown and investigated at 82.3 K, near the triple point. X-ray diffraction photographs taken in transmission were used to verify that the crystals were single and to determine their orientation. Brillouin spectra were obtained for several different orientations of three crystals. The observed spectra contained the longitudinal component and at least one, and sometimes both transverse components. Their frequency shifts were used to determine the adiabatic elastic constants at 82.3 K: ${C}_{11}=2.38\ifmmode\pm\else\textpm\fi{}0.04$, ${C}_{12}=1.56\ifmmode\pm\else\textpm\fi{}0.03$, ${C}_{44}=1.12\ifmmode\pm\else\textpm\fi{}0.03$, in units ${10}^{10}$ dyn/${\mathrm{cm}}^{2}$, and the elastic anisotropy $A=2.73\ifmmode\pm\else\textpm\fi{}0.10$. These values differ significantly from earlier results derived from neutron scattering and ultrasonic experiments. However, there is good agreement with recent Monte Carlo calculations which use multiparameter pair potentials and the triple-dipole interaction.

Lattice vibrational dispersion curves for the ``intermolecular'' modes in the triclinic, one molecule per unit cell β phase of p‐C6D4Cl2 and p‐C6H4Cl2 have been obtained by inelastic neutron scattering. The deuterated sample was investigated at 295 and at 90°K and a linear extrapolation to 0°K was applied in order to correct for anharmonic effects. Calculations based on the atom‐atom model for van der Waals' interaction and on general potential parameters for the aromatic compounds agree reasonably well with the experimental observations. There is no substantial improvement in fit obtained either by consideration of electrostatic forces or by further anisotropy in the dispersion forces not described in the atom‐atom model. Anharmonic effects are shown to be large, but the dominant features in the temperature variation of frequencies are describable by a quasiharmonic model.

Absolute small-angle neutron scattering measurements have been made on six aluminium single crystals irradiated with fast neutrons (>0·18MeV) to fluences between 0·3 and 2·0 × 1021 n/cm2. The results are interpreted in terms of the truncated octahedral shape of voids, and are compared with companion transmission electron microscopy and immersion density measurements. The swelling, total void surface area, radius of gyration, and the moment ratios of the size distribution ( )/ and / ) are in good agreement. These quantities are not only fluence-dependent but also show a marked temperature dependence resulting from the small thermal gradient in the reactor core.

An analytic expression for the dilatation and the stress tensor in reciprocal space due to dislocations in anisotropic cubic crystals is deduced. From this absolute values of nuclear and magnetic small angle scattering cross sections are calculated. For Cu and Ni they differ considerably from the values calculated with the assumption of elastic isotropy. The new presentation of scattering theory allows further the discussion of the interference in scattering between dislocations in a dislocation network.