Neutron-photon studies of condensed matter

A theory of simultaneous photon absorption and inelastic neutron scattering is developed by treating the photon and neutron-matter interactions perturbatively. The leading-order mixing between the interactions shows that the neutron scattering cross-section is proportional to the dynamic structure factor (or Van Hove function) evaluated at an energy that is enhanced by the photon energy. The photon induced modification of the scattering vector is negligible. Thus, the proposed technique affords the possibility of measuring the dynamic structure factor at large energies and modest wavevectors which is a domain that is usually difficult to access because of kinematic constraints. The theory is developed in detail for some models of nuclear and magnetic systems. The results show that, in most cases, the experiments are likely to demand the use of very high intensity light sources. A particularly promising application appears to be in the study of electron plasmas since, using readily available pulsed lasers, the neutron cross-section is comparable with that for pure magnetic scattering.     

Absence of voids in fast neutron irradiated zirconium by small angle neutron scattering

Abstract

The aim of this research was to resolve a difference of opinion in the literature on the presence of voids in fast neutron irradiated zirconium. There is a great interest in the study of zirconium, since zirconium and its alloys are used extensively in modern power reactors, for example in the fuel rods as a containment material for enriched uranium. A polycrystalline sample of zirconium was irradiated in the HERALD reactor at 40°C with 10²⁰ fast neutrons per cm^?2. The neutron scattering from irradiated and unirradiated standard samples was studied over a wide Q range from 0.001 to 1.12 Å^?1 on a D11 Spectrometer at the ILL (France). The defect cross-section (the difference between the scattering of the standard zirconium crystal and irradiated crystal) was nearly flat as a function of Q (momentum transfer vector) with an average value of 8.5 mb/Str/atom. This indicates a point defect concentration of about 1.8%. Thus the absence of any small angle (Q dependent) defect scattering indicates that large damage regions (e.g. voids) are not produced in zirconium by fast neutron irradiation.     

Magnetic octupole order in : A polarized neutron diffraction study

Recently, in phase IV of Ce_xLa_1-xB₆, weak but distinct superlattice reflections from the order parameter of phase IV have been detected by our unpolarized neutron scattering experiment [K. Kuwahara, K. Iwasa, M. Kohgi, N. Aso, M. Sera, F. Iga, J. Phys. Soc. Japan 76 (2007) 093702]. The scattering vector dependence of the intensity of superlattice reflections is quite unusual; the intensity is stronger for high scattering vectors. This result strongly indicates that the order parameter of phase IV is the magnetic octupole. However, the possibility that the observed superlattice reflections are due to lattice distortions could not be completely ruled out only on the basis of the unpolarized neutron scattering experiment. To confirm that the superlattice reflections are magnetic, therefore, we have performed a single crystal polarized neutron diffraction experiment on Ce_0.7La_0.3B₆. The obtained result has clearly shown that the time reversal symmetry is broken by the order parameter of phase IV. This is further evidence for the magnetic octupole order in Ce_xLa_1-xB₆.     

Evidence on the influence of fission channels on fission phenomena

Partial fission channel widths can be extracted from fission cross-section analysis only up to a rotation in the space of fission vectors. We propose to obtain a physically significant basis for fission vectors taking into account information from other fission characteristics such as the valley-to-peak ratio of the mass distribution and the number of prompt neutrons emitted per fission event. Fission widths and other channel characteristics are calculated for 0⁺ resonances in low energy neutron induced fission of ²³⁹Pu.     

Linear spin dynamics of incommensurably modulated magnets

The linear spin dynamics of an incommensurably modulated Heisenberg magnet, with a single-Q structure, is studied using an analytic technique designed to calculate the transverse spin response observed in neutron scattering. Results are presented for a specialQ and also special scattering wave vectors. An approximate expression is proposed that is fully determined by the exchange and anisotropy parameters. The spin response is studied as a function ofQ and shown to be distinctly different from the case in which it is exhausted by a single collective spin oscillation.     

Electric-field influence on the neutron diffuse scattering near the ferroelectric transition of Sr0.61Ba0.39Nb2O6

ABSTRACT

Uniaxial relaxor ferroelectric Sr_0.61Ba_0.39Nb₂O₆ single crystal has been investigated in the vicinity of its phase transition using neutron scattering and dielectric spectroscopy. A global-type thermal hysteresis is evidenced by both techniques in the ferroelectric phase and up to about 15 K above T_c. In addition, a part of the transverse neutron diffuse scattering in the 001 Brillouin zone, presumably related to static nanodomain structure, can be suppressed by prior poling the crystal in electric field of 3 kV/cm. The remaining part of the transverse neutron diffuse scattering and the real part of permittivity show a similar temperature dependence. The temperature position of the maximal scattering intensity T_max depends significantly on the scattering wave vector. T_max shifts monotonically to higher temperature with the increasing wave vector in all investigated cooling and heating regimes. It is concluded that the critical fluctuations have space correlations which depend on frequency and wave vector.     

Interactions of neutrons with239Pu in the energy range between 1.5 and 5.5 MeV

Neutron scattering angular distributions of²³⁹Pu were measured at seven primary neutron energies between 1.5 and 5.5 MeV. Absolute differential scattering cross-section results are plotted and tabulated. Cross section calculations using a central optical model were made and the results were compared with the experimental values. Moreover, nuclear temperatures of the fission and the inelastic neutron evaporation processes were extracted from the measured spectra.     

Theoretical study of incoherent φ photoproduction on a deuteron target

We study the photoproduction of φ mesons in deuteron, paying attention to the modification of the cross-section from bound protons to the free ones. For this purpose we take into account Fermi motion in single scattering and rescattering of φ to account for φ absorption on a second nucleon as well as the rescattering of the proton on the neutron. We find that the contribution of the double scattering for φ is much smaller than the typical cross-section of γp → φp in free space, which implies a very small screening of the φ production in deuteron. The contribution from the proton rescattering, on the other hand, is found to be not negligible compared to the cross-section of γp → φp in free space, and leads to a moderate reduction of the φ photoproduction cross-section on a deuteron at forward angles if the LEPS set-up is taken into account. The Fermi motion allows contribution of the single scattering in regions forbidden by phase-space in the free case. In particular, we find that for momentum transfer squared close to the maximum value, the Fermi motion changes drastically the shape of dσ/dt, to the point that the ratio of this cross-section to the free one becomes very sensitive to the precise value of t chosen, or the size of the bin used in an experimental analysis. Hence, this particular region of t does not seem to be the most indicated to find effects of a possible φ absorption in the deuteron. This reaction is studied theoretically as a function of t and the results are contrasted with recent experiments at LEPS and Jefferson Lab. The effect of the experimental angular cuts at LEPS is also discussed, providing guidelines for future experimental analyses of the reaction.     

An analytical expression of the amplitude of stripping reaction in the coulomb approximation

A method is derived for calculating the matrix element of stripping reaction (d,p) in the socalled distorted-wave Born approximation; only Coulomb scattering of incident and outgoing particles is taken into consideration. Coulomb wave functions are expressed by means of integral representation permitting integration over angular variables and, when the radial wave function of the trapped neutron is specially chosen, also calculation of the radial integral for non-zero orbital momentum of the trapped neutron. Relations are given for calculating the differential cross-section of reaction and the polarization of products. The special case, when the orbital momentum of the captured neutron is equal to one or two, is discussed in detail.     

Dynamic spin susceptibility of hole-doped high-temperature superconductors in a singlet-correlated conduction band model

We have derived an expression for the dynamical spin susceptibility of a hole-doped high-temperature superconductor taking into account a strong correlation between the magnetization of spins of the localized and itinerant electrons. This formula has been used to calculate the imaginary part of the susceptibility as a function of the frequency and wave vector. The results are compared to experimental data on the inelastic neutron scattering in compounds of the YBa₂Cu₃O_6+y type. A peak in the scattering intensity observed at an energy of about 40 meV in the region of wave vectors Q = (π, π) and an arc-shaped dispersion relief are interpreted as manifestations of the collective spin excitations in the system, the energy of which falls within a superconducting gap (spin exciton). The U-shaped divergent relief observed in the neutron scattering intensity is assigned to collective short-rage-order spin oscillations.     

Multiple scattering theory for slow neutrons (from thermal to ultracold)

The general theory of neutron scattering is presented, valid for the whole domain of slow neutrons from thermal to ultracold. Particular attention is given to multiple scattering which is the dominant process for ultracold neutrons (UCN). For thermal and cold neutrons, when the multiple scattering in the target can be neglected, the cross-section is reduced to the known value. A new expression for inelastic scattering cross-section for UCN is proposed. Dynamical processes in the target are taken into account and their influence on inelastic scattering of UCN is analyzed. Received 21 July 1999     

A SEMI-CLASSICAL ANALYSIS ON THE REACTION 12C+209Bi AT BOMBARDING ENERGIES SLIGHTLY ABOVE THE COULOMB BARRIER

For reactions induced by light heavy ion such as ¹²C, at bombarding energy slightly above the coulomb barrier, using semi-classical theory, neglecting macroscopic frictional force, the reaction mechnisms are sorted by the orbital angular momentum of the entrance channel from the classical deflection functions fitting elastic scattering. Moreover, inserting a transfer probability factor representing the Q-Window effect into the semi-classical angular distribution formula of Kalinkin and Grabowski, we obtain a formula for the differential cross-section per unit energy interval. The calculated results, including the elastic scattering angular distributions, energy spectrum and angular distributions of emitted α-particles in quasi-elastic process, complete fusion cross-section, fusion-fission cross-sections and the exitation functions of evaporated neutron, agree with the experimental data on the reaction ¹²C+²⁰⁹Bi reported by our Institute.     

Resonance neutron capture in 56Fe

The neutron capture cross section of ⁵⁶Fe has been measured with 0.2–0.3% energy resolution from 2.5 keV up to the inelastic neutron scattering threshold. Results are compared with recent total cross-section data and average parameters are derived for s-, p- and d-wave resonances. The low correlation coefficient observed between the s-wave reduced neutron and radiative widths is consistent with the minor contribution of the valence capture mechanism as calculated in the framework of the optical model. Broad E1 and M1 doorway states for s-, p- and d-wave resonances are postulated to explain the cross-section data and γ-ray spectra up to 1 MeV.     

Neutron diffraction study of the plastic phases of polycrystalline SF6 and CBr4

An investigation of the plastic phases of polycrystalline specimens of sulphur hexafluoride (SF₆) and carbon tetrabromide (CBr₄) by neutron elastic scattering and neutron diffraction experiments is reported. A theory of neutron diffraction in plastic crystals, which treats the Bragg scattering and the diffuse scattering from a unified point of view, is developed and applied in the interpretation of the neutron results. The Debye-Scherrer peaks are analysed, both by a cumulant expansion technique and a cubic harmonic analysis, to determine the crystal structures of the plastic phase which are found to be body-centred cubic (space group Im3_m) for SF₆ and face-centred cubic (space group Fm3m) for CBr₄. The bond-orientation distribution function, f(Ω), has maxima in the <100> directions for SF₆ and in the <110> directions for CBr₄. Since, in both cases, f(Ω) is appreciably different from zero for all orientations, it is apparent that significant thermal reorientation takes place in both these crystals. The translational and librational displacements in CBr₄ are exceptionally large and give rise to extensive diffuse scattering which is analysed on the basis of a simple Einstein model. The model predicts that the centre-of-mass thermal vibration and the orientational disorder give approximately equal contributions to the total diffuse scattering. The calculated scattering is in good agreement with experiment for all wave vector transfers outside the range 2 to 3 Å^-1. Inside this range discrepancies occur which are interpreted as evidence for the existence of orientational short-range order in CBr₄.     

Compton scattering of 0.279 MeV gamma rays fromK-shell electrons of lead

Differential cross-sections for Compton scatterig of 0.279 MeV gamma rays fromK-shell electrons of lead are measured at scattering angles ranging from 30 to 150° to study the effect of binding on the scattering process. Measurements are made employing two Nal(Tl) scintillation spectrometers and a slow-fast coincidence set-up of 30 nsec resolving time. The experimental results are compared with the available theoretical data. The totalK-shell Compton scattering cross-section is 34% of the free electron Compton cross-section.     

Unitarity constraints and role of geometrical effects in deep-inelastic scattering and vector meson electroproduction

Deep-inelastic scattering at low x and elastic vector meson electroproduction are analyzed on the basis of the s-channel unitarity extended to off-shell particle scattering. It appeared that the role of unitarity is important, but contrary to the case of on-shell scattering it does not rule out a power-like behavior of the total cross sections. We discuss the behavior of the total cross section of virtual photon–proton scattering in the geometrical approach and obtain the result that the exponent of the power-like energy dependence of is related to the constituent quark interaction radius. The mass effects and energy dependence of vector meson electroproduction are discussed along with the angular distributions at large momentum transfers in these processes. Received: 10 September 2001 / Published online: 7 December 2001     

Correlated Huang scattering in hexagonal Jahn Teller compounds

This is a theoretical investigation on structural precursors in diffuse neutron scattering of disordered phases of cooperative Jahn-Teller compounds above their structural phase transitions. The theory is based on Huang scattering off elastic dipoles. Softening of shear modes in the smallq regime known from inelastic scattering predicts monoclinic and orthorhombic structures which are found in some of these compounds. For these smallq the Jahn-Teller effect looks dynamic and Huang scattering is not applicable. With larger wave vectors the dipoles look static and Huang theory works but one picks up neighbor correlations which have to be included. We believe to have identified the spiral correlation announcing the helical structure of CsCuCl₃ in its ordered phase. We also calculate diffuse scattering for RbCrCl₃ and the experimentally observed satellites announcing the cell doubling of the ordered phase.     

Measurement of the total cross sections of ultracold neutrons with noble gases and search for long-range forces

The comparison of results of cross section measurements by the different methods can provide useful information on existence of long-range interaction. The total neutron cross sections of He, Ne, Ar, Kr, and Xe were measured using a method of ultracold neutrons. Measurements with ultra cold neutrons confirm the discrepancy between coherent cross-section of scattering for He measured by a neutron interferometer and scattering cross-section measured by the transmission method. The discrepancy makes up 5.3 standard deviations.     

Neutron scattering by anharmonic crystals and the effect of sublattice displacements

A theory has been given for the scattering of neutrons by anharmonic crystals, for which terms of the typeV ⁽³⁾ (k _1j1; —k _1j1;o _j) which contribute to the sublattice displacements are not neglected. Using the standard perturbation theory in the interaction picture or Green’s function method, an expression has been derived for the differential scattering cross-section which brings in the shift and the width of the phonons in one-phonon energy exchange processes. It is shown that the sublattice displacements will modify the phase factor arising from the scattering by any atom in the unit cell, and the Debye-Waller factor also gets altered both by the sublattice displacements as well as by higher order terms arising from anharmonicity. It is shown that the differential scattering cross-section contains a term linearly depending on the third order anharmonicity coefficientV ⁽³⁾ (k _1j1;k _2j2;k _3j3) and neutron scattering by crystals should provide a useful method for evaluating the third order anharmonicity coefficients.     

SaxsMDView: a three‐dimensional graphics program for displaying force vectors

A new three‐dimensional graphics program, SaxsMDView, is described. The program performs a three‐dimensional graphical representation for protein molecules along with the force vector (or vector potential) applying to each atom. The displayed object can be rotated and translated in arbitrary directions by interactive mouse manipulation. While SaxsMDView was originally intended to visualize the result of SAXS_MD, a previously developed program based on the restrained molecular dynamics with small‐angle X‐ray scattering constraints, it can also be useful for graphical representation of other objects such as coarse‐grained molecular models reconstructed by ab initio modelling or solvent site‐dipole field vectors induced around the protein molecule. Some examples of the application of the program including the graphical analyses of the results with SAXS_MD are also presented.