The inelastic scattering of neutrons by magnetic spin waves

1955 ◽  
Vol 230 (1180) ◽  
pp. 46-73 ◽  
Keyword(s):  
Inelastic Scattering ◽  
Spin Wave ◽  
Cross Sections ◽  
Phonon Scattering ◽  
Wave Theory ◽  
Dipole Interaction ◽  
Bragg Angle ◽  
X Rays ◽  
Bragg Scattering ◽  
Critical Temperatures

The inelastic scattering of neutrons by ferromagnetic and antiferromagnetic crystals is considered on spin-wave theory, using the formalism of Holstein & Primakoff. The influence of dipole-dipole interaction and of an applied magnetic field is examined in detail for ferromagnetic crystals. Scattered intensity distributions and total cross-sections are derived in terms of the angular setting of the crystal; they are valid at temperatures low compared with the relevant critical temperatures. The spin-wave interaction leads to magnetic diffuse reflexion of neutrons from the crystal planes, closely analogous to the phonon diffuse reflexion of neutrons and X-rays. These reflexions become intense near the positions for magnetic Bragg scattering; with antiferromagnetic crystals there is an additional set of feeble diffuse reflexions near the directions of nuclear Bragg scattering. The spin-wave diffuse reflexions are always superposed on phonon reflexions. However, in antiferromagnetics the nuclear and magnetic parts of phonon scattering are separated, so that the principal spin-wave reflexions fall on the magnetic part only. Anisotropy forces affect the intensity only for settings very near the Bragg angle. The phenomenon is capable of giving very direct information on the low-lying energy states of magnetic crystals. Cross-sections, however, are of the order of millibams and detailed consideration is given to the problem of their experimental isolation.

scholarly journals Comments on A new theory for X-ray diffraction

2018 ◽  
Vol 74 (5) ◽  
pp. 447-456 ◽  
Author(s):  
Jack T. Fraser ◽  
Justin S. Wark
Keyword(s):  
Diffraction Pattern ◽  
Bragg Angle ◽  
X Rays ◽  
Bragg Scattering ◽  
Bragg Condition ◽  
X Ray Diffraction ◽  
Acta Cryst ◽  
X Ray ◽  
Individual Crystallite ◽  
Small Crystallite

In an article entitled A new theory for X-ray diffraction [Fewster (2014). Acta Cryst. A70, 257–282], hereafter referred to as NTXRD, it is claimed that when X-rays are scattered from a small crystallite, whatever its size and shape, the diffraction pattern will contain enhanced scattering at angles of exactly 2θB, whatever the orientation of the crystal. It is claimed that in this way scattering from a powder, with randomly oriented crystals, gives rise to Bragg scattering even if the Bragg condition is never satisfied by an individual crystallite. The claims of the theory put forward in NTXRD are examined and they are found to be in error. Whilst for a certain restricted set of shapes of crystals it is possible to obtain some diffraction close to (but not exactly at) the Bragg angle as the crystallite is oriented away from the Bragg condition, this is generally not the case. Furthermore, contrary to the claims made within NTXRD, the recognition of the origin of the type of effects described is not new, and has been known since the earliest days of X-ray diffraction.

Analysis of STEM micrographs of thick objects

1978 ◽  
Vol 36 (2) ◽  
pp. 106-107
Author(s):  
S. Golladay
Keyword(s):  
Inelastic Scattering ◽  
Multiple Scattering ◽  
Mass Distribution ◽  
Cross Sections ◽  
Phase Contrast ◽  
Image Point ◽  
Contrast Effects ◽  
Total Cross Sections ◽  
Elastic And Inelastic Scattering

The theory of multiple scattering has been worked out by Groves and comparisons have been made between predicted and observed signals for thick specimens observed in a STEM under conditions where phase contrast effects are unimportant. Independent measurements of the collection efficiencies of the two STEM detectors, calculations of the ratio σe/σi = R, where σe, σi are the total cross sections for elastic and inelastic scattering respectively, and a model of the unknown mass distribution are needed for these comparisons. In this paper an extension of this work will be described which allows the determination of the required efficiencies, R, and the unknown mass distribution from the data without additional measurements or models. Essential to the analysis is the fact that in a STEM two or more signal measurements can be made simultaneously at each image point.

Neutron diffraction, inelastic scattering and the structure of amphiphiles and macromolecules in solution

1975 ◽  
Vol 345 (1640) ◽  
pp. 119-144 ◽  
Keyword(s):  
Neutron Diffraction ◽  
Inelastic Scattering ◽  
Cross Sections ◽  
Biological Molecules ◽  
Variation Method ◽  
Contrast Variation ◽  
Structure And Dynamics ◽  
Spin Resonance ◽  
Scattering Lengths ◽  
Scattering Cross Sections

The methods by which neutron diffraction and inelastic scattering may be used to study the structure and dynamics of solutions are reviewed, with particular reference to solutions of amphiphile and biological molecules in water. Neutron methods have particular power because the scattering lengths for protons and deuterons are of opposite sign, and hence there exists the possibility of obtaining variable contrast between the scattering of the aqueous medium and the molecules in it. In addition, the contrast variation method is also applicable to inelastic scattering studies whereby the dynamics of one component of the solution can be preferentially studied due to large and variable differences in the scattering cross sections. Both applications of contrast variation are illustrated with examples of amphiphile-water lamellar mesophases, diffraction from collagen, viruses, and polymer solutions. Inelastic scattering observations and the dynamics of water between the lamellar sheets allow microscopic measurements of the water diffusion along and perpendicular to the layers. The information obtained is complementary to that from nuclear magnetic resonance and electron spin resonance studies of diffusion.

scholarly journals Saturation effects in SIDIS at very forward rapidities

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
E. Iancu ◽  
A. H. Mueller ◽  
D. N. Triantafyllopoulos ◽  
S. Y. Wei
Keyword(s):  
Inelastic Scattering ◽  
Cross Section ◽  
Cross Sections ◽  
Virtual Photon ◽  
Large Fraction ◽  
Quark Distribution ◽  
High Energy ◽  
Longitudinal Momentum ◽  
Black Disk ◽  
Gluon Saturation

Abstract Using the dipole picture for electron-nucleus deep inelastic scattering at small Bjorken x, we study the effects of gluon saturation in the nuclear target on the cross-section for SIDIS (single inclusive hadron, or jet, production). We argue that the sensitivity of this process to gluon saturation can be enhanced by tagging on a hadron (or jet) which carries a large fraction z ≃ 1 of the longitudinal momentum of the virtual photon. This opens the possibility to study gluon saturation in relatively hard processes, where the virtuality Q2 is (much) larger than the target saturation momentum $$ {Q}_s^2 $$ Q s 2 , but such that z(1 − z)Q2 ≲ $$ {Q}_s^2 $$ Q s 2 . Working in the limit z(1 − z)Q2 ≪ $$ {Q}_s^2 $$ Q s 2 , we predict new phenomena which would signal saturation in the SIDIS cross-section. For sufficiently low transverse momenta k⊥ ≪ Qs of the produced particle, the dominant contribution comes from elastic scattering in the black disk limit, which exposes the unintegrated quark distribution in the virtual photon. For larger momenta k⊥ ≳ Qs, inelastic collisions take the leading role. They explore gluon saturation via multiple scattering, leading to a Gaussian distribution in k⊥ centred around Qs. When z(1 − z)Q2 ≪ Q2, this results in a Cronin peak in the nuclear modification factor (the RpA ratio) at moderate values of x. With decreasing x, this peak is washed out by the high-energy evolution and replaced by nuclear suppression (RpA< 1) up to large momenta k⊥ ≫ Qs. Still for z(1 − z)Q2 ≪ $$ {Q}_s^2 $$ Q s 2 , we also compute SIDIS cross-sections integrated over k⊥. We find that both elastic and inelastic scattering are controlled by the black disk limit, so they yield similar contributions, of zeroth order in the QCD coupling.

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