Nuclear Scattering

2020 ◽  
pp. 127-184
Author(s):  
Andrew T. Boothroyd
Keyword(s):  
Cross Sections ◽  
Phonon Scattering ◽  
Phonon Dispersion ◽  
Spin Echo ◽  
Harmonic Approximation ◽  
Approximate Expression ◽  
Neutron Spin ◽  
Response Functions ◽  
Nuclear Scattering ◽  
Scattering Cross

This chapter contains an overview of the different types of structural dynamics found in condensed matter, and the associated neutron scattering cross-sections. The scattering dynamics of the harmonic oscillator is discussed, and an expression for the Debye-Waller factor is obtained. In the case of crystalline solids, the vibrational spectrum in the harmonic approximation is described, including the phonon dispersion and the cross-sections for one-phonon coherent and incoherent scattering. Multi-phonon scattering is discussed briefly. For non-crystalline matter, the time-dependent van Hove correlation and response functions are introduced, and their relation to the scattering cross-section established. An approximate expression for the correlation function is obtained from the classical form. Partial correlation and response functions are defined for multicomponent systems. The technique of neutron Compton scattering as a probe of single-particle recoil dynamics is described. Quasielastic and neutron spin-echo spectroscopy are introduced, as well as examples of relaxational dynamics which these techniques can measure.

scholarly journals Total interference between nuclear and magnetovibrational one-phonon scattering cross sections

2019 ◽  
Vol 1316 ◽  
pp. 012018
Author(s):  
S. Raymond ◽  
N. Biniskos ◽  
K. Schmalzl ◽  
J. Persson ◽  
T. Brückel
Keyword(s):  
Cross Sections ◽  
Phonon Scattering ◽  
Scattering Cross ◽  
Total Interference ◽  
Scattering Cross Sections

Neutron filter efficiency of beryllium and magnesium fluorides

2017 ◽  
Vol 50 (2) ◽  
pp. 441-450 ◽  
Author(s):  
Iyad Al-Qasir ◽  
Abdallah Qteish
Keyword(s):  
Inelastic Scattering ◽  
Cross Sections ◽  
Phonon Dispersion ◽  
Mass Difference ◽  
Neutron Transmission ◽  
Filter Efficiency ◽  
Scattering Cross ◽  
Different Temperatures ◽  
Neutron Filter ◽  
Scattering Cross Sections

The neutron filter efficiency of MgF2 and BeF2 has been investigated as a function of neutron incident energy at different temperatures, starting from the phonon density of states (PDOS) calculated using first-principles techniques, and the results are compared with those of MgO and BeO. Recently, MgF2 has been suggested as a neutron filter and neutron transmission through it has been experimentally studied. For MgF2, excellent agreement between calculated and available experimental data has been achieved for the phonon dispersion relations, constant-volume specific heat, inelastic scattering cross sections and neutron transmission. The PDOSs of MgF2 and BeF2 are found to differ significantly owing to the crystal structure and the cations' mass difference. The inelastic scattering cross sections and filter efficiencies of MgF2 and BeF2 show different behaviours, which can be understood to originate from the above PDOS incongruity and the large difference in absorption cross sections of Be and Mg nuclei. BeF2 is predicted to be a better neutron filter than MgF2 and MgO, over the temperature range of interest, while it has less ability than BeO to transmit low-energy neutrons.

PHONON SCATTERING VIA AN ATOMIC WELL IN FREE STANDING THIN SOLID FILMS

2009 ◽  
Vol 16 (02) ◽  
pp. 271-280 ◽  
Author(s):  
A. KHATER ◽  
M. BELHADI
Keyword(s):  
Cross Sections ◽  
Phonon Scattering ◽  
Incidence Angle ◽  
Elastic Force ◽  
Force Constants ◽  
Reflection And Transmission ◽  
Solid Films ◽  
Scattering Cross ◽  
Coherent Reflection ◽  
Scattering Cross Sections

A theoretical model is presented for the study of the scattering of phonons at an extended inhomogeneous boundary separating thin solid monatomic films. The model system consists of two solid films with otherwise stress-free surfaces on either side of an atomic well boundary. The coherent reflection and transmission scattering cross sections for phonons incident from the interior of the thin films on the inhomogeneous atomic well boundary are calculated in accordance with the Landauer–Büttiker coherent scattering description, using the matching method with nearest and next-nearest neighbor elastic force constants. This is done specifically for two different cases of elastic interactions on the boundary to investigate the consequences of their softening and hardening for the coherently scattered spectra. The numerical results yield an understanding for the effects on coherent phonon conductance due to phonon incidence and to the elastic nature of the boundary. The coherent reflection and transmission scattering cross sections show characteristic spectral features that are invariant with the change of the boundary force constants, depending solely on the cutoff frequencies for the propagating phonons and on incidence angle. They also show the Fano resonances that result from the interactions of propagating phonons with the localized vibrational Rayleigh-like modes on the boundary, depending on the boundary elastic force constants. The evolution of the system average conductance per phonon mode with incidence illustrates an interesting effect. An experimental observable this average conductance remains constant at half a phonon in intensity over significant frequency intervals. The effect is remarkable inasmuch as it permits in principle the possibility of a constant intensity phonon source.

scholarly journals High-resolution phonon energy shift measurements with the inelastic neutron spin echo technique

2019 ◽  
Vol 52 (4) ◽  
pp. 755-760 ◽  
Author(s):  
Fankang Li ◽  
Jiazhou Shen ◽  
Steven R. Parnell ◽  
Alex N. Thaler ◽  
Masaaki Matsuda ◽  
...  
Keyword(s):  
Energy Resolution ◽  
Phonon Dispersion ◽  
Spin Echo ◽  
National Laboratory ◽  
Energy Shift ◽  
Inelastic Neutron ◽  
Phonon Energy ◽  
Neutron Spin ◽  
Oak Ridge ◽  
Neutron Spin Echo

The energy resolution of the conventional way of measuring a small change in a phonon dispersion curve using neutron scattering is restricted by the relatively coarse intrinsic resolution ellipsoid of the neutron triple-axis spectrometer (TAS). By implementing inelastic neutron spin echo on the host TAS using the Larmor precession of the neutron spin, the energy resolution of such measurements can be further improved without reducing the resolution ellipsoid. Measurements of the temperature-dependent phonon energy change are demonstrated using superconducting magnetic Wollaston prisms at the HB-1 instrument of the High-Flux Isotope Reactor at Oak Ridge National Laboratory, and the achievable resolution is <10 µeV.

Remarks on the scattering of electrons by atomic fields

1930 ◽  
Vol 26 (4) ◽  
pp. 556-563 ◽  
Author(s):  
E. C. Bullard ◽  
H. S. W. Massey
Keyword(s):  
Angular Distribution ◽  
Atomic Number ◽  
Cross Sections ◽  
Approximate Expression ◽  
Thomas Fermi ◽  
Scattering Cross ◽  
Single Curve ◽  
Scattering Cross Sections

It is shown that, by use of the Thomas-Fermi atom, effective scattering cross-sections may be obtained from a single curve for all atoms (provided that the atomic number is not too small). This curve is calculated. The range of validity of such values has been obtained and Born's formula shown to be inaccurate for representing the scattering of electrons with velocities less than 400 volts except by atoms of very low atomic number. For the case of high velocities an approximate expression is obtained for the angular distribution allowing for screening by the extra-nuclear electrons.

Paramagnetic and Nuclear Scattering Cross Sections of Holmium Sesquioxide

1958 ◽  
Vol 110 (1) ◽  
pp. 37-40 ◽  
Author(s):  
W. C. Koehler ◽  
E. O. Wollan ◽  
M. K. Wilkinson
Keyword(s):  
Cross Sections ◽  
Nuclear Scattering ◽  
Scattering Cross ◽  
Scattering Cross Sections

Spin-echo small-angle neutron scattering for magnetic samples

2006 ◽  
Vol 39 (2) ◽  
pp. 252-258 ◽  
Author(s):  
Sergey V. Grigoriev ◽  
Wicher H. Kraan ◽  
M. Theo Rekveldt ◽  
Timofey Kruglov ◽  
Wim G. Bouwman
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Spin Echo ◽  
Real Space ◽  
Magnetic Scattering ◽  
Neutron Spin ◽  
Magnetic Contribution ◽  
Nuclear Scattering ◽  
Density Correlation

A novel real-space scattering technique, spin-echo small-angle neutron scattering for magnetic samples, is described. Previously, this method has been exploited for non-magnetic samples only, in order to measure the nuclear density correlation function. Magnetic scattering is different from nuclear scattering as in the former a partial neutron spin-flip that affects the phase accumulation of the Larmor precession occurs just at the moment of scattering. Because of this intrinsic property of magnetic scattering, one can use a magnetic sample as a flipper in the spin-echo technique. This enables the separation of the magnetic contribution from other sources of scattering. Particular features of the technique are pointed out. Some model examples are considered. The similarity and the differences of magnetic SESANS with respect to the technique of three-dimensional neutron depolarization are discussed. The theoretical description is proven by experiments.

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