Magnetic Scattering: General Properties

2020 ◽  
pp. 185-212
Author(s):  
Andrew T. Boothroyd
Keyword(s):  
Form Factor ◽  
Partial Response ◽  
Response Function ◽  
Absorptive Part ◽  
Form Factors ◽  
Dipole Approximation ◽  
Magnetic Form Factor ◽  
Magnetic Scattering ◽  
Response Functions ◽  
Fluctuation Dissipation

The basic theory of magnetic scattering is presented. A response function for magnetic scattering is defined, and expressed in terms partial response functions. The relation between the partial response functions and the correlation function for components of the magnetization is obtained, and the dynamical part of the partial reponse functions is linked via the fluctuation-dissipation theorem to the absorptive part of the generalized susceptibility. It is shown how the dipole approximation can be used to simply the magnetic scattering operator for localized electrons, and the magnetic form factor is introduced. Examples of the use of the dipole magnetic form factor, as well as more general anisotropic magnetic form factors, are given. A comparison with the X-ray atomic form factor is given. Various sum rules for the magnetic response function and generalized susceptibility are obtained.

A Study of Spin and Orbital Magnetic Form Factors of CeRh3B2 by X-Ray Magnetic Diffraction

2011 ◽  
Vol 497 ◽  
pp. 3-7 ◽  
Author(s):  
Masahisa Ito ◽  
Ryota Nagayasu ◽  
Tatsuki Tadenuma ◽  
Kosuke Suzuki ◽  
Ayako Sato ◽  
...  
Keyword(s):  
Form Factor ◽  
Form Factors ◽  
Real Space ◽  
Dipole Approximation ◽  
Magnetic Form Factor ◽  
Rare Earth Compound ◽  
X Ray ◽  
Curve Fitting Analysis ◽  
Magnetic Form Factors ◽  
First Time

An experimental method of X-ray magnetic diffraction was applied to the ferromagnetic rare-earth compound CeRh3B2, and its spin and orbital magnetic form factors were measured independently for the first time. Our curve-fitting analysis shows that the orbital magnetic form factor is reproduced by the calculated atomic-model form factor of Ce-4f electrons under the dipole approximation. The comparison of the sum of form factors and the total magnetic form factor measured by the polarized neutron diffraction reveals anisotropic distribution of the magnetic moment in real space.

Kinematical Theory of Scattering

2020 ◽  
pp. 73-98
Author(s):  
Andrew T. Boothroyd
Keyword(s):  
Correlation Function ◽  
Response Function ◽  
Detailed Balance ◽  
Absorptive Part ◽  
Spectral Weight ◽  
Static Approximation ◽  
Dynamic Correlations ◽  
Fluctuation Dissipation ◽  
Intermediate Scattering Function ◽  
Kinematical Theory

The chapter introduces the kinematical theory of scattering, which is based on the Born approximation. It is shown that the neutron scattering response function can be written as the time Fourier transform of a correlation function, or intermediate scattering function. Several general properties of the correlation function are derived, and the response function is shown to satisfy the Principle of Detailed Balance. The distinction between static and dynamic correlations is explained, and their correspondence to elastic and inelastic scattering is established. The meaning of the static approximation is explained, and the link between the dynamical part of the response function and the absorptive part of the generalized susceptibility via the Fluctuation-Dissipation theorem is established. Some general sum rules are proved, and a spectral-weight function is defined. Response functions are obtained for some simple models.

scholarly journals Pauli Radius of the Proton

2021 ◽  
Vol 38 (12) ◽  
pp. 121401
Author(s):  
Zhu-Fang Cui ◽  
Daniele Binosi ◽  
Craig D. Roberts ◽  
Sebastian M. Schmidt
Keyword(s):  
Form Factor ◽  
Form Factors ◽  
Magnetic Form Factor ◽  
Proton Scattering ◽  
Statistical Sampling ◽  
Function Form ◽  
The Difference ◽  
Factor Data ◽  
Form Factor Data ◽  
Prime 2

Using a procedure based on interpolation via continued fractions supplemented by statistical sampling, we analyze proton magnetic form factor data obtained via electron+proton scattering on Q 2 ∈ [0.027, 0.55] GeV2 with the goal of determining the proton magnetic radius. The approach avoids assumptions about the function form used for data interpolation and ensuing extrapolation onto Q 2 ≃ 0 for extraction of the form factor slope. In this way, we find r M = 0.817(27) fm. Regarding the difference between proton electric and magnetic radii calculated in this way, extant data are seen to be compatible with the possibility that the slopes of the proton Dirac and Pauli form factors, F 1,2(Q 2), are not truly independent observables; to wit, the difference F ′ 1 ( 0 ) − F ′ 2 ( 0 ) / κ p = [ 1 + κ p ] / [ 4 m p 2 ] , viz., the proton Foldy term.

scholarly journals The electromagnetic form factors of Λ hyperon in e+e−→Λ̄Λ

2018 ◽  
Vol 33 (22) ◽  
pp. 1850133 ◽  
Author(s):  
Yongliang Yang ◽  
Zhun Lu
Keyword(s):  
Form Factor ◽  
Cross Sections ◽  
Form Factors ◽  
Magnetic Form Factor ◽  
Electromagnetic Form Factors ◽  
Threshold Region ◽  
Double Spin ◽  
Electron Positron Annihilation ◽  
Effective Form ◽  
Two Parameters

We study the electromagnetic form factors of [Formula: see text] hyperon in the time-like region using the experimental data in the exclusive production of [Formula: see text] pair in electron–positron annihilation. We present a pQCD inspired parametrization of [Formula: see text] and [Formula: see text] with only two parameters, and we consider a suppression mechanism of the electric form factor [Formula: see text] compared to the magnetic form factor [Formula: see text]. The parameters are determined through fitting our parametrization to the data of the effective form factor [Formula: see text] from the DM2, BaBar and BESIII Collaborations in the reaction [Formula: see text]. We use the parametrizations for [Formula: see text] and [Formula: see text] to calculate the Born cross-sections as well as the ratio [Formula: see text]. Except the threshold region, our parametrization can describe the known behavior of the existing data of effective form factor, Born cross-section and the ratio [Formula: see text] from the BaBar, DM2 and BESIII Collaborations. We also predict the double spin polarization observables [Formula: see text], [Formula: see text] and [Formula: see text] in [Formula: see text] which could provide more information on the size of the lambda EMFFs as well as their phase angles.

NEW RESULTS FROM THE BATES LARGE ACCEPTANCE SPECTROMETER TOROID (BLAST)

2009 ◽  
Vol 18 (02) ◽  
pp. 209-219
Author(s):  
◽  
HAIYAN GAO
Keyword(s):  
Form Factor ◽  
Form Factors ◽  
Magnetic Form Factor ◽  
The Novel ◽  
Hydrogen Deuterium ◽  
Nucleon Form Factors ◽  
Gas Targets ◽  
Large Acceptance ◽  
First Time ◽  
Deuterium Gas

An experiment using the novel technique of scattering a longitudinally polarized electron beam from polarized internal hydrogen/deuterium gas targets was carried out in the South Hall Ring at the MIT-Bates Accelerator Center. The scattered particles were detected by the Bates Large Acceptance Spectrometer Toroid (BLAST) detector. The proton electric to magnetic form factor ratio, [Formula: see text] at Q 2 = 0.1 - 0.65 ( GeV/c )2 has been determined from the experiment by measuring the spin-dependent ep elastic scattering asymmetry in the two symmetric sectors of the BLAST simultaneously for the first time. The neutron electric form factor [Formula: see text] in the same Q2 range has been extracted by measuring the spin-dependent asymmetry from the [Formula: see text] process with a vector polarized deuterium target. These results on the nucleon form factors from the BLAST experiment are presented.

MAGNETIC FORM FACTOR MEASUREMENTS IN CERIUM HEXABORIDE

1982 ◽  
Vol 43 (C7) ◽  
pp. C7-273-C7-278 ◽  
Author(s):  
P. Burlet ◽  
J. X. Boucherle ◽  
J. Rossat-Mignod ◽  
J. W. Cable ◽  
W. C. Koehler ◽  
...  
Keyword(s):  
Form Factor ◽  
Magnetic Form Factor

The influence of the nuclear and atomic form factors on the muon bremsstrahlung cross section

1968 ◽  
Vol 46 (10) ◽  
pp. S377-S380 ◽  
Author(s):  
A. A. Petrukhin ◽  
V. V. Shestakov
Keyword(s):  
Form Factor ◽  
Cross Section ◽  
Born Approximation ◽  
Form Factors ◽  
Experimental Results ◽  
Simple Analytical Expression ◽  
Nuclear Form Factor ◽  
The Cross ◽  
Atomic Electrons ◽  
Bremsstrahlung Process

The cross section for the muon bremsstrahlung process is calculated as a function of the nuclear form factor in the Born approximation following the Bethe and Heitler theory. The influence of the nuclear form factor is greater than that taken by Christy and Kusaka. The simple analytical expression for the effect of the screening of the atomic electrons is found. The influence of a decrease in the cross section upon the interpretation of some experimental results is estimated.

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