Polarization phenomena of electrons and photons. II

Lipps, F.W.; Tolhoek, H.A.

doi:10.1016/s0031-8914(54)80054-1

Cited by 100 publications

(45 citation statements)

References 12 publications

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“…For an automatic computation of E, we have made use of the computer program SCHOONSCHIP from CERN, on the Centre de Calcul de Physique Nuclraire CDC-6600; the result is given in Table 4. It differs from the corresponding result given by Lipps & Tolhoek (1954) for Compton scattering, because we have to take into account the Fourier transforms F and S, which are different from one another and complex; other differences come from the final electron state, from the order of approximation, and from slightly different definitions of the final polarization.Experimental set up often includes a monochromator, which plays the role of a polarizer or analyzer. Suppose it is placed after the sample; let A be …”

mentioning

confidence: 66%

“…This formalism is exposed for example by Lipps & Tolhoek (1954), Robson (1974) (B-6) The elements of this matrix are represented, divided by r~. The indices here called (i) and (f) are respectively n and m in (B-6).…”

Section: Appendix Bmentioning

confidence: 99%

“…Lipps & Tolhoek (1954) published the complete formula giving the cross section for the scattering of photons by electrons as a function of the polarizations 316 DIFFRACTION OF X-RAYS BY MAGNETIC MATERIALS. I of all particles.…”

Section: Introductionmentioning

confidence: 99%

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Diffraction of X-rays by magnetic materials. I. General formulae and measurements on ferro- and ferrimagnetic compounds

Bergevin¹,

Brunel²

1981

Acta Cryst A

240

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The calculation of the amplitude of X-rays scattered by a magnetically ordered substance, carried out in the relativistic quantum theory (i.e. taking the spin into account), is detailed. The effect of the orbital momentum is described in an appendix. The practical formulae dealing with the polarization of the beams are given both in a simple form for the usual experiments and in a complete form, using the Stokes vectors, for the most general case. The experiments show a change in the intensity of the X-rays diffracted by a ferromagnetic (pure iron) or a ferrimagnetic (zinc-substituted magnetite) powder when the magnetization, perpendicular to the diffraction plane, is reversed. The relative values of these intensity changes range from 10 -4 to 5 x 10 -3 and agree in sign and magnitude with the predictions. They are proportional to the spin-density structure factor multiplied by the imaginary part of the chargedensity structure factor; the large anomalous scattering of the Cu Ka radiation in the iron-containing samples is used in the present experiments. moment associated with the spin does interact with the magnetic field of the radiation (Fig. 1). This effect can Driving force Reradiation-eE E -e E-dipol.-eE H -e ~ H-quadr. E grad/~.H --e~ffj ~C_.,~ ~ ~H $ E-dipol. IntroductionX-ray diffraction is usually interpreted through the Thomson scattering mechanism, i.e. the interaction between the electromagnetic radiation and the charge of the electrons. X-rays therefore seem to give information about the charge density only and not about the spin density. If one examines the phenomenon more thoroughly, it appears that the electronic spin also plays some role; the magnetic 0567-7394/81/030314-11 $01.00Tor qUeHx/ z ~; ~H H-dipol. be treated with relativistic quantum theory. The Klein & Nishina (1929) formula for the Compton effect takes this effect into account, but only implicitly since it concerns mean values taken over all spin states. In relativistic theory space and spin wave functions cannot be separated as they can be in the nonrelativistic limit. A perturbation on the movement of an electron has an effect which depends upon the spin. During the collision with a photon of momentum k(0 (k¢f) after collision) the electron is accelerated. One may admit that the effect of this acceleration depends upon the direction of the spin by some term of the order of I k(f) -k(0 I/mc, which expresses the relativistic character of the acceleration undergone by the electron (Fig. 2a). This is analogous to the Mott asymmetry (Tolhoek, 1956) observed in the scattering of an electron by the electric field of a nucleus, or to the Schwinger (1948) scattering (see a recent review by Felcher & Peterson, 1975), which is similar to the Mott assymetry but concerns neutrons instead of electrons (Fig. 2b). These effects can also be compared to the spin-orbit coupling (Fig. 2c), the magnitude of which is still determined by the ratio I pl/mc (p is the electron momentum). One should not forget that these comparisons do not account f...

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confidence: 66%

Section: Appendix Bmentioning

confidence: 99%

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Diffraction of X-rays by magnetic materials. I. General formulae and measurements on ferro- and ferrimagnetic compounds

Bergevin¹,

Brunel²

1981

Acta Cryst A

240

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“…In 1929, Oskar Klein and Yoshio Nishina published a first-order cross section for Compton scattering, in one of the very first successes of the nascent field of quantum electrodynamics [197]. As improved experimental techniques allowed greater interest in spin-dependent processes, it was realized that Compton scattering was just such a process: in 1954, Frederick Lipps and Hendrik Tolhoek [198,199] proved that the Klein-Nishina cross-section is sensitive to the relative spins of the incoming photon (Alternate derivations may be found in a variety of textbooks, e.g. that of Stephen Gasiorowicz [200].…”

Section: Principles Of Compton Polarimetrymentioning

confidence: 99%

Measurements of the Double-Spin Asymmetry A<sub>1</sub> on Helium-3: Toward a Precise Measurement of the Neutron A<sub>1</sub>

Parno

2011

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The spin structure of protons and neutrons has been an open question for nearly twenty-five years, after surprising experimental results disproved the simple model in which valence quarks were responsible for nearly 100% of the nucleon spin. Diverse theoretical approaches have been brought to bear on the problem, but a shortage of precise data -especially on neutron spin structure -has prevented a thorough understanding.Experiment E06-014, conducted in Hall A of Jefferson Laboratory in 2009, presented an opportunity to add to the world data set for the neutron in the poorly covered valence-quark region. Jefferson Laboratory's highly polarized electron beam, combined with Hall A's facilities for a high-density, highly polarized 3 He target, allowed a high-luminosity double-polarized experiment, while the large acceptance of the BigBite spectrometer gave coverage over a wide kinematic range: 0.15 < x < 0.95. In this work, we present the analysis of a portion of the E06-014 data, measured with an incident beam energy of 4.74 GeV and spanning 1.5 < Q 2 < 5.5 (GeV/c) 2 . From these data, we extract the longitudinal asymmetry in virtual photon-nucleon scattering, A 1 , on the 3 He nucleus. Combined with the remaining E06-014 data, this will form the basis of a measurement of the neutron asymmetry A n 1 that will extend the kinematic range of the data available to test models of spin-dependent parton distributions in the nucleon. AcknowledgmentsNo one in this age can earn a physics PhD based solely on her own work and study; the making of a doctor, like the making of a modern particle-physics experiment, requires the goodwill and support of many. In my own life and studies, I have been profoundly blessed by the presence of my family, friends, and colleagues. It is traditional to thank these wonderful people in these pages, as though words were enough. They aren't, but they are a start.My parents, Christine Marwick and Richard Seymour, brought me up to have both a deep curiosity about the world and the work ethic I needed to answer my own questions. The love of language my mother gave me made writing this dissertation far less painful than it might have been; my father urged me to take my first voluntary science course and then kindly refrained from saying "I told you so" at the sudden fascination with physics that resulted. My not-so-little brother, Matthew, kept me honest with everything I did.The love and support of my extended family has been invaluable. My grandparents, Bob and Dolores Marwick, generously funded my undergraduate education. They and my aunts, uncles, and assorted cousins, scattered around the continent, taught me that I could find something of home wherever I am. To Rob and Ann Marwick, Mike and Monica Marwick, Lorrie Marwick and Guy Marsh, Nancy and Don DeMuth, and Josephine Marwick, thank you for the delicious meals, the fascinating conversations and your willingness to talk physics. To my beloved cousins, thank you for everything. Growing up, I was also lucky to enjoy the love of many peo...

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“…Many theoretical works on Compton scattering cross sections were published by nuclear physicists. The most notable work was done by Lipps & Tolhoek (1954), who treated the spindependent Compton scattering on the basis of relativistic quantum electrodynamics for electrons at rest in the initial state. It had already been recognized by Du Mond (1929) that Compton scattered X-rays provide information on the momentum distribution of moving electrons in matter.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Magnetic Compton Scattering and Measurements of Momentum Distribution of Magnetic Electrons

Sakai¹

1996

J Appl Cryst

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Recent progress in the field of magnetic Compton scattering is reviewed and new momentum-space information about electronic states in magnetic materials is emphasized. Theoretical derivation of the magnetic Compton scattering cross section is made within the framework of the nonrelativistic Hamiltonian of electrons in the electromagnetic field. Discussion on the orbital-spin contribution to the magnetic Compton scattering is also included as a Compton limit. The feasibility of the magnetic Compton scattering experiment using circularly polarized hard synchrotron radiation is demonstrated by many recent experimental results.

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Polarization phenomena of electrons and photons. II

Cited by 100 publications

References 12 publications

Diffraction of X-rays by magnetic materials. I. General formulae and measurements on ferro- and ferrimagnetic compounds

Diffraction of X-rays by magnetic materials. I. General formulae and measurements on ferro- and ferrimagnetic compounds

Measurements of the Double-Spin Asymmetry A<sub>1</sub> on Helium-3: Toward a Precise Measurement of the Neutron A<sub>1</sub>

Magnetic Compton Scattering and Measurements of Momentum Distribution of Magnetic Electrons

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