Magnetic Neutron Scattering and Spin-Polarized Neutrons

Use trick to simplify this expression:1dp ip rcos22 eipr d p e d cosp0 1 2 sin p r 22 d p p r r0Here, p is an auxiliary variable without physical meaning.1 1 dp iprse 2 2 se re 2p1 ipr ˆ2 pse pˆe dp2 1 1 k s k dre dp p s p er 24Qˆs ˆe Q iQriprf e i ˆ 2 eˆs e The last line follows by doing the r -integration first and using 1 ipQr dr e 3 p Q2Q s esecollect all prefactors:2 2 mn 2 0 2 2 2 2NB 4 r024 15where r 02.810m is the “classical electron radius” that also appeared in theThompson cross section for x-ray scattering.d2 2r0 mf semidFor an unpolarized neutron beam, one has to average over the neutron spinstates m . For convenience, take the neutron spin quantization axis ẑ to beparallel to se. Then m s m s m mf ei ef z iseif mf mi 0 otherwiseThe cross section for a single electron at rest for an unpolarized neutron beamis therefored 2 r20sedwith the projection of the electron spin perpendicular to Q .se2

EditorialDear Reader,We want to show you our flexibility and the versatility of our special solutions in all product groups with this slogan.ACE sets the standard in lots of areas for industrial absorption technology with an innovative range of stockedcatalogue products that you will find on the following pages. Some supplementary product lines such as theclamping elements of the LOCKED range, stainless steel industrial gas springs (we have both V2A and V4A qualities) or theinnovative absorption plates, SLAB, have already made it into the catalogue but only present a fraction of our possibilities.Contact our professional sales team when you see the technical information “upon request”. Our service team is pleasedto offer specific customer amendments to catalogue items, such as other oil fillings, surface treatments, thread sizes andspecial characteristics. Developments such as the smart shock absorber, V-sensors and the innovative TUBUS blankholder absorbers belong to the “on a project basis” category.ACE offers customised brake systems that can help your drives, machines or systems achieve more productivity,durability, speed and a better energy balance.Please pay attention to our new ACEman. He will point out advantages and innovations in the catalogue.Issue 6.2011 Specifications subject to changeThe innovative TUBUS blank holder absorberfinds a new application as an absorber in press toolsand replaces the over-worked PU springs. More sheetmoulds are being made by faster presses in the automobileindustry. When openingthe press after the pressingprocess, the retainer boltsand the actual tool aresustainably protected. Thespecial TUBUS is availablefor the different retainer screwsfrom M10 to M30. The maximumenergy absorption isbetween 5 and 269 Nm at alow settlement reaction.The smart shock absorber is living proof of activeshock absorption. The controller, which is fitted withsensors, supplies the optimum adjustment to theactuator, which is directly connected with the adjustingsleeve of the classic MAGNUM shock absorber. Theconcept is available for all MAGNUM model sizes.The vibration sensor detects thedelay in a range of 0 - 35 g and worksas a “Condition Monitoring Tool”. Whenexceeding the pre-selected triggerrange, a signal is issued as a fault reportto the machine control. The V sensor is available as analogueand digital versions with 10 setting levels. Interlockeddirect installation in a C-nut or by adapter in a T-nut ordovetail nut is possible.ACE is already actively committed to the field of combattingpassive vibration with the proven SLAB absorption andvibration plates and currently offers a significant simulationprogram and vibration measurements on-site. ACE Calctakes a new approach and shows, in the solutions, a varietyof vibration isolationsfor the applicationcase and in the subsequentanalysisrange, and the insulationand isolationvalues expected fromthe selected SLABversion.All rights to the production, trade names, design and illustrations of this catalogue are reserved. No part of thispublication may be reproduced, copied or printed without permission; violations will be prosecuted. Construction,dimensions and specifications of ACE products are subject to change.Stoßdämpfer GmbH · PO Box 1510 · D-40740 Langenfeld · Tel. +49-2173-9226-4100 · Fax +49-2173-9226-89 · E-Mail: info@ace-int.eu 3

Hax0where0ha ~ is theH2emagnetic flux quantuma~ 500Å for H 1TThe periodic magnetic field distribution generated by the flux line lattice insidethe superconductor can be revealed by magnetic neutron scattering. Becausethe lattice constant a is large, the scattering angle ~ is small. Even for cold2aneutrons ~5Å and relatively high magnetic fields H~ 1 T, is less than1°. In order to obtain the resolution required to separate the Bragg reflectionsfrom the unscattered beam, one uses a dedicated Small Angle NeutronScattering (SANS) diffractometer with a long distance (>10 m) between sampleand detector:Small angle neutron diffraction patterns from flux lines lattice in a type-II superconductorNote that the structure of the flux line lattice changes as a function of magnetic field(M.R. Eskildsen et al., PRL 86, 320 (2001))As we have seen, nuclear and magnetic neutron scattering have comparablestrengths. They can be distinguished experimentally through three differentmethods:1 The magnetic form factor reduces the intensity of magnetic Bragg reflectionswith large K , whereas there is no form factor for nuclear scattering. Strongreflections with large K must therefore be nuclear in origin.2 Magnetic Bragg peaks vanish at the magnetic ordering temperature (theCurie temperature T C for ferromagnets, or the Néel temperature T N forantiferromagnets). Nuclear Bragg peaks vanish at the melting temperature,which is typically larger than T N or T C .3 The neutron spin operator does not appear the the cross section for coherentnuclear scattering. The neutron spin state is therefore unaffected by nuclearscattering. By contrast, magnetic neutron scattering can be (but does nothave to be) associated with a spin-flip of the neutron.5

For C C, only spin-up neutrons are reflected:ferromagnetic mirrornonmagnetic filmsmagnetic filmsNeutron reflectivity from nonmagnetic and magnetic filmshttp://www.orau.org/council/02presentations/klose.pdfFerromagnetic “supermirrors” with larger critical angles (see chapter on neutronreflectivity) are commonly used to produce spin-polarized neutrons in modernneutron scattering instruments:Polarized-beam reflectometerhttp://www.orau.org/council/02presentations/klose.pdf8

2 A method that has been developed in the past few years is the neutron spinfilter. A spin-polarized 3 He gas absorbs neutrons through the reaction3 4 3n He He ( S 0) pH .H 3 HeBecause the reaction proceeds via an intermediate state with S 0 , theabsorption cross section for neutrons with spins antiparallel to those of the3 Henuclei is therefore about three orders of magnitude larger than if neutron and3 He spins are parallel.9