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Coherent Bremsstrahlung and the Quantum Theory of Measurement E.H

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Coherent Bremsstrahlung and the Quantum Theory of Measurement E.H Coherent Bremsstrahlung and the Quantum Theory of Measurement E.H. Du Marchie van Voorthuysen To cite this version: E.H. Du Marchie van Voorthuysen. Coherent Bremsstrahlung and the Quantum Theory of Mea- surement. Journal de Physique I, EDP Sciences, 1995, 5 (2), pp.245-262. 10.1051/jp1:1995126. jpa-00247055 HAL Id: jpa-00247055 https://hal.archives-ouvertes.fr/jpa-00247055 Submitted on 1 Jan 1995 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. (1995) Phys. I OEYance J. 245-262 5 1995, 245 FEBRUARY PAGE Classification Physics Abstracts 78.70F 03.658 Bremsstrahlung Quantum Theory Coherent and the of Measurement Voorthuysen E-H- Marchie du van Gromngen, Physics Centre, Nuclear Solid and Materials Nijenborgh University State Science of Groningen, Netherlands NL 4, AG The 9747 (Received accepted September 1994) 1993, October December revised 29 19g4, 21 18 (CB) brernsstrahlung Bragg Coherent Abstract. is the result inelastic of scattering of elec- crystal. kev, hundreds elfect of few of collective trie whole microscope of In electron trons a a an theoretically possible inelastically electron of where the deterrnine trie is it atoms to row was contradictory. path These Optical scattered. calculations made kev for 160 staternents are are [Ill] by inelastically crystal scattered silicon compared with electrons and the results a are application by rneasured CB The results understood be Kampen's theory Van of spectra. can Experimental CB of mechanical of the result be quantum spectra measurement. tum out to summation coherent within and incoherent the of intensitie8 from of scattering atoms row, same words, other the electrons CB locabsed in within atomic dilferent that rows, or, cause are rows. Introduction l. During of of of collisions electrons few hundreds BREMSSTRAHLUNG. COHERENT 1-1. a i) resulting following shell the ionisation inelastic inner in kev with events atoms can occur: for resulting charac- X-ray radiation, shell and ii) ionisation excitation in charactenstic outer (EELS) iii) region, loss the eV and peaks the electron emission in 10 in teristic spectrum energy bremsstrahlung changed by Coulomb the photon the electron the field of of when orbit is a nudeus. atomic physics partide electromagnetic when is that radiation dassical electron emits is In it an a /3(t) velocity bremsstrahlung by electron The of emitted with intensity the accelerated. an = v(t)/c is [1] / (l) d~I/duJdfl ((n /3) /(1 e~ /(47r~c) e~~(~~~'~(~)/~)dt(~ /3) /3 in n)~j x x = r(t) connecting the of and emitted radiation the direction the the where is in vector vector unit n without bremsstrahlung continuous, Normally the is detector. with spectrum the electron the structure. any interatomic equidistant with trajectory close of with consider electron atoms We to a row an a We change velocity Ad nucleus. each undergoes time L. This distance electron it passes a a IOIIRNAL PHYSIQUE11 5, OE T N° PEIIRUARY 1995 2, 4 Physique Q de Les Editions 1995 PHYSIQUE JOURNAL DE I N°2 246 (Ad( straight (p(, fl and fine time between trajectory is the the successive < a + so assume L/(flc). velocity change At is for The interactions is /3 radiative except constant, zero = bremsstrahlung frequency Fourier of with the the the is integer, mât C spectrum t + so m = equidistant sharp pulses the domain: of in time transform j.27rflc/(L(1 f(uJ) /3))] (2) j à Const integer. n [uJ = = , perpendicular ground the of the photons for direction electrons that emitted the We observe to velocity proportional proportional the frequency electron the and inverse interatomic is to to distance. spread spread the angular incoming electrons of and the the beam the If in energy are regarded regarded but be sufliciently small be entities, the localised electrons must not may as electron, plane the which assumed of manifestations wavefunction be of the is to wave, a as a wavelength wavelength Àf, the electron leaves with When with The À;. À;. Àf atom > we wave crystal, scattered from of dealing extended the all with like atoms, structure a waves an are (the added and number of electrons detected far intensity be the atoms must away screen on a time) squared. equal of the modulus of of Constructive the is unit to unit wave, per sum per area scattering, Àf, interference effects like the of where elastic in and destructive À; occur, case = (electron diffraction). Bragg scattering the well give effects As known these rise matter to a elastically practically leaving fact, by crystal electrons that scattered of the ail thin are are a interference place. inelastically where takes crystal directions For scattered in constructive completely by bremsstrahlung if electrons the the removed true energy same excess one is is Bragg photon. construction, which useful Ewald for visualising The is scattering, very con coherent used Figure therefore illustrate inelastic electron also scattering, Coherent be 1. to (CB) bremsstrahlung k; kf relation satisfied the when and (kf(, vector (k;( +g > occurs q is = 1/À, k connecting lattice the electron k points is is vector, (k( in two vector g e wave a = photon. reciprocal hq the of the CB and is momentum space, photon of The the CB is energy [2] g2/2k;)/(1 pcos9) hep(g~ (3) ~ = projection of k; the the of with angle direction and of the the between direction g gz on (3). k;. channeling and Effects photon of the neglected Diffraction radiation effects in are bremsstrahlung neglected, lattice itself with wavelength of the also the coherent of the are bremsstrahlung generally large. is too parallel incoming electron When beam the points of reciprocal the all to axis, is zone a belonging lattice have Figures Laue the the value for They ld. and to lc same same zone gz, peak bremsstrahlung the the contribute k;, in because and equations the spectrum to < same g (2) (3) equivalent. and are between observed the CB be characteristic the in X-rays, continuum Figure The CB 2. can peaks marked equal numbers the with of the order Laue Vecchio and Williams to are [3] zone. have study made expenmental of the extensive optimum producing conditions for peaks. CB an (no These conditions specimens thin X-rays elements impurities), of intervening from are: pure surfaces, crystal dean (to orientation, low vibrations), lattice axis reduce temperature and zone detection with semi-conductor angle detector solid with steradians 0.01 direction > a a a m perpendicular Carstanjen beam. the from and observed CB Sigle quasicrystal. to [4] a bremsstrahlung considered effect be analytical side elec- Coherent is in to annoymg an X-ray peaks peaks from impurities CB obscure lead microscopy, tron to wrong or can can problem interesting CB lead X-rays. of But also impurity determinations to intensity an can fundamental of nature. COHERENT N°2 BREMSSTRAHLUNG QUANTUM AND THEORY 247 o . , k~ , i~ . .i 1. o . ~ a) b) . i~ i~ , k ç 3 -3 ~ ) q 2 -2 . ~ . ) -1 - Î o -o ~ c) d) . , a) b) (kf(; reciprocal (k,( Ewald lattice: elastic Fig. constructions the inelastic scattering, l. in = hq photon; the CB inelastic of (kf(, c) the emitted (k,( (k,( scattering, scattering, momentum > > is towards third the order k, axis trie (kf(, axis, Laue scattering point zone; in zone a on zone a ii d) k, (kf(, in first towards order Laue the scattering inelastic point scattering, (k,( > axis, zone a a ii zone. intriguing physics One of the of the is PROBLEM. DEFINITION 1.2. aspects most THE oF particle electron localised manifestation duality. question the the particle-wave The is it is or a nicely experiment, the double-slit for extended illustrated with instance of wave? be see can an detector, function of measured position The flux of the is Feynman electron it [5]. on as as a factors, and slits, diffraction factor of the behind wall with the consists two two a a screen factor, diffraction. Fraunhofer interference observe interference When it like is not we m an PHYSIQUE JOURNAL DE N°2 I 248 Cu sumoeak Si Si Fe Cu Fe 7 5 JO 6 8 4 2 Ioss (kev) energy [loo] crystal Experimental photon A silicon bombarded Fig. temperature 2. spectrum. at is room [Ill] microscope. parallel electrons axis JEOL JEM CX Photons by kev 200 120 to in a are an Si(Li) angle 90° detector eV. The of by with resolution of130 sobd direction H detected the in a a = 10~~ by peaks X-rays dominated of characteristic that is The 1.8 srad. spectrum is acceptance X are height peak Si-Ka is symbol; their 120,ooo the The of the kev by chemical 1.8 indicated courts. at indicating they by bremsstrahlung marked numbers the from which Laue peaks of coherent zone are origmate. actually really observed which electron through possible deduce slit the to went. to measure or the detect the slits disturbance electron of As of the try to at passage cause we we one a soon as interference the phase of the wavefunction the electron such that factor of result the as a m terminology through measuring The that the of the value. usual into constant act turns is a collapsed. wavefunction electron has the of slit electron the the at electron electron diffraction observed be for the of said the The it is in can same case as There which passed microscope.
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