X-ray spectroscopy. Crystal spectrometers. Reflection gratings. Transmission gratings. Solid state detectors

Transcription

1 X-ray spectroscopy Crystal spectrometers Reflection gratings Transmission gratings Solid state detectors

2 Bragg s law

3 How are X-rays reflected from a surface? At short wavelengths, mirrors do not work well. Reflectivity of all materials becomes nearly zero at energies beyond 30 ev for normal incidence. At grazing incidence, reflectivity is maintained up to much higher energies. Spectrometers have to use as few reflections as possible.

4 How are X-rays reflected from a surface? Reflection of x rays from a surface is caused by the electrons which give it a refractive index n<1 at x ray wavelengths (solids have n>1at optical wavelengths). X rays striking vacuum-metal interfaces are going from optically moredense to optically less-dense media. In these circumstances total internal reflection of the light can occur. If the incidence angle is great enough (or the grazing angle is small enough) the X-rays are reflected from the surface. Value of the critical angle depends on the electron density of the mirror material. This number is particularly large for gold, platinum, iridium Reflectivity of a gold mirror Incidence angle 90 o 2 o 0.5 o Photon energy (ev)

5 Multilayer optics for x-rays Reflectivity of X-rays from a solid surface can be enhanced by using multilayers with nanometer spacing. Change of refractive index at each interface causes a partial reflection Interference effects enhance constructively total reflection efficiency Reflectivity Wavelength (nm) Reflectivity of molybdenum/silicon multilayer mirror 40 layers 6.9 nm period Reflectivity is tailored to optimize a certain wavelength of interest

6 Multilayer optics for x-rays Curved mirror geometries are also possible X-ray analysis of chemical elements in microscopic samples

7 Crystal x-ray spectrometers Some types: Von Hamos (cylindrical) Dumond (crystal in transmission) Johann (cylindrical) High resolution spectra (up to R=20000) can be obtained.

8 The Rowland mounting a l 1 detector slit l 2 grating Geometry suggested by Rowland in Combines the focusing properties of a spherical mirror with the diffraction properties of a grating. If a source and the grating are placed on a circle with half the radius R of the grating, all wavelengths will be focussed on the same circle: The Rowland circle.

9 Von Hamos crystal x-ray spectrometer By bending crystals in sophisticated ways, focusing and imaging of x-ray sources can be achieved.

10 Transmission crystal x-ray spectrometer Dumond geometry: crystal works in transmission not affected by refractive index of crystal material application for hard x-rays, which are transmitted through crystal and partially reflected by many lattice layers

11 Johann x-ray spectrometer

12 The equivalence of mass and energy The direct test of Einstein s equation is based on the prediction that when a nucleus captures a neutron, the resulting isotope (mass number A+1) is somewhat lighter than the sum of the masses of the original nucleus (mass number A) and the free neutron (mass number 1). The energy equivalent to this mass difference is emitted as a spectra of gamma-rays. The mass difference in Einstein s equation using two silicon isotopes Si and two sulphur isotopes S has been measured with very high accuracy at the MIT, using a novel experimental technique.

13 The equivalence of mass and energy The mass differences betweeen the nuclei involved in the reaction are converted into photon energy. The masses are weighted in a Penning trap. The photon energy is measured with the crystal spectrometer: The quantity 1-Δmc 2 /E = (-1.4 +/- 4.4) 10-7 is obtained. Equivalence of mass and energy tested to a level of at least %.

14 Mass measurement at the MIT Penning trap The mass difference Δm is measured by simultaneous comparisons of the cyclotron frequencies (inversely proportional to the mass) of ions of the initial and final isotopes confined over a period of weeks in a Penning trap. (S. Rainville et al., Science 2004)

15 Wavelength measurement at ILL The energies of the gamma-rays emitted after neutron capture by both silicon and sulphur have been measured at the using the world s highest resolution gamma-ray interferometer GAMS4. Precision of better than 5 parts in

16 Wavelength measurement at ILL High angular resolution is obtained by using high precision optical interferometers. The crystals are mounted on interferometer arms which can be rotated in angular steps as small as arcsec (10-7 or rad).

17 Measurement of the 788 kev transition in 36 Cl.

18 Data for testing E=mc 2 a) Wavelength data and fitted curves. The energy of the emitted 5,421-keV γ- rays is measured from the angular separation of the second-order Bragg peaks resulting from diffraction from a silicon crystal. b) Measured mass ratio M[ 33 S]/M[ 32 SH] (which largely determines the mass change, m) as a function of the distance between the ions, s, in the Penning trap. The final mass ratio (solid line) is determined with fractional accuracy of 7 parts in (dashed lines). Simon Rainville et al., Nature 438 (2005) 1096

19 Flat crystal x-ray spectrometer

20 Absolute x-ray spectroscopy light beams laser crystal A novel methode removes the largest error sources found in crystal spectrometers x-ray source (EBIT) mirror fiducial 2 x-ray line fiducial 1 CCD Bruhns, Braun et al., Rev. Sci. Inst. 76, (2005)

21 Laboratory setup

22 Absolute measurements CCD 2 Γ = 180-2Θ 180-2Θ θ EBIT a/b θ crystal 180-2Θ ξ CCD 1 Bond method (W.L. Bond, Acta Cryst. 13, 814 (1960))

23 The Lyman-α spectrum of hydrogenic Ar

24 Hydrogenic standards? Current x-ray standards impaired by satellites Calibration line Fe Kα (1 ppm) Best HCI line elsewhere Ar 17+ Ly α1 (5 ppm) Counts Wavelength (pm) satellites

25 The Lyman-alpha spectrum of hydrogenic Ar ~2 ev

26 The Lyman-alpha spectrum of hydrogenic Ar

27 The He-like S 14+ spectrum Relative measurements Heidelberg EBIT Absolute measurements

28 Two-electron QED Contributions to ground state in He-like Ar ev 5 ev 1 ev + + h. o. experimental error bar: ± 0.01 ev E nuclear recoil 0.06 ev higher orders ev 0.1 ev

29 Lamb shift in Li-like Bi 80+ Measurement of the Bi 80+ 2s 1/2-2p 3/2 transition energy Hyperfine splitting of the F=4,5 levels

30 Lamb shift in Li-like Bi 80+ Hyperfine splitting of the F=4,5 levels

31 Grazing incidence spectrometer

32 Reflection grating spectrum

33

34 Seya-Namioka VUV spectrometer The Seya-Namioka mounting is used at wavelengths > 30 nm for which reflectivity at normal incidence is still sufficient Special case of the Rowland mounting with an acceptable spectral resolution. It is widely used in plasma diagnostics and at synchrotrons.

35 Transmission gratings for x-rays Height of grating structure has a strong effect on grating efficiency by imposing an additional diffrection condition The HETG gratings have a period of 0.2μm or 2000Å for the high-energy gratings, and 0.4μm or 4000Å, for the medium energy gratings. Gratings with grooves/mm (1000Å) are used already

36 A pinhole transmission grating spectrometer two spectra X-ray experiment with a two pinhole grating (a and b) spectrograph. PFS: plasma focus x-ray source C: capacitor for energy storage to feed discharge SH: shutter PH: pinhole to collimate x rays PG: pinhole gratings

37 Grazing incidence soft-x-ray spectrometer At wavelengths shorter than 30 nm, small grazing angles are needed. Detectors are mounted on the Rowland circle and moved under vacuum with bellows. Curved photographic plates and MCPs can also be used.

38 Grazing incidence imaging optics Kirkpatrik-Baez geometry uses two cylindrical x-ray mirrors at grazing incidence Each of the two cylindrical mirrors focuses in one coordinate.

39 Wolter telescope Grazing incidence mirror telescope for x rays in satellites Uses concentric conic surfaces with a single common point Paraboloid-hyperboloid combination with two internal reflections.

40 Wolter telescope and Rowland spectrometer After focusing by mirror, transmission or reflection gratings are used to add spectral dispersion when needed This spectrograph produces images in individual wavelengths

41 Chandra s Wolter telescope

42 Spectral imaging with XMM and Chandra Composite image Images of a supernova remnant at different soft x-ray wavelengths

43 Space based x-ray telescopes Coronal Diagnostic Spectrometer (CDS) on SOHO (ESA/NASA Solar and Heliospheric Observatory) Two compementary systems; the Normal Incidence Spectrometer (NIS) and the Grazing Incidence Spectrometer (GIS). Spectral range of operation

44 Diagnostics of fusion plasmas with VUV and x-rays The diagnostic of temperature, density, plasma composition, radiative losses material transport in fusion reactors in tokamaks requires the use of many spectrometers

45 The spectrum of hydrogen One needs three quantum numbers to define the state of a hydrogen (hydrogen-like) atom: n = 1, 2, 3 (principal) l = 0,, n-1 (orbital) m = -l,, +l (magnetic) The energy depends only on the principal quantum number n: E n 2 Z = 2n 2 ψ ( r) = ψ ( r, θ, ϕ) = R ( r) Y ( θ, ϕ) Energy (au) 0-1/18-1/8 3s (n=3, l=0) 2s (n=2, l=0).... nl 3p (n=3, l=1) 2p (n=2, l=1) lm free electron bound electron 3d (n=3, l=2) i.e. in a non-relativistic theory the (l,m) states are degenerate! -1/2 1s (n=1, l=0)

46 Dirac theory E nj = mc 2 1+ n j + 1/ 2 + Zα ( j + 1/ 2) 2 ( Zα) mc2 Positive continuum bound states e - n: principle quantum number j: total angular momentum α: fine structure constant- α = 1/ ) mc 2 : electron rest mass (511 kev) 0 Dirac-Theorie: (complete relativistic treatment of single electron systems) - mc 2 All levels with the same n and j are degenerate. Negative energy continuum e +

47 The Lamb shift Experiment: Lamb-Retherford 1947; Theoretical Explanation: Bethe 1947 Experiment proves that 2s 1/2 and 2p 1/2 are not degenerate Contradicts Dirac theory 2s 1/2 2E1 1s 1/2 2p 3/2 Lyα 1 (E1) Lyα 2 (E1) 2p 1/2 Lamb shift (LS) includes all deviations from the Dirac theory for a point like nucleus Consequence of the interaction of the bound electron with its own radiation field (self energy). Level scheme for hydrogen

48 The effects of QED on the binding energy increase with the strength of the electric field. s electrons are most affected since their. Lamb shift (three effects) QED Self-energy Self energy Bohr-trajectory Vacuum polarization Vacuum polarization Z Sizeof thenucleus

49 Laser spectroscopy of hydrogen relative accuracy laser spectroscopy frequency measurements year

50 Lamb shift: An effect of strong fields QED corrections to binding energy ΔE scale as: ΔE Z 4 /n s 2s Z: nuclear charge n: principal quantum number ψ Probability density in the region of highest field gradients is essential r (r) nucleus 2p 1/2 2p 3/ , radius [fm]

51 Average field strength of 1s electron <E> (V/cm) s changes by six orders of magnitude H-like U H atom Nuclear charge Z

52 Self energy (SE) Self-energy: Describes the emission and reabsorption of a virtual photon (Bethe 1947) The self energy decreases the binding energy. virtual photon electron in the outer field (Coulomb field of the nucleus) Mass renormalization m = me m m e m: measurable electron mass. It already includes the radiation correction. The self-energy decreases the binding energy. Classical theory: infinitely high mass corresponding to an infinitely high self energy. First calculations for H were made by Bethe based on an idea of Kramer: mass renormalization. The interaction with virtual photon modifies the electron mass. Measured electron mass m already includes this radiation correction. The self-energy correction for a bound state is equivalent to mass difference between the bound electron and a non-interacting free electron of the mass m e. m electron mass of the free electron without interaction with a field.

53 Vacuum Polarization (VP) Virtual creation and annihilation of an e + e pair VP acts attractive

54 Summary of Lamb shift contributions ΔΕ=α/π (αz) 4 F(αZ) m e c 2 Self energy Vacuum polarization s Lamb Shift, ΔE / Z 4 [mev] self energy (-) vacuum polarization Lamb- Shift nuclear size Individual corrections in detail 2p 1/2 1s 1 /2 Fine structure 2sLS 1sLS Hydrogen, H 10.2 ev 45.4 μev 4.4 μev 35.6 μev H-like uranium, U kev 4.56 kev 75.3 ev ev nuclear charge number, Z

55 Bound-State QED: 1s Lamb Shift at High-Z Sum of all corrections, leading to deviations from the Dirac theory for a point-like nucleus Self energy Vacuum polarization U 92+ SE VP NS ev ev ev Goal: ΔΕ=α/π (αz) 4 F(αZ) m e c 2 ±1 ev Low Z-Regime: αz << 1 F(αZ): series expansion in αz High Z-Regime: αz 1 F(αZ): series expansion in αz not appropriate

56 QED correction in second order α SE SE VP VP SE VP S(VP)E

57 GSI accelerator gacility UNILAC ESR 11.4 MeV/u U MeV/u U 92+ up to 1000 MeV/u U 92+ SIS

58 U 91+ X-Ray Spectroscopy at the ESR Storage Ring Storage rings for heavy ions particle detection U 92+ U MeV/u ESR (GSI, Darmstadt) 48º Ge(i) 90º 132º 48º GAS JET Elektronenkühlker particle detection U 91+ Ge(i) Operation parameters v/c = β 0.65 Revolution frequency f 10 6 s -1 Circumfence: 108 m Number of ions: 10 8 Production of characteristic x-rays by electron capture into bare ions (electron cooler or jet-target)

59 ESR Storage Ring

60 Storage rings: cooled ion beams electron collector electron gun electron collector electron gun high voltage platform high voltage platform magnetic field electron beam ion beam magnetic field electron beam ion beam

61 Electron cooling in storage rings I: ma U: kv Ions Electrons Ions Properties of the cold ions: Momentum spread Δp/p : Beam diameter 2 mm Ions interact 10 6 times per second with a collinear beam of cold electrons at nearly the same speed: cooling in the cold electron bath. The transversal components of the ion motion are efficiently cooled.

62 The effect of cooling before cooling after cooling ion intensity rel. ion velocity v/v 0 Ions interact 10 6 times per second with collinear beam of cold electrons Propertiesof thecoldionbeam Momentum spread Δp/p : Beamdiameter 2 mm

63 Merged-beams kinematics 17 ev Relative energy, E rel (ev) ev Electron energy, E e (ev) Provides precise access to low relative collision energies m e E cool = m E ion ion relative velocity: v rel = v e v ion relative energy: E rel = ( E e - E cool ) 2

64 The GSI Electron Cooler Electron Cooler 2.5 m interaction zone Voltage: 5 to 200 kv Current: 10 to 1000 ma

65 Dielectronic recombination: SR technique electron beam cathode voltage U cath ion beam recombination detector electron cooler merged-beams rate coefficient: α = σv U cath meas time cool

66 Experimental challenges Relativistic Doppler transformation E lab Eproj = γ (1 β cosθ lab E lab : Photon energy in the laboratory system E proj : Photon energy in the emitter system ) E lab /E proj MeV/u (β =0.69) 220 MeV/u (β =0.59) 68 MeV/u (β =0.36) 49 MeV/u (β =0.31) Doppler correction: Strong dependence on the velocity and the observation angle θ LAB observation anglel, θ lab [deg] 1 γ = ; β = 1 β 2 v c

67 X-Ray Spectroscopy at the ESR Storage Ring Injection Energy 400 MeV/u deceleration 10 MeV/u Excited states are produced by electron capture (gas jet target) / recombination (electron target)

68 0 o Spectroscopy at the Electron Cooler After capture of one electron by a U 92+, a photon is emitted and detected 600 H-like Uranium Lyα 1 Dipole Magnet Coincidence with the downcharged projectile (U 91+ ) reduces background counts Balmer L-RR j=1/2 j=3/2 Lyα 2 K-RR Energy [kev] Blue shift has its maximum β 0.29 E lab 1.43 E proj Δθ LAB not critical, almost no Doppler width Uncertainty caused by Δβ has its maximum

69 Ground state Lamb shift in H-like uranium 200 Lyα 1 Counts Lyα 2 50 Lyβ K-RR Photon energy (kev) 1s Lamb shift in U ±2.3±3.5 ev statistical 4.6 ev uncertainty in β

70 Ground state Lamb shift in H-like uranium 2s 1/2 M1 2p 3/2 Lyα 1 (E1) 2p 1/2 Lyα 2 (E1) counts Lyα 2 Lyα 1 1s Lamb shift 1s 1/2 50 2p 3/2 B. E. Lyβ photon energy [kev] K-RR Presently most accurate test of the bound-state QED for one-electron systems in the regime of strong fields carried out at the ESR.

71 Test of quantum electrodynamics 1s Lamb shift in H-like uranium counts Lyα 1 Lyα 2 K-RR Experiment: ev ± 4.6 ev Theory: ev 2s 1/2 M1 2p 3/2 Lyα 1 (E1) 2p 1/2 Lyα 2 (E1) photon energy [kev] 1s Lamb shift 1s 1/2 Research Highlights Nature 435, (16 June 2005) Lamb Shift [ev] U 91+ Gasjet Cooler Decelerated Ions: Jet Decelerated Ions: Cooler (our exp.) Year Theory A. Gumberidze PhD thesis 2003, PRL 94, (2005)