free electron plus He-like ion

Transcription

1 free electron plus He-like ion E e I p,n E 2 E 1 ΔE=E e +I p,n aber: ΔE=E 2 -E 1 n n n n n n=1 n=2 n=3 AAMOP

2 dielectronic recombination E 2 E 1 n n n n n n=1 n=2 n=3 AAMOP

3 doubly excited ion E 2 E 1 n n n n n n=1 n=2 n=3 AAMOP

4 radiate deexcitation γ E 2 h ν = E 2 -E 1 E 1 n n n n n n=1 n=2 n=3 AAMOP

5 Li-like ion n n n n n n=1 n=2 n=3 AAMOP

6 More complex even: trielectronic and quadruelectronic recombination AAMOP

7 Dielectronic recombination AAMOP

8 Trielectronic and quadruelectronic recombination AAMOP

9 Contributions of trielectronic and quadruelectronic processes to resonant photorecombination AAMOP

10 Accelerators Acceleration schemes for ions Electrostatic accelerators RF accelerators AAMOP

11 Van de Graaff principle Purely electrostatic acceleration Ion source is installed at high voltage terminal Potential is caused by charging up the terminal with a mechanical charge transport chain AAMOP

12 Tandem van de Graaff accelerator (1930) Tank with insulating gas (SF 6 ) Potential negative ions stripping positive ions C - C MV 0 Volt 0 Volt Energy MeV 20 kev MeV AAMOP

13 Negative ion source Van de Graaff accelerator MPI-K: 12 MV tandem accelerator Tank (5.3 bar SF 6 ) Terminal inside the tank High voltage terminal van de Graaff principle Charge Rubber conveyor belt or metal/insulator chain (Pelletron) Ground AAMOP

14 The cyclotron In 1930 the New York Times announced that a "new apparatus to hurl particles at a speed of 37,000 miles per second in an effort to obtain a long-sought goal the breaking up of the atom was described here today by Professor Ernest O. Lawrence of the University of California." One of the original Lawrence cyclotrons AAMOP

15 The synchrotron Ring with bending magnets and RF cavity synchronously accelerate particle bunches Magnetic focusing by quadrupoles and by radial field gradients in the bending magnets AAMOP

16 HF linear accelerator structures Deliver bunched beams Use powerful RF generators High voltage generated by resonantly driven drift tubes Wideröe (1928) AAMOP

17 Heavy ion linear accelerators at the GSI Darmstadt AAMOP

18 Radio-frequency quadrupoles as accelerators RFQs do not use drift tubes but resonant waveguides at f MHz Oscillating electric field and shape of electrodes induces an longitudinal accelerating component in z direction GSI AAMOP

19 Ion accelerators: beam foil technique ion source accelerator stripper foil storage ring Storage ring = synchrotron without acceleration To produce higher charge states in accelerators, ions in low charge states pass through a very thin foil where electrons are stripped. Example: ion source produces a beam of 20 kev Ne 2+ accelerated to: 20 MeV Ne 2+ after passing stripper: 20 MeV Ne 10+ AAMOP

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

21 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/ , AAMOP ra d ius [fm ]

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

23 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) AAMOP

24 ESR Storage ring at GSI AAMOP

25 Heidelberg Test Storage Ring TSR Heidelberg AAMOP

26 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 AAMOP

27 Electron cooling in storage rings I: ma U: kv Electrons Ions Ions In theelectron cooler of a storage ring, an electron beam is superimposed to the stored ion beam The electron beam overlaps with the ion beam on a straight section and is then removed. AAMOP

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

29 Momentum exchange of comoving particles Ions interact 10 6 times per second with cold electrons moving at nearly thesamespeed: smalllongitudinal momentum exchange. Thetransversal components of the ion motion are cooled. After cooling time: Momentum spread Δp/p : Beam diameter : 2 mm AAMOP

30 The effect of cooling before cooling after cooling ion intensity rel. ion velocity v/v 0 Ions interact 10 6 s -1 with collinear beam of cold electrons Properties of the cold ion beam Momentum spread Δp/p : Beam diameter 2 mm AAMOP

31 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 AAMOP

32 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 AAMOP

33 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 AAMOP

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

35 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 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 Δ β has its maximum Energy [kev] AAMOP

36 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 AAMOP

37 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. AAMOP

38 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] Research Highlights Nature 435, (16 June 2005) Lamb Shift [ev] U 91+ Gasjet Cooler Decelerated Ions: Jet Decelerated Ions: Cooler (our exp.) Year 1s Lamb shift Theory 1s 1/2 A. Gumberidze PhD thesis 2003, PRL 94, (2005) AAMOP

39 Additional slides AAMOP

40 Dielectronic recombination nl 2p 2s A q+ (1s 2 2s) + e - A (q-1)+ (1s 2 2p nl) doubly excited intermediate state A (q-1)+ (1s 2 2s 2 ) + hn dielectronic capture radiative stabilization AAMOP

41 Principle of DR measurements at storage ring AAMOP

42 Recombination of Na-like Se 23+ Recombination rate coeff. (10-9 cm 3 s -1 ) RR n = 11 3s 3p nl 3s 4s 4s 3s 4s 4p CM energy (ev) Lab. energy (ev) CM energy (ev) Lab. energy (ev) n = 12 3s 4s 4d TSR: J. Linkemann et al. (1996) AAMOP

43 Experimental energy spread DR of Li-like C 3+ Rate coefficient (10-11 cm 3 s -1 ) e - n=4 + C 3+ (1s 2 2s) C 2+ (1s 2 2p nl) Electron-ion collision energy (ev) 1983: Dittner et al., PRL 51, 31 electron beam compression no cooling of ion beam kt^ = 5000 mev, kt = 1 mev 1990: Andersen et al., PRA 41, 1293 constant electron-beam diameter no cooling of ion beam kt^ = 135 mev, kt = 1 mev 2001: Schippers et al., ApJ 555, 1027 electron-beam expansion electron cooling of ion beam kt^ = 10 mev, kt = 0.15 mev AAMOP

44 Recombination of Li-like U 89+ (ESR experiment) 1s 2 2p 3/2 5l j resonances 1s 2 2p 1/2 nl j resonances Rate coefficient (10-9 cm 3 s -1 ) 10 5 j=3/2 n=20 n=21 n=22 j=5/2 n=23 n=24 j=7/2 n=25 n=26 j=9/2 n=27 n=28 n=29 n=30 n=31 n=32 n=33 n= Electron-ion collision energy (ev) C. Brandau et al., NIMB 205, 66 (2003) AAMOP

45 Extrapolation of Rydberg Series Au 75+ (2p 1/2 nl) resonances Rate coefficient (arb. units) n=23 n=24 n=25 ESR experiment DR of Li-like Au 76+ n=30 n=35 E(2s 1/2-2p 1/2 ) /n Electron-ion collision energy (ev) AAMOP

46 Results for Au 76+ AAMOP

47 Lamb-Shift in Heavy Li-like Ions 2s 1/2 2p 1/2 splitting Brandau et al., PRL 91, (2002) Schweppe et al. PRL 66, 1434 (1991) Au 76+ Pb 79+ U (29)(67) ev (30)(51) ev (34)(65) ev (10) ev experiment Yerokhin et al. PRA 64, (2001) (13)(11) ev (6)(13) ev (11)(21) ev theory theoretical uncertainties due to uncertainty of nuclear size and due to missing QED diagrams AAMOP

48 Lamb shift in Li-like U 89+ The 2s 1/2-2p 1/2 transitions in U 88+ and U 89+ were measured at the LLNL SuperEBIT. The measured value of ( / ev) for Li-like U 89+ improves the available precision by nearly an order of magnitude. Benchmark for testing the total QED contribution to the transition energy; fractional accuracy of s two-loop Lamb shift in U 89+ = 0.23 ev 1s two-loop Lamb shift in U 91+ = 1.27 ev Measurement of the Two-Loop Lamb Shift in Lithiumlike U 89+ P. Beiersdorfer,* H. Chen, D. B. Thorn, and E. Träbert AAMOP

49 Lamb shift in Li-like U 89+ Measurement of the U 89+ 2s 1/2-2p 1/2 transition energy can be used to determine the two-loop Lamb shift. Calculations of all two-electron contributions include two-photon exchange term as well as estimates of higher-order photon exchange contributions. Adding these to the one-photon exchange, first-order QED, nuclear recoil, nuclear polarization, and one-electron finite size contributions yield a value for the 2s 1/2-2p 1/2 transition energy that misses only the twoloop Lamb shift contribution. AAMOP

50 Disagreement C. Brandau et al., Phys. Rev. Lett. 91, (2003) AAMOP

51 DR measurements of H-like U at GSI AAMOP

52 Sensitivity to nuclear charge radius DR of Li-like U 89+, 2p 3/2 5l 5/2 resonances Rate coefficient (10-9 cm 3 s -1 ) 10 ESR experiment 238 U 89+ theory 238 U 89+ (rms = 5.86 fm) 8 theory 233 U 89+ (rms = 5.81 fm) Electron-ion collision energy (ev) Model independent test of nuclear structure theories C. Brandau et al., NIMB 205, 66 (2003) AAMOP

53 The Heidelberg Electron Target AAMOP

54 Electron target: Expanded electron beam Expanded electron beam cools down transversally Energy definition for collisions improves greatly AAMOP

55 Improved resolution using with photocathode Electrons emitted from a photocathode have a lower initial temperature than those produced by a thermoionic cathode. Their energy definition becomes much better when accelerated AAMOP

56 DR measurements of Fe at MPIK AAMOP

57 Dielectronic recombination Hyperfine splitting due to nuclear spin = 5.4 mev Electron temperature: kt = 40 μev AAMOP

58 Hyperfine resolution (MPIK) Electron collision spectroscopy using DR resonances of Sc 18+ ions at TSR. Rydberg resonances have hyperfine splitting Center energies measured with 0.5% uncertainty. Rydberg binding energies (1000 times higher) can be accurately predicted Center energies yield precise values for the 2s 1/2-2p 3/2 excitation energy. AAMOP