PRECISION TESTS OF QED IN STRONG FIELDS: EXPERIMENTS ON HYDROGEN- AND HELIUM-LIKE URANIUM

A. Gumberidze, Th. Stöhlker, D. Banas, K. Beckert, P. Beller, H.F. Beyer, F. Bosch, X. Cai, S. Hagmann, C. Kozhuharov, D. Liesen, F. Nolden, X. Ma, P.H. Mokler, M. Steck, D. Sierpowski, S. Tashenov, A. Warczak, Y. Zou Atomic Physics Group, GSI Darmstadt, Germany ESR Group, GSI-Darmstadt, Germany University of Cracow, Poland University of Frankfurt, Germany Kansas State University, Kansas, USA IMP, Lanzhou, China Swiatokrzyska Academy, Kielce, Poland Fudan University, Shanghai, China

Uranium-Ion QED

vacuum polarization self- energy + + ... Z=92 PRECISION TESTS OF QED IN STRONG FIELDS: EXPERIMENTS ON HYDROGEN- AND HELIUM-LIKE URANIUM

• Introduction: QED, Lamb shift and the structure of one- and two-electron systems at high-Z

• Experiment at the storage ring ESR at GSI • Production and storage of high-Z few-electron (or bare) ions • X-ray spectroscopy at the ESR electron cooler, relativistic doppler effect

• Results in comparison with theoretical predicitions

• Summary

• Outlook (towards ∼1 eV precision) • Crystal spectrometer • Detector development One of the most precise predictions in prototype (first) Fundamental physics theory of EM of all field interactions theories

QED

… Fundamental masses constants Atomic Physics in Extremly Strong Coulomb Fields

H-like Uranium 3 16 EK = -132 • 10 eV 10 = 1.8 • 1016 V/cm 1015 1s Z = 92 10-4 14 10 10-5 m] Quantum Strong Influence on binding energies c -6 1013 10 IntensiveElectro- Laser 10-7 laser 12 - spectroscopy 10 10-8 l e

[V/ l Dynamics he -s 1011 10K-9 Hydrogen -10 10 frequency 10 EK = -13.6 eV relative accuracy 10 Z = 1 10 measurements = 1 • 10 V/cm 10-11 109 10-12 1 102030405060708090 Z=92 10-13 Nuclear Charge, Z 10-14 1s-ground state: increase of the electric field strength by s1920ix ord1940ers of m1960agnit1980ude 2000 year The Atomic Structure of One-electron System

Dirac 2p3/2 + QED Lyα1 (E1) 2s 2sLS 1/2 2p1/2

M1 Lyα2 (E1)

Experimental Method ħω

1sLS 1s1/2 Finite De te nuclear ct or size The Lamb shift: Z=92 The sum of all corrections which lead to the discrepancy from the predictions of the Dirac- Theory for a point-like nucleus. Self energy • Decrease of the binding energies • dominantly for s-states Vacuum poliariztion Bound-State QED: 1s Lamb shift

Self- Vacuum- energy polarization

U91+ SE VP NS 355.0 eV -88.6 eV 198.7 eV

4 2 ∆Ε=α/π (αZ) F(αZ) mec Low Z-regime: αZ << 1 F(αZ): expansion in αZ Tests of Bound-state QED

High Z-regime: αZ ≈ 1 F(αZ): expansion in αZ not applicable (calculation of all orders)

±1 eV Production of highly charged heavy ions

Traps (EBIT): axial Potential production of highly charged ions upper Drift tube by collisions with high energy electron beams Ions Accelerator: production of middle + Drift tube highly-charged ions by fast collisions with target atoms.

lower Drift tube - Charge-state distribution for Uranium 50 radial Potential 50 300 MeV/u

Electron beam Super-EBIT SIS ( y β

40 40 ≈ 0.65) nerg e 30

e [%] 30

20 20 Ausbeut t rest) a 10 s 10 200 keV electron (ion 0 0 92 91 90 89 88 87 86 92 91 90 89 88 87 86 Ladung Q GSI-ACCELERATOR FACILITY

UNILAC

11.4 MeV/u U73+ ESR

10 - 500 MeV/u 92+ SIS U up to 1000 MeV/u U92+ Experiments at the ESR

Ions β≈ 0.65

E≈300 MeV/u

Revolution Frequency f: ≈ 106 1/s

ESR circumference: 108 m number of Ions: 108 COOLED HEAVY-ION BEAMS

Electron collector Electron gun

High voltage

Magnetic field Electron beam

Ion beam COOLED HEAVY-ION BEAMS

electron collector electron gun

high voltage platform

magnetic field electron beam

ion beam

Electron cooler

Voltage: 5 to 200 kV

Current: 10 to 1000 mA

2.5 m interaction zone COOLED HEAVY-ION BEAMS

electron collector electron gun

high voltage platform

magnetic field before cooling electron beam ion beam aftrer cooling y intensit

0.97 1 1.03

relative ion-velocity v/v0 ions interact 106 1/s with the collinear cold electron beam

properties of cold ion beams

momentum width ∆p/p : 10-4 –10-5 size 2 mm Experiments at the ESR

Ions β≈ 0.65

E≈300 MeV/u

Revolution Frequency f: ≈ 106 1/s

ESR circumference: 108 m number of Ions: 108 0o Spectroscopy at the Electron Cooler

• maximum blueshift

β≈ 0.29 ⇒ Elab ≈ 1.43 × E proj - coincidence e • ∆θLAB not critical, minimum Doppler broadening ion q+ • uncertainty due to ∆βmaximum

ESR Dipole- (q-1)+ RR magnet q+

EKIN

600 H-like Uranium Lyα ∞ 1 500 Lyα L 2

400 Balmer sse i

300 gn

ω ei h r L-RR E 200 2 2

K / 1/ 3 j= j= K-RR 100

0 20 40 60 80 100 120 140 160 180 200 Energie [keV] The Experimental Challenge

2.5 Relativistic Doppler-Transformation 358 MeV/u (β =0.69) 220 MeV/u (β =0.59) 2.0 68 MeV/u (β =0.36) 49 MeV/u (β =0.31)

E proj proj 1.5

Elab = /E

γ⋅(1−β⋅cosθlab) lab

E 1.0

Elab: Photon energy in the laboratory frame E : Photon energy in the Emitter frame proj 0.5

Doppler correction 0 30 60 90 120 150 180 Strong dependence on velocity v Beobachtungswinkel, θ [deg] lab and on observation angle θLAB 1 v γ = ; β = c 1−β2 Experiments at the ESR

Ions β≈ 0.65

E≈300 MeV/u

Revolution Frequency f: ≈ 106 1/s

300 MeV/u

deceleration

ESR circumference: 108 m number of Ions: 108 4 MeV/u Ge(i) Detector 600 Lyα Center of the H-like uranium 1 500 electron Lyα 2 cooler 400 Balmer

300 tails counts L-RR Time of flight [ns] 200 2 2

/ 010203040 / 1 j= j=3 K-RR 100 0 100 200 300 400 0 20 40 60 80 100 120 140 160 180 200 distance [cm] photon energy [keV] Time

Recombination into Rydberg states leads to the delayed Lyman

ce time [ns] (distance) ce time [ns] emission, by up to microsecond. ciden n coi

100 200 300 400 500 600 counts 140 600 120 500 100 400 80

300 60 counts 200

counts 40

10020

00 8080 100 120120 140140 160160 180180 200200 photonphoton energyenergy [kev][kev]

time 400 condition 300 Tails disappear when

one applies a proper 200 counts condition to the time

100 spectrum

280 260 240 220 200 180 160 time [ns] The Ground State Lamb Shift in H-like Uranium

E Lyα Continuum 200 1

2p3/2 B. E. K-RR (=1s B. E.) 2p 150 3/2 Lyα2 s

count 100 Lyα1 K-RR 2p B. E. 50 3/2 Lyβ

1s1/2 0 250 100 120 140 160 180 200 Lyman photon energy [keV] 200

476 150 s t

472 un

468 co 100 K-RR e

V] r

a 91+ B

464 e 1s Lamb shift in U ift [e h 50 lik - H S 460 mb 0 La 456 s 450 460.2±2.3±3.5 eV 1 V] keV] e

Calibration k

452 .5 2

300 . 30 [1 177

b [ Y 448 b

150 Y 169

169 4.6 eV 0 123 statistical uncertainty in the β 120 130 14nu0mbe150r of a 160strip 170 180 190

energy (keV) Experimental Results in Comparison with Theory

520 : 510 91+ ons er

U l

500 Theory d I e 490 Coo Gasjet lerat

480 e 470

Dec Cooler (our exp.)

460 d te

450 ra Lamb Shift [eV] Lamb Shift le Jet

440 e 430 c ons: De I 420 1990 1992 1994 1996 1998 2000 2002 Year

Experiment: 460.2±4.6 eV 1% sensitivity to the 1s Lamb shift Theory (Yerokhin et al. 2003): 464.26±0.5 eV 4% Sensitivity to the self energy SE = 355.0 eV, VP = -88.6 eV 15% Sensitivity to the vacuum NS= 198.7 eV, HO ∼ 1.8 eV polarization Relative Measurement of the Two-electron Contribution to the Ground State Binding Energy in He-like Uranium

Electron-Electron Interaction in Strong Fields Electron beam Relativistic Many Body (RMB) + 2eQED 250 Bare

H-like e EKIN Continuum H

I

200 , 8

y

g

r

150 2eSE e M

∆E n

H

E L

n

I

counts

o ,

100i n

t y

o

i

a g hωH hωHe t -

r

z

i

a e - e n 50 z n 2eVP i

o e

n

I E 1

o 2 1 S0 I 1S1/2 K 0 H-like He-like 450 ∆E E +I =h ω EKIN+I He=h ωHe 300 H-likeCalibrationHe-like KIN H H Yb [130.5 keV] Yb [177.2 keV] 150 169 IH -IHe IH – IHe = ∆E169 ∆E(ħωH - ħωHe) = 0 ∆E120: Two-Electron130 140 150Contribution160 170 to180 the 190 Relative measurement Ionization potential in the He-like System All one electron contributions energyke( V) cancel out (e.g. finite nuclear size) Relative Measurement of the Two-electron Contribution to the Ground State Binding Energy in He-like Uranium

• Data subdivided into several groups • Checked for consistency

2.32

2.28 he -E h E

2.24 2248 ± 9 eV

2.20 123 number of strip Statistical uncertainty for ∆E: 9 eV

Uncertainty caused by doppler shift:

The result for the splitting ∆E is 2248 ± 9 eV Experimental Results in Comparison with Theory

ESR (First experiment for the two-contribution U90+): 2248(9) eV Theory (Yerokhin et al. 1997): 2246 eV 2 photon exchange ∼14 eV 2eSE ∼ 9.7 eV

Super-EBIT (First measurement of the 2e contribution) (Marrs et al, 1995)

But!! Results limited by counting statistics (Z<83)

As an example; for Bismuth an uncertainty of 14 eV has been achieved for the value of 1876 eV. 2eQED ∼ 6.7 eV

ƒ Our result agrees well with the most recent theoretical value. ƒ The experimental uncertainty is of the order of two-electron QED contributions. ƒ Compared to the former studies at Super-EBIT in Livermore, we could substantially improve the statistical accuracy and extend studies to the higher-Z regime. SUMMARY AND OUTLOOK

• Two-electron QED Studies at the ESR ƒ First measurement for helium-like uranium (U90+), ƒ Improvement of experimental sensitivity by a factor of two compared to former exp., ƒ resu180lt sensito ive to two-electron self 0energyo (2eSE) contribution, ƒ The result is limited only by counting statistics. • 1s Lamb shift Experiment for Hydrogen-like uranium (U91+) ƒ First experiment with decelerated ions at the ESR electron cooler, ƒ Kinematic separation of Rydberg transitions, dipole magnet ƒ Improvement electronin precisioncooler compared to former experiment by factor of three, ƒ Test of first order QED effects at the 1 % level, FOCAL project; Post. by R. Reuschl ƒ The result is limited by an uncertainty in the velocity determination. Simultaneous measurement at 0 and 180 deg. High resolution detection devices; spectrometer + PSG, calorimeter Excellent agreement between experimental results and theory for both cases ‘No test can prove a theory but any single test can disprove it.‘ Karl Popper