AAMOP 2011-2012 2011-11-16 1

nn

nnn

n=1

n=2n=3

free electron plus He-like ion

ΔE=Ee+Ip,naber:

ΔE=E2-E1

Ee

Ip,n

E2

E1

AAMOP 2011-2012 2011-11-16 2

nn

nnn

n=1

n=2n=3

dielectronic recombination

E2

E1

AAMOP 2011-2012 2011-11-16 3

nn

nnn

n=1

n=2n=3

doubly excited ion

E2

E1

AAMOP 2011-2012 2011-11-16 4

nn

nnn

n=1

n=2n=3

γ

radiate deexcitation

h⋅ν = E2- E1E2

E1

AAMOP 2011-2012 2011-11-16 5

nn

nnn

n=1

n=2n=3

Li-like ion

AAMOP 2011-2012 2011-11-16 6

More complex even: trielectronic and quadruelectronic recombination

AAMOP 2011-2012 2011-11-16 7

Dielectronic recombination

AAMOP 2011-2012 2011-11-16 8

Trielectronic and quadruelectronic recombination

AAMOP 2011-2012 2011-11-16 9

Contributions of trielectronic and quadruelectronicprocesses to resonant photorecombination

AAMOP 2011-2012 2011-11-16 10

• Acceleration schemes for ions• Electrostatic accelerators• RF accelerators

Accelerators

AAMOP 2011-2012 2011-11-16 11

Van de Graaff principle

• Purely electrostaticacceleration• Ion source is installed at high voltage terminal• Potential is caused bycharging up the terminalwith a mechanical chargetransport chain

AAMOP 2011-2012 2011-11-16 12

Potential

0 Volt 0 Volt

10 MV

Energy

20 keV10.02 MeV

70.02 MeV

negative ionsC-

stripping positive ionsC6+

Tank with insulating gas (SF6)

Tandem van de Graaff accelerator (1930)

AAMOP 2011-2012 2011-11-16 13

MPI-K: 12 MV tandem accelerator

High voltageterminal

GroundCharge

Rubber conveyor beltor metal/insulatorchain (Pelletron)

van de Graaff principle

Tank (5.3 bar SF6)Terminal inside the tank

Negative ionsource

Van de Graaff accelerator

AAMOP 2011-2012 2011-11-16 14

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."

The cyclotron

One of the original Lawrence cyclotrons

AAMOP 2011-2012 2011-11-16 15

The synchrotron• Ring with bending magnets and RF cavity synchronouslyaccelerate particle bunches• Magnetic focusing by quadrupoles and by radial fieldgradients in the bending magnets

AAMOP 2011-2012 2011-11-16 16

HF linear accelerator structures

Wideröe (1928)

• Deliver bunched beams• Use powerful RF generators• High voltage generated by

resonantly driven drift tubes

AAMOP 2011-2012 2011-11-16 17

Heavy ion linear accelerators at the GSI Darmstadt

AAMOP 2011-2012 2011-11-16 18

++

-

-

GSI

• RFQs do not use drift tubes but resonant waveguides at f ≅ 100-500 MHz

• Oscillating electric field and shape of electrodes induces an longitudinalaccelerating component in z direction

Radio-frequency quadrupoles as accelerators

AAMOP 2011-2012 2011-11-16 19

Ion accelerators: beam foil technique

To produce higher charge states in accelerators, ions in low charge statespass through a very thin foil where electrons are stripped.

Example:• ion source produces a beam of 20 keV Ne2+

• accelerated to: 20 MeV Ne2+

• after passing stripper: 20 MeV Ne10+

ion source accelerator stripper foil

storagering

Storage ring = synchrotron without acceleration

AAMOP 2011-2012 2011-11-16 20

UNILAC

SIS

ESR

11.4 MeV/uU73+

10 - 500 MeV/uU92+

up to 1000 MeV/u

U92+

GSI accelerator gacility

AAMOP 2011-2012 2011-11-16 210 ,1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0

1 0 -5

1 0 -4

1 0 -3

1 0 -2

1 0 -1

1 0 0

( r )

2r nucl

eus

ψ

ra d iu s [f m ]

1s2s

2p1/2

2p3/2

Lamb shift: An effect of strong fields•QED corrections to binding energy ΔEscale as:

ΔE ∼ Z4/n3

Z: nuclear charge n: principal quantum

number

•Probability density in the region of highest field gradients is essential

AAMOP 2011-2012 2011-11-16 22

0 10 20 30 40 50 60 70 80 90109

1010

1011

1012

1013

1014

1015

1016

1s

<E>

(V/c

m)

Nuclear charge Z

Average field strength of 1s electron

changes by six

orders of m

agnitude

H atom

H-likeU91+

AAMOP 2011-2012 2011-11-16 23

Operation parametersv/c = β ≈ 0.65

Revolution frequencyf ≈ 106 s-1

Circumfence: 108 mNumber of ions: 108

Production of characteristic x-rays by electron captureinto bare ions (electron cooler or jet-target)

particledetection

GAS JET

X-Ray Spectroscopy at the ESR Storage Ring

U92+

300 MeV/u U92+

Ge(i)

90º

48º48º

132º

U91+

particledetection U91+

Ge(i)E

lekt

rone

nküh

lker

ESR (GSI, Darmstadt)

Storage rings for heavy ions

AAMOP 2011-2012 2011-11-16 24

ESR Storage ring at GSI

AAMOP 2011-2012 2011-11-16 25

TSR Heidelberg http://www.mpi-hd.mpg.de

Heidelberg Test Storage Ring

AAMOP 2011-2012 2011-11-16 26

electron collector electron gun

high voltage platform

magnetic fieldelectron beam

ion beam

electron collector electron gun

high voltage platform

magnetic field electron beam

ion beam

Storage rings: cooled ion beams

AAMOP 2011-2012 2011-11-16 27

• In the electron cooler of a storage ring, an electron beam issuperimposed to the stored ion beam• The electron beam overlaps with the ion beam on a straightsection and is then removed.

IonsIons

I: 5-500 mAU: 10 - 200 kV

Electrons

Electron cooling in storage rings

AAMOP 2011-2012 2011-11-16 28

Electron Cooler

•2.5 m interaction zone

•Voltage: 5 to 200 kV

•Current: 10 to 1000 mA

The GSI Electron Cooler

AAMOP 2011-2012 2011-11-16 29

• Ions interact 106 times per second with cold electrons moving at nearlythe same speed: small longitudinal momentum exchange. • The transversal components of the ion motion are cooled.

After cooling time: •Momentum spread Δp/p : 10-4 – 10-5

• Beam diameter : 2 mm

Momentum exchange of comoving particles

AAMOP 2011-2012 2011-11-16 30

0.97 1 1.03

rel. ion velocity v/v0

ion

inte

nsity

before coolingafter cooling

Ions interact 106 s-1 with collinear beam of cold electrons

Properties of the cold ion beam•Momentum spread Δp/p : 10-4 – 10-5

• Beam diameter 2 mm

The effect of cooling

AAMOP 2011-2012 2011-11-16 31

2000 2250 2500 2750 3000 3250 3500 3750 40000

10

20

30

40

50

60

70

80

90

Rel

ativ

e en

erg

y, E

rel (e

V)

Electron energy, Ee (eV)

Merged-beams kinematics

relative velocity: vrel = |ve – vion|relative energy: Erel = (√Ee - √Ecool)2

Ecool = Eion

me

mion

•Provides precise access to low relative collision energies

250 eV

17

eV

AAMOP 2011-2012 2011-11-16 32

time

Ucath

cool

meas

merged-beams rate coefficient: α = ⟨σv⟩

Dielectronic recombination: SR technique

cathodevoltage Ucath

recombinationdetector

electron cooler

electronbeam

ionbeam

AAMOP 2011-2012 2011-11-16 33

Relativistic Doppler transformation

Elab: Photon energy in the laboratory systemEproj: Photon energy in the emitter system

0 30 60 90 120 150 180

0.5

1.0

1.5

2.0

2.5 358 MeV/u (β =0.69) 220 MeV/u (β =0.59) 68 MeV/u (β =0.36) 49 MeV/u (β =0.31)

E lab/E

proj

observation anglel, θlab [deg]Doppler correction: Strong dependence on the velocity and the observation angle θLAB

)cosθβ(1E

Elab

projlab ⋅−⋅

=γ

cvβ ;

2β1

1γ =−

=

Experimental challenges

AAMOP 2011-2012 2011-11-16 34

X-Ray Spectroscopy at the ESR Storage Ring

Injection Energy400 MeV/u

Experiment 10 MeV/u

dec

eler

atio

nInjection Energy

400 MeV/u

Excited states are produced by electron capture (gas jet target) /recombination (electron target)

AAMOP 2011-2012 2011-11-16 35

• Blue shift has its maximumβ≈ 0.29 ⇒ Elab ≈ 1.43 × E proj

•ΔθLAB not critical, almost no Doppler width• Uncertainty caused by Δ βhas its maximum

0o Spectroscopy at the Electron Cooler

20 40 60 80 100 120 140 160 180 2000

100

200

300

400

500

600

Lyα2

Lyα1

Balmer

j=3/

2j=

1/2

L-RR

K-RR

coun

ts

Energy [keV]

H-like Uranium

Dipole Magnet

After capture of one electronby a U92+, a photon is emitted and detected

Coincidence with the “downcharged”projectile (U91+) reduces background

AAMOP 2011-2012 2011-11-16 36

460.2±2.3±3.5 eV

4.6 eV

1s Lamb shift in U91+

statistical uncertainty in β

Ground state Lamb shift in H-like uranium

100 120 140 160 180 200

0

50

100

150

200

Lyβ

Lyα2Co

un

ts

Photon energy (keV)

K-RR

Lyα1

AAMOP 2011-2012 2011-11-16 37

100 120 140 160 180 2000

50

100

150

200

Lyβ

Lyα2

coun

tsphoton energy [keV]

K-RR

Lyα1

2p3/2 B. E.

2p3/2

2p1/2

2s1/2

1s1/2

Lyα1 (E1)

Lyα2 (E1)M1

1s Lamb shift

Presently most accurate test of the bound-state QED for one-electron systems in the regime of strong fields carried out at the ESR.

Ground state Lamb shift in H-like uranium

AAMOP 2011-2012 2011-11-16 38

1990 1992 1994 1996 1998 2000 2002420430440450460470480490500510520

Dec

eler

ated

Ions

: C

oole

r (ou

r exp

.)Year

Lam

b S

hift

[eV

]

U91+

Gas

jet

Coo

ler

Dec

eler

ated

Ions

: Jet

Theory

1s Lamb shift in H-like uranium

Test of quantum electrodynamics

80 100 120 140 160 180 2000

20

40

60

80

100

120

140

cou

nts

photon energy [kev]

Lyα1

Lyα2

K-RR

1s Lamb shift

2p3/2

2p1/2

2s1/2

1s1/2

Lyα1 (E1)

Lyα2 (E1)M1

Experiment: 459.8 eV ± 4.6 eVTheory: 463.95 eV

A. GumberidzePhD thesis 2003,PRL 94, 223001 (2005)

Research HighlightsNature 435, 858-859

(16 June 2005)

AAMOP 2011-2012 2011-11-16 39

Additional slides 16.11.2011

AAMOP 2011-2012 2011-11-16 40

A(q-1)+(1s2 2p nl)

doubly excitedintermediate state

Aq+(1s2 2s) + e-

2s

2p

nl

A(q-1)+(1s2 2s2) + hn

radiative stabilizationdielectronic capture

Dielectronic recombination

AAMOP 2011-2012 2011-11-16 41

Principle of DR measurements at storage ring

AAMOP 2011-2012 2011-11-16 42

-1.0 -0.5 0.0 0.5 1.00

10

20

30

RR

n = 12n = 11 3s → 3p nl

3s →

4s

4d

3s →

4s

4p

3s →

4s

4s

Reco

mb

inat

ion

rat

e co

eff.

(10

-9 c

m3 s

-1)

CM energy (eV)

2350 2400 2450 25000

10

20

30

Lab. energy (eV)

2325 2425 25250

1

CM

ene

rgy

(eV)

Lab. energy (eV)

TSR: J. Linkemann et al. (1996)

Recombination of Na-like Se23+

AAMOP 2011-2012 2011-11-16 43

Experimental energy spread DR of Li-like C3+

0

10

e- + C3+(1s22s) → C2+(1s22p nl)

010203040

n=4

Rat

e co

effic

ient

(10-1

1 cm3 s-1

)

0 2 4 6 8 100

10 8...765

Electron-ion collision energy (eV)

1983: Dittner et al., PRL 51, 31electron beam compressionno cooling of ion beamkT^ = 5000 meV, kT|| = 1 meV

1990: Andersen et al., PRA 41, 1293constant electron-beam diameterno cooling of ion beamkT^ = 135 meV, kT|| = 1 meV

2001: Schippers et al., ApJ 555, 1027electron-beam expansionelectron cooling of ion beamkT^ = 10 meV, kT|| = 0.15 meV

AAMOP 2011-2012 2011-11-16 44

Recombination of Li-like U89+

(ESR experiment)

C. Brandau et al.,NIMB 205, 66 (2003)

0 20 40 60 80 100 120 140 160 180

5

10

j=9/2

j=7/2

j=5/2

j=3/2

n=34

n=33

n=32

n=31

n=30

n=29

n=28

n=27

n=26

n=25

n=24

n=23

n=22n=

21

n=20

Rat

e co

effic

ient

(10

-9 cm3

s-1)

Electron-ion collision energy (eV)

1s2 2p3/2 5lj resonances 1s2 2p1/2 nlj resonances

AAMOP 2011-2012 2011-11-16 45

Extrapolation of Rydberg SeriesAu75+(2p1/2 nl) resonances

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

E(2s1/2 - 2p

1/2 )

1000/n2

Rat

e co

effic

ient

(arb

. uni

ts)

60 80 100 120 140 160 180 200 220

n=35

n=24n=25

n=30

n=23

Electron-ion collision energy (eV)

ESR experimentDR of Li-like Au76+

AAMOP 2011-2012 2011-11-16 46

Results for Au76+

AAMOP 2011-2012 2011-11-16 47

Lamb-Shift in Heavy Li-like Ions2s1/2 – 2p1/2 splitting

Au76+ Pb79+ U89+

280.59(10) eVSchweppe et al. PRL 66, 1434 (1991)

216.167(29)(67) eV 230.650(30)(51) eV 280.516(34)(65) eVBrandau et al.,PRL 91, 073202 (2002)

experim

ent

216.17(13)(11) eV 230.68(6)(13) eV 280.48(11)(21) eVYerokhin et al.PRA 64, 032109(2001)

theo

ry

theoretical uncertainties due to uncertainty of nuclear size and due to missing QED diagrams

AAMOP 2011-2012 2011-11-16 48Measurement of the Two-Loop Lamb Shift in Lithiumlike U89+

P. Beiersdorfer,* H. Chen, D. B. Thorn, and E. Träbert

The 2s1/2-2p1/2 transitions in U88+ and U89+ were measured at the LLNL SuperEBIT.

The measured value of (280.645 +/- 0.015 eV) for Li-like U89+ improves the available precision by nearly an order of magnitude.

Benchmark for testing the total QED contribution to the transition energy; fractional accuracy of 3.6 × 10-4.

•2s two-loop Lamb shift in U89+ = 0.23 eV

•1s two-loop Lamb shift in U91+ = 1.27 eV

Lamb shift in Li-like U89+

AAMOP 2011-2012 2011-11-16 49

• Measurement of the U89+ 2s1/2-2p1/2 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 2s1/2-2p1/2 transition energy that misses only the two-loop Lamb shift contribution.

Lamb shift in Li-like U89+

AAMOP 2011-2012 2011-11-16 50

C. Brandau et al., Phys. Rev. Lett. 91, 073202 (2003)

Disagreement

AAMOP 2011-2012 2011-11-16 51

DR measurements of H-like U at GSI

AAMOP 2011-2012 2011-11-16 52

Sensitivity to nuclear charge radiusDR of Li-like U89+, 2p3/2 5l5/2 resonances

70 72 74 76 78 80 82 840

2

4

6

8

10 ESR experiment 238U89+

theory 238U89+ (rms = 5.86 fm) theory 233U89+ (rms = 5.81 fm)

Rat

e co

effic

ient

(10-9

cm

3 s-1)

Electron-ion collision energy (eV)

C. Brandau et al.,NIMB 205, 66 (2003)

Model independent test of

nuclear structure theories

AAMOP 2011-2012 2011-11-16 53

The Heidelberg Electron Target

AAMOP 2011-2012 2011-11-16 54

Electron target: Expanded electron beam

•Expanded electron beam cools down transversally•Energy definition for collisions improves greatly

AAMOP 2011-2012 2011-11-16 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 2011-2012 2011-11-16 56

DR measurements of Fe at MPIK

AAMOP 2011-2012 2011-11-16 57

Electron temperature:kT|| = 40 μeV

Dielectronic recombination

Hyperfine splitting due to nuclear spin = 5.4 meV

AAMOP 2011-2012 2011-11-16 58

• Electron collision spectroscopy using DR resonances of Sc18+ 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 2s1/2-2p3/2 excitation energy.

Hyperfine resolution (MPIK)