free electron plus he-like ion - physikalisches institut...aamop 2011-2012 2011-11-16 33...
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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
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• 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)