Modern Atomic Physics: Experiment and Theory Preliminary plan of the lectures
• 1 15.04.2015 Preliminary Discussion / Introduction
Experiments • 2 22.04.2015 Experiments (discovery of the positron, formation of antihydrogen, ...) • 3 29.04.2015 Experiments (Lamb shift, hyperfine structure, quasimolecules and MO spectra) • 4 06.05.2015 Theory (from Schrödinger to Dirac equation, solutions with negative energy) Lamb shift, hyperfine structure, • 5 13.05.2015 Theory (photon, quantum field theory (just few words), Feynman diagrams, QED corrections)
• 6 20.05.2015 Theory (matrix elements and their evaluation, radiative decay and absorption) quasimolecules and MO spectra • 7 27.05.2015 Experiment (photoionization, radiative recombination, ATI, HHG...)
• 8 03.06.2015 Theory (single and multiple scattering, energy loss mechanisms, channeling regime) Lecture 3 • 9 10.06.2015 Experiment (Kamiokande, cancer therapy, ….)
• 10 17.06.2015 Experiment (Auger decay, dielectronic recombination, double ionization) April 29th, 2014 • 11 24.06.2015 Theory (interelectronic interactions, extension of Dirac (and Schrödinger) theory for the description of many-electron systems, approximate methods)
• 12 01.07.2015 Theory (atomic-physics tests of the Standard Model, search for a new physics) • 13 08.07.2015 Experiment (Atomic physics PNC experiments (Cs,...), heavy ion PV research)
1 Hydrogenic spectrum Prediction of anti-matter
One needs three quantum numbers (r) (r, , ) R (r)Y (,) nl lm E to define the state of a hydrogen positive continuum (hydrogen-like) atom:
n = 1, 2, 3… (principal) l = 0, … n-1 (orbital) Electron is free Energy (au)Energy 2 m = -l, …. +l (magnetic) 0 +m0c Electron is bound to ion ……….. ……….. bound 3s (n=3, l=0) 3p (n=3, l=1) 3d (n=3, l=2) 0 The energy depends only on the -1/18 states principal quantum number: 2s (n=2, l=0) 2p (n=2, l=1) -1/8 2 2 Z -m0c E n 2n 2 i.e. in nonrelativistic theory the negative continuum 1s (n=1, l=0) states are degenerate (l, m)! -1/2 Dirac, Anderson, the Positron and the anti-matter. In his famous equation Paul Dirac combined (1929)the fundamental equation of quantum mechanics, the Schrödinger-equation with the theory of special relativity. He did not discard the negative energy –solutions of his equation as unphysical but interpreted them as states of the anti- particle of the electron (positron, having the same mass but opposite charge). In 1932 Carl Anderson discovered the Why set (n,l,m) is good for the description of bound hydrogenic states? positron the first time in the cosmic radiation. This was the proof of the existence of 'anti-matter', with incalculable Let us re-consider the set of (nonrelativistic) quantum numbers one more time! consequences for the future of physics.
2 Electron-positron pair production
The first confirmation In order to produce electron-positron pairs we would need: of a positron at least two times the rest mass of the elecreon !!!
E
electron energy of about
2 2 +m0c mc 1 MeV -quantum with to induce pair production The first 'fingerprint' of anti-matter. Anderson discovers the trace of a positron energy ћ in his cloud chamber (in the middle one can see a lead-plate of 6mm thickness). 0
1. The upper part of the bending gives information about the incoming-direction. -m c2 2. The lower part gives the positive charge of the particle by its bending-direction. 0 In case a whole in the negative hole continuum excits, an electron will (positron) immediately fill the vacancy and 3. By analyzing the radius of curvature before and after the transition the momentum two 511 keV quanta are emitted. can be estimated
3 Experiments Content
Lamb shift in one and two-electron QED: Radiative correction viewed by an experimentalist ions, hyperfine structure Experiments on Hydrogen
Strong fields: High-Z ions versus exotic atomic systems
The lamb shift in uranium
The hyperfine structure at high-Z
4 DIRAC Theory Critical electromagnetic fields 2 Let us come back to Dirac energy of a single hydrogen-like 2 Z Enj mc 1 ion: n | j 1/ 2 | ( j 1/ 2)2 (Z)2 2 2 E1s mc 1 Z Positive Continuum n: principle quantum number e- j: total angular momentum α: fine structure constant- α = 1/137.036) + mc2 What happens if we increase mc2: electron rest mass the nuclear charge Z? bound states (511 keV) If nuclear charge of the ion is 0 greater than Zcrit the ionic levels can “dive” into Dirac’s negative continuum. - mc2 Dirac-Theorie: (complete relativistic Physical vacuum becomes unstable: creation of pairs may + treatment of single electron systems) Negative Energy Continuum e take place! All levels with the same n and j are degenerated.
5 Relativistic quantum numbers and spectroscopic notations Supercritical fields: Formation of Quasi-Molecules
n j parity spectroscopic Merged Beams notation
11/2+ 1s1/2 U91+
21/2+ 2s1/2
21/2- 2p1/2
23/2 - 2p3/2 U92+ Finally, we know how to characterize bound states of (relativistic) hydrogen.
A. Artemyev, et al. J. Phys. B 43 (2010) 235207 What are the energies of these states?
6 The Lamb shift Lamb shift: idea of radiation corrections
Experiment: Lamb-Retherford 1947; Theoretical Explanation: Bethe 1947 This experiment proves that for hydrogen the 2s1/2 and the 2p1/2 From the end of 1930th : interaction of electron with are not degenerated radiation field. But which field?
=> In contradiction to Dirac-Theory Ideas: electron may interact with its own field. The Coulomb potential is therefore perturbed by a small amount and the degeneracy of the two energy Lamb-Shift levels is removed. 2p3/2 deviations from the Dirac Ly1 (E1) theory for a point like But: problems with divergence of results! 2s1/2 nucleus 2p1/2
Hans Bethe The Lamb shift (LS) is In 1947 Hans Bethe has shown how to identify the 2E1 Ly2 (E1) essentially a consequence of divergent terms and to substract them from the the interaction of the bound theoretical expression. electron with its own radiation field Development of 1s1/2 Quantum Electrodynamics (QED) and Quantum Field Theory (QFT) Level sheme for hydrogen
7 The effects of QED increase with the intensity of the electrical field, the electrons Feynman diagrams are exposed to. That means the s electrons are most affected.
Richard Feynman Feynman diagrams are a nice tool to represent exchange forces and, hence, to perform calculations Lamb-Shift QED of scattering processes. (three effects)
Self Energy • self-energy Electron-electron repulsion
real electrons • Vacuum-polarization Vacuum Polarization virtual photon (carrier of interaction)
time Z • size of the nucleus
From: http://www.slac.stanford.edu/
8 Lamb Shift: An effect of strong fields Appendix: probability density of the electrons at the nucleus (non-relativistic) 100 QED corrections E Z4/n3 r = Z/n in atomic units. With the normalization condition -1 1s 10 2 2s (r) d3r 1 Z: nuclear charge 3/ 2 n: principal quantum Z number 10 -2 follows: (r) n 2 r(r) nucleus 10 -3 What is the electron density at the nucleus (r=0)?
2p1/2 3 2 Z -4 2p for l = 0 (r 0) 10 3/2 n3
10 -5 0,1 1 10 100 1000 10000 radius [fm]
9 Self energy Self-energy: Describes the emission and reabsorption of a virtual photon Vacuum Polarization (VP) (Bethe 1947) The Self-energy decreases the binding energy. virtual photon
electron in the outer field (z.B. nucleus-Coulombfield)
Mass- m me m m: measurable electron mass. renormalization It already includes the radiation correction. m Virtual creation and annihilation of an e+e--pair me electron mass of the free electron without interaction with a field. Charge renormalization The self-energy is the most important radiation correction for light systems and decreases the binding energy. Here the electron emits and reabsorbs one and the same virtual photon. In every classical theory the consequence would be an infinitely high mass corresponding to an infinitely high self energy. The first calculations on the self-energy which explains the lamb shift of Hydrogen were made by Bethe. His success is based on an idea of Kramer, called mass-renormalization. The interaction with the virtual VP acts attractive photon leads to a modification of the electron mass. This effect is always present and the measured electron mass m already includes the radiation correction. Therefore the self-energy correction for a bound state can be regarded as the mass difference between the bound electron and a free electron of the mass me that is not liable to any interaction with the electromagnetic field at the time t
10 Summary of the Lamb Shift Effects Bound-State QED: 1s Lamb Shift at High-Z
Vacuum Sum of all corrections, leading to deviations from (Z)4 F(Z) m c2 e Polarization the Dirac theory for a point like nucleus Self Energy 10-1 Self energy Vacuum polarization
self energy Lamb- [meV] 4 10-2 Shift 92+
E / Z E / U SE VP NS 355.0 eV -88.6 eV 198.7 eV
-3 (-) vacuum polarization The size of the individual corrections in detail 10 Low Z-Regime: Z << 1 Hydrogen, H H-like uranium, U91+ F(Z): series expansion in Z 2p1/21s1/2 10.2 eV 97.6 keV nuclear size Finestructure 45.4 μeV 4.56 keV 4 2 2sLS 4.4 μeV 75.3 eV (Z) F(Z) m c -4 e
1s Lamb Shift , 1s Lamb Shift 10 1sLS 35.6 μeV 463.95 eV High Z-Regime: Z 1 F(Z): series expansion in Z not appropriate 1 20406080100 1 eV nuclear charge number, Z Goal:
11 QED correction in second order The Lamb-Shift The effects of QED increase with the intensity of the electrical field, that the electrons are exposed to. That means the s electrons are most affected. SE – SE QED-corrections
E Z4/n3
Z: nuclear charge n: principal quantum number VP – VP 1016
1015 1s 1s
1014 2s
1013 field strength: 1s electron SE – VP 1012 in ground state
11 10 2p1/2
1010 2p3/2 109 S(VP)E 1 102030405060708090 Nuclear Charge, Z
12 Test of Bound-State QED at high-Z Content Vacuum Self Energy Polarization
Experiments QED: Radiative correction viewed by an experimentalist 1s1s Lamb Lamb Shift Shift Experiments on Hydrogen 2eQED for He-like ions Strong fields: High-Z ions versus exotic atomic systems
2s-2p transitions The lamb shift in uranium in Li-like heavy ions The hyperfine structure at high-Z hyperfine-structure
g-factor of bound electrons
13 Laser Spectroscopy of Hydrogen Hydrogen Atom (http://www.mpq.mpg.de/~haensch/hydrogen/h.html) 10-4 f(1S-2S) = 2 466 061 102 474 851(34) Hz 10-5 10-6
10-7 Rydberg Constant laser 10-8 spectroscopy -1 R = 10 973 731.568 525(84) m 10-9
-10 10 frequency relative accuracy measurements Lamb Shift 10-11 -12 L1S = 8 172.840(22) MHz 10 10-13
10-14 1920 1940 1960 1980 2000 year
14 Laser spectroscopy 2s 2s Laser frequency: f f0 excitation frequency: f0 f f0 1s 1s v << c
f f0
v f f (1 ) 0 c v f f (1 ) 0 c
Large Doppler broadening by http://nobelprize.org/physics/laureates/2005/index.html thermal distribution
15 Two-photon laser spectroscopy Real precision is achieved by relative measurements !!!
2s f0 = 2 x f Assumption: The corrections (relativistic, QED etc.) are much better known for high n Laser f Laser f (much smaller !!!) than for n=1 and n=2
Idea: Compare Balmer-β radiation with Lyman-α 1s 1 1 Balmer-β: E Ry f v Ba 22 42 f 0 (1 ) 1 4EBa 1ELy 2 c 1 Lyman-: E Ry 1 f v Ly 22 classically correct !!! f 0 (1 ) 2 2 c Effectively it is: E and E are measurement f f1 f2 Ba Ly 4EBa 1ELy C categories in the experiment Doppler free-Spectroscopy C is the parameter for the ground state, one has to determine Condition for Precision-spectroscopy Detection of fluorescence-radiation for checking the theories as a function of the laser frequency
16 Applications: Bose-Einstein of atoms
http://nobelprize.org/nobel_prizes/physics/laureates/1997/illpres/ http://nobelprize.org/nobel_prizes/physics/laureates/2001/index.html
17 Extremly Strong Coulomb Fields H-like Uranium Content 3 EK = -132 10 eV 1016
1015 1s Z = 92 QED: Radiative correction viewed by an experimentalist 1014 Experiments on Hydrogen 1013
Strong fields: High-Z ions versus exotic atomic systems 12 10 Intense Laser
18 Muonic atoms vs. HCI 1s Lamb shift in muonic atoms and HCI
Muonic atoms Z Higly charged ions Muonic hydrogen (-2.5 keV) H-like silicon (-2.6 keV) 2p3/2 2 2p3/2
2s1/2 Z Lamb shift: -1.9 eV Lamb shift: 0.48 eV 2p1/2 2p1/2 En m 2s Self energy 0.4% Self energy 93.6% n 2 1/2 H-like ions Vacuum Polarization 97.9% Vacuum Polarization 5.9% muonic hydrogen Nuclear size 1.6% Nuclear size 0.5%
1s 1 1/2 1s r0 1/2 mZ Muonic nitrogen (-136 keV) H-like uranium (-132 keV)
• Z >> 1 • m >>melectron Lamb shift: 199 eV Lamb shift: 462 eV • Relativistic corrections • QED effects (vacuum polarization) Self energy 0.7% Self energy 54.3% • QED effects (self-energy) • Nuclear structure probe Vacuum Polarization 42.8% Vacuum Polarization 13.8% • Electron-electron interaction Nuclear size 56.5% Nuclear size 30.4% • Diffcult to produce • High quantity production • Obtained using intense pion beam (ECRIS, EBIT, storage rings,…) (TRIUMF, PSI,…) Complementary systems!!
19 More exotic bound systems...... and more!
Pionic and kaonic atoms Antiprotonic atoms
• H-like systems • EM and strong interaction • EM and strong interaction • Nucleon-antiproton interaction (Z=1,2,..) • Nucleon-meson interaction (Z=1,2,..) -> nucleon-nucleon interaction • Nuclear probe (high Z) • Nuclear probe (high Z) • Recoil and QED corrections
• Soon available in high quantities at FAIR Obtained at LEAR (Gotta 1999)
pH(3p-1s) d u d Pion (-) strong strong 1S u u interaction interaction 1.2 bar T=30K H or Kaon (-) QED (10 bar) only electro- s 1S electro- u @ d magnetic magnetic 2878.8 u u interaction interaction 1KeV
20 The Structure of One-Electron Systems Content 2p3/2 QED corrections
Ly1 (E1) 4 3 2s1/2 E Z /n QED: Radiative correction viewed by an experimentalist 2p1/2 Z: nuclear charge number n: prinzipal quantum Experiments on Hydrogen number M1 Ly2 (E1) Strong fields: High-Z ions versus exotic atomic systems
The Lamb shift of uranium (Z=92) 1s1/2 The hyperfine structure at high-Z • Large relativistic effects on energy levels and transition rates (e.g. shell and subshell splitting) Atomic systems at high-Z • Large QED corrections
• Transition energies close to 100 keV
21 GSI-Accelerator Facility X-Ray Spectroscopy at the ESR Storage Ring
Injection Energy 300 - 400 MeV/U
UNILAC Ly 11.4 MeV/u 1 73+ U Ly2 ESR M1
10 - 500 MeV/u 1s1/2 92+ SIS U up to 1000 MeV/u At the ESR, production of characteristic U92+ Circumference: 108 m x-rays by electron capture into the bare Number of Ions: 108 ions (electron cooler or jet-target) Frequency: 106 1/s
22 Storage Rings: Cooled Ion Beams ESR Storage Ring
electron collector electron gun electron collector electron gun high voltage platform
magnetic field electron beam
ion beam high voltage platform
magnetic field electron beam
ion beam
23 The Electron Cooler electron collector The Effect of Cooling electron gun
high voltage platform
magnetic field before cooling electron beam ion beam
electron collector electron gun after cooling
high voltage platform
magnetic field electron beam
ion beam ion intensity
Electron Cooler
0.97 1 1.03 2.5 m interaction zone rel. ion velocity v/v0
Voltage: 5 to 200 kV Ions interact 106 1/s with a collinear beam of cold electrons Current: 10 to 1000 mA Properties of the cold ions
Momentum spread p/p : 10-4 –10-5 Diameter 2 mm
24 The Experimental Challenge X-Ray Spectroscopy at the ESR Storage Ring
2.5 Injection Energy Relativistic Doppler-Transformation 358 MeV/u ( =0.69) 220 MeV/u ( =0.59) 400 MeV/u 2.0 68 MeV/u ( =0.36) 49 MeV/u ( =0.31)
E proj proj 1.5
Elab /E
γ(1βcosθlab) lab E 1.0 deceleration
Elab: Photon energy in the laboratory system Eproj: Photon energy in the emitter system 0.5
Doppler-Correction: Strong dependence on 0 30 60 90 120 150 180 Experiment observation anglel, [deg] velocity and the observation angle LAB lab @ 10 MeV/u 1 v γ ; β 2 c 1β Excited states are produced by electron capture (jet target) / recombination (electron target)
25 Principle of LS Experiments Experiments at the Jet-Target
Particle Counter 1. Production of bare ions (MWPC)
Coincidence 2. Cooling
3. Electron capture in excited states Dipole Magnet (jet-target or electron cooler) Electron transfer from K-REC 4. Detection of x-rays the target E atom into the KIN HCI 5. Doppler correction Ly Gas Jet 400 2 L Ly K-REC 1 QL-REC 6. Comparison with Dirac theory Ge Detector 200 -REC
Z M-REC e Ly 8 Ereignisse ω (Q1) Stored Ions (Z=Q) K 1s Lamb Shift 0 Z ω ... 50 100 150 200 250 300 350 Photonenenergie (keV)
26 Result of the jet-target experiment using Lamb Shift-Experiment at the Jet-Target decelerated uranium ions Ly (2p 1s ) 1 3/2 ½ Geometry Fit Ly1 (2p3/2 1s½) 102 171 13.2 eV 8.5 eV 2.6 eV 9.7 eV 102 171 13.2 eV segmented 25 mm 250 Ge(i) detector
48R Ly1 250 92+ 48O 200 U 25 mm The 1s-Lamb Shift (x,y) 200 Ly 92+ 150 2 Gasjet U 91+ U 150 Experiment: 468 eV 13 eV 132 100 Ereignisse 100 Counts Counts
Theory: 466 eV* 13 O 2 O 48 50 90O 90(7) *Theory: T. Beier et al., 1998 48L(7) 50
0 • Simultaneous observation at various angles 0 110 115 120 125 130 90 100 110 120 130 • Forward/Backward symmetry Energy (keV) Energie [keV] 3.0 deg 3% Sensitivity to Lamb Shift (466 eV) • Left/Right symmetry 1s-Lamb Shift 4% Sensitivity to Self Energy (355 eV) 15% Sensitivity to Vacuum Polarization (-88.6 eV) Experiment: 468 eV 13 eV Theory: 466 eV*
27 0o Spectroscopy at the Electron Cooler The Ground State Lamb Shift in H-like Uranium
Ly 200
150 Ly
Dipole counts 100 K-RR Magnet 50 Ly 600 H-like Uranium Ly 0 500 Ly • Blue shift has its maximum 100 120 140 160 180 200
400 0.29 Elab 1.43 E proj photon energy [keV] Balmer
300 • LAB not critical, almost no 91+ counts L-RR Doppler width 1s Lamb shift in U 200 j=1/2 j=3/2 K-RR 100 • Uncertainty caused by 460.2±2.3±3.5 eV has its maximum 0 20 40 60 80 100 120 140 160 180 200 4.6 eV Energy [keV] statistical uncertainty in the
28 Test of Quantum Electrodynamics (1s-LS)
H. Beyer, et al The 1s-LS in H-like Uranium Scanning technique versus Bragg-Lauemicro-strip Relation detectors 140 2p3/2 120 Ly λ (pm) z 1 2s Ly (E1) 1s-Lamb Shift 1/2 1 λ 2 d sinθ 2d 100 2p 80 1/2 R Ly2 Experiment: 459.8 eV 4.6 eV Scanning 60 -8 counts M1 Ly2 (E1) FOCAL Spectrometer: ε≈10 40 K-RR Theory: 463.95 eV 3 Events per Hour 20 0 1s1/2 80 100 120 140 160 180 200 Micro-Strip Germanium Detector photon energy [kev] 1s Lamb shift Timing, Energy and Position Resolution
520 z (mm) 510 U91+ 500 Theory 490 Cooler
Gasjet microstrip 480 470
Decelerated Ions: Decelerated Cooler (our exp.) 460 450
Lamb Shift [eV] A. Gumberidze Research Highlights 440 200 Strips PhD thesis 2003, Nature 435, 858-859 430
Decelerated Ions: Jet ∆x ≈ 200 μm (16 June 2005) 420 PRL 94, 223001 1990 1992 1994 1996 1998 2000 2002 (2005) ∆E ≈ 1.6 keV Year Alexandre Gumberidze Wavel∆τength st≈andards 50 in the ns x-ray region, Helmholtz-Institut Jena, 19.04.2013 58
29 Prototype 2D STRIP X-Ray Detector
There is a need for 2D detectors ! 2D STRIP planar detector systems for precision x-ray spectroscopy experiments (FOCAL)
energy resolution – timing - 2D position sensitiviy
p+-contact (128 strips)
stationary source 11 mm fast moving source a-Ge-contact +0.6 (48 strips) x STRIP detector developed by -0.6 front: 128 strips pitch ~250µm [mm] -60 +60 back: 48 strips pitch ~1167µm z-direction equivalent to 6144 pixel Alexandre Gumberidze Wavelength standards in the [mm]x-ray region, Helmholtz-Institut Jena, 19.04.2013 59 Alexandre Gumberidze Wavelength standards in the x-ray region, Helmholtz-Institut Jena, 19.04.2013 60
30 The FOCAL setup Preliminary results April 2012
Au79+ gasjet target supersonic Argon-jet Au78+ density: ~1012 atoms/cm2 width: ~5 mm ion-beam Au79+ ion beam Raw 2D energy:125 MeV/u Ar spectrum 79+ Au78+ Au
dipole magnet Au79+ particle- detector Au78+ Target 2D spectrum EC with energy and 2p 3/2 time condition Ly1
coincidence between K-REC 3 – 5 counts/h particle- and x-ray detector 1s Alexandre Gumberidze Wavelength standards in the x-ray region, Helmholtz-Institut Jena,1/2 19.04.2013 61 Alexandre Gumberidze Wavelength standards in the x-ray region, Helmholtz-Institut Jena, 19.04.2013 62
31 Energy levels of hydrogen atom: Content From Schrödinger to Dirac to QED
QED: Radiative correction viewed by an experimentalist
Experiments on Hydrogen Do we expect some more effects Strong fields: High-Z ions versus exotic atomic systems which can influence the level structure? The Lamb shift of uranium (Z=92)
The hyperfine structure at high-Z Actually yes!
32 Hyperfine interaction Hyperfine interaction
Hyperfine structure is a perturbation in the energy For the case of ground 1s1/2 state (j=1/2) of F = I +1/2 levels of atoms/ions due to the magnetic dipole- I J hydrogen, HF interaction results in splitting dipole interaction, arising from the interaction of of energy level into two levels. F = I -1/2 the nuclear magnetic moment with the magnetic field of the electron.
From: http://www.wikipedia.org Coupling of electron and nuclear momenta give One can observe transition between two HF rise to the total angular momentum of the system: levels: famous 21 cm line in astrophysics! F J I The HF splitting is: From: http://http://hyperphysics.phy-astr.gsu.edu
EHF a F(F 1) I(I 1) J (J 1) 21 cm radiation is used, for example, to measure radial velocities of the spiral Levels are spitted one more time! arms of the Milky Way.
From http://antwrp.gsfc.nasa.gov/apod/ap050825.html
33 Hyperfine Structure at High-Z Hydrogen Atom: Groundstate Hydrogen: 21.10608180988(2) cm 7 A 3A 10 years E1 E 0 HFS 4 HFS 4
for j=1/2, sp=1/2, F=1 for j=1/2, sp=1/2, F=0
F=1 (2F+1)=3 j=1/2 Eta Carinae
6 ΔEHFS 610 eV (2F+1)=1 F=0
34 Hyperfine Structure at High-Z HFS: Test of QED in strong magnetic fields (high-Z)
strong magnetic fields ≈ 1012 Gauss Fermiformula for the HFS
1 8 hc 3 2 M I 3 Z Ry g I 2 3 n me F( j, Z) relativistic correction 1 Nuclear-Charge distribution (Breit-Rosental-Corwford-Effect)
1 current distribution (Bohr-Weisskopf-Effect)
QED ???
35 Hyperfine Structure at high-Z The Candidates
Fermi Formula for HFS 1 8 hc M 3 2 ∆E ≈ 5 eV I 3 Z Ry g I 2 3 n me F( j, Z) Relativistic Correction 1 Nuclear Charge Distribution (Breit-Rosental-Corwford-Effekt)
1 Magnetisation Distribution (Bohr-Weisskopf-Effekt) QED ???
36 Laser Experiments at the ESR
Bi82+
Bi82+ Klaft et al., 1994
37 We have a problem ! In-ring spectroscopy of Li-like Bi AP
209 82+ 207 81+ Bi Pb laser ( 10 m) RMS radius 5.519 fm 5.497 fm First observation of Hyperfine-Splitting Magn.Mom.(corr.) 4.1106 n.m. 0.58219 n.m. in a Li-like heavy ion
Point nucl.(Dirac) 212.320 nm 880.017 nm rot 2 MHz Breit-Schawlow + 26.561(50) nm +109.64(1) nm result of 14 accumulated scans Ext. Nucleus 238.888(50) nm 989.65(1) nm t 0 accumulated Zoran counts Anđelković Bohr-Weisskopf + 5.025(330) nm + 29.5(20) nm Ref.-Bunch Theory, no QED 243.91(38) nm 1019.1(21) nm Reference Vac. polarisation - 1.64 nm - 6.83 nm Self energy + 2.86 nm + 11.9 nm Total QED + 1.22 nm + 5.08 nm ~ 0.2 nm Theory incl.QED 245.13(58) nm 1024.2(25)nm t 1/ 2 Experimental 243.87(2) nm 1019.5(2) rot Signal-Bunch wavelength [a.u.]
Zoran Andelkovic, Christopher Geppert, Matthias ? Signal Lochmann, Wilfried Nörtershäuser, et. al. to be published
38 DIRAC Theory (relativistic formulation of quantum mechanics) 2 Z E mc2 1 nj 2 2 n | j 1/ 2 | ( j 1/ 2) (Z) E
positive n: principal quantum number j: total angular momentum continuum α: Finestructure- or Sommerfeld- 2 +m0c constant α = 1/137.036) bound mc2: electron mass at rest states (511 keV)
0
2 -m0c Dirac-Theory: Relativistic complete negative description of quantum mechanics All states with same n and j are continuum degenerated.
39