Relativistic dynamics of (slow) highly-charged ions

Transcription

1 Relativistic dynamics of (slow) highly-charged ions Stephan Fritzsche GSI Darmstadt & Oulu University Eisenach, 28th June 2010 electron-photon interaction electron-electron interaction Thanks to: N.M. Kabachnik, A. Surzhykov, T. Stöhlker and GSI Atomic Physics Group

2 Highly-charged ions provide a unique tool -- for probing strong electro-magnetic fields ultra-strong E V /c m In te n s e L a s e r

3 Highly-charged ions provide a unique tool -- for probing strong electro-magnetic fields 1s-Lamb Shift ultra-strong Experiment: ev ± 4.6 ev Theory: ev E V /c m 2p3/2 2s1/2 Lyα1 (E1) 2p1/2 M1 Lyα2 (E1) Cooler (our exp. ) Theory Ions: Jet Decelerated Cooler 91+ U Gasjet Lamb Shift [ev] Decelerated Ions: 1s1/2 In te n s e L a s e r Year A. Gumberidze et al., PRL 94 (2005)

4 Highly-charged ions provide a unique tool -- for probing strong electro-magnetic fields ultra-strong ultra-short = E V /c m In te n s e L a s e r t 0.1 a s I W /c m In contrast to: few-cycle laser pulses decelerated ion beams, HITRAP v / c

5 Relativistic dynamics of (slow) highly-charged ions Stephan Fritzsche GSI Darmstadt & Oulu University Eisenach, 28th June 2010 electron-photon interaction electron-electron interaction Plan of this talk Electron capture: angular correlations & polarization Multipole mixing in strong fields Two-step processes: Capture vs. excitation Thanks to: N.M. Kabachnik, A. Surzhykov, T. Stöhlker and GSI Atomic Physics Group Atomic PNC: Two-photon processes Spectroscopy of (super-) heavy elements Conclusions

6 Electron capture by bare ions -- angular correlation and polarization studies

7 Electron capture into bare high-z ions ~ d M 2 So far... polarization total cross sections angular distributions d ~ M 2 d polarization

8 Electron capture into bare high-z ions ~ d M 2 So far... polarization total cross sections d ~ M 2 d polarization New directions... angular distributions polarization ~ M 2 Alignment studies No summation over polarization states!

9 Multipole mixing of the radiation field -- in the capture and decay of highly-charged ions

10 Capture into the 2p3/2 excited states of initially bare ions Lyman α 1 But: knowledge on population of excited ion state may be derived from the properties of subsequent decay 1s1/2 U91+ Tp = 310 MeV/u fitting observation angle (deg) Th. Stöhlker et al. PRL 79 (1997) 3270 W 1 P 2 cos anisotropy parameter angular distribution (arb. units) 2p3/2 Magnetic sublevel population of the residual ion can not be measured directly beam energy (MeV/u) J. Eichler et al. PRA 58 (1998) 2128

11 Capture into the 2p3/2 excited states of initially bare ions Magnetic sublevel population of the residual ion can not be measured directly Lyman α 1 But: knowledge on population of excited ion state may be derived from the properties of subsequent decay 1s1/2 U91+ Tp = 310 MeV/u fitting W 1 P 2 cos Theory: anisotropy parameter angular distribution (arb. units) 2p3/2 1 =±3/ 2 =±1/ 2 = 2 =±3/ 2 =±1/ 2 b b b b alignment of the 2p3/2 state: relative sublevel jb mb> population observation angle (deg) Th. Stöhlker et al. PRL 79 (1997) 3270 beam energy (MeV/u) J. Eichler et al. PRA 58 (1998) 2128

12 Effective anisotropy parameter: Multipole contributions W 1 eff P 2 cos effective anisotropy parameter eff = 1 ±3 / 2 ±1/ 2 f E1, M2 2 ±3 / 2 ±1/ 2 alignment parameter structure function f E1, M M2 E1 P1 ~ φ 2 2p3/2 E1 M2 1s1/2 P12 = φ1 + φ2 2 Double slit screen

13 Effective anisotropy parameter: Multipole contributions W 1 eff P 2 cos effective anisotropy parameter eff = 1 ±3 / 2 ±1/ 2 f E1, M2 2 ±3 / 2 ±1/ 2 alignment parameter structure function f E1, M p3/2 E1 1s1/2 M2 M2 E1

14 Effective anisotropy parameter: Multipole contributions W 1 eff P 2 cos effective anisotropy parameter eff = 1 ±3 / 2 ±1/ 2 f E1, M2 2 ±3 / 2 ±1/ 2 alignment parameter structure function f E1, M M2 E1 2p3/2 E1 1s1/2 M2 In contrast, contributions to decay rates appear additive: 2 M2 M tot E1 even for U91+

15 E1-M2 multipole mixing: Alignment of the 2p3/2 state U91+ Tp = 310 MeV/u observation angle (deg) W 1 eff P 2 cos fitti ng eff effective anisotropy parameter angular distribution (arb. units) A. Surzhykov et al. PRL 88 (2002) beam energy (MeV/u) Dynamical alignment studies enables one to explore magnetic interactions in the bound-bound transitions in H-like ions!

16 Two-photon coincidence studies Normal (independent) measurement Photon-photon correlation functions: W RR, =? Coincidence measurement

17 Two-photon coincidence studies Normal (independent) measurement Coincidence measurement Photon-photon correlation functions: θrr = 0 deg Lengthy derivation in the framework of the density matrix theory. U91+ θrr = 15 deg θrr = 90 deg observation angle θrr angular distribution 4 A 2q RR Y 2q 5 q differential alignment W RR, 1 θrr = 0 deg θrr = 15 deg θrr = 90 deg observation angle θ

18 X-ray polarimetry for HCI -- exploring a new `dimension' in the electron-photon interaction position sensitive detector U92+ gas jet K-shell capture or subsequent decay ion beam S. Tachenov, G. Weber, T. Stöhlker, a.o.

19 Linear polarization of emitted x-ray photons -- theoretical expectation photoionization recombination electric dipole approximation Linear polarization is described in the plane, perpendicular to the photon momentum. only 2 (Stokes) parameters are required! P L = P 21 P 22 cos 2 = P1 PL

20 Linear polarization of emitted x-ray photons -- Statistical characteristics for photon ensembles photoionization electric dipole approximation photoelectron angular distribution: W PI sin 2 cos 2 photoelectrons are emitted predominantly within the plane of the electric field Stobbe, Ann. Phys. 5 (1930) 661 recombination P 1= I 0 I 90 I 0 I 90

21 Linear polarization of emitted x-ray photons -- Statistical characteristics for photon ensembles photoionization recombination electric dipole approximation Relativistic effects decrease the linear polarization! Cross-over behaviour!! F. Sauter, Ann. Phys. 9 (1931) 217 U. Fano, Phys. Rev. 116 (1959) 1156 A. Surzhykov et al, PLA 289 (2001) 213 J. Eichler et al, PRA 65 (2002) U MeV/u 300 MeV/u 500 MeV/u 800 MeV/u

22 Linear polarization of emitted x-ray photons: Applications -- Diagnostics of highly-charged ion beams Proposal: to use REC linear polarization as a probe for ion spin polarization. Established theory from the polarization transfer in atomic photoionization. U. Fano et al., Phys. Rev. 116 (1959) 1147; R. Pratt et al., Phys. Rev. 134 (1964) A916.

23 Linear polarization of emitted x-ray photons: Applications -- Diagnostics of highly-charged ion beams Proposal: to use REC linear polarization as a probe for ion spin polarization. Established theory from the polarization transfer in atomic photoionization. U. Fano et al., Phys. Rev. 116 (1959) 1147; R. Pratt et al., Phys. Rev. 134 (1964) A916. Calculations performed for the REC into (initially) hydrogen-like bismuth Bi82+ ions (I = 9/2) for the energy Tp = 420 MeV/u. P 2= P 1= I 0 I 90 I 0 I 90 I 45 I 135 I 45 I 135 λf = 0.0 λf = 0.3 λf = 0.7 λf = 1.0

24 Linear polarization of emitted x-ray photons: Applications -- Diagnostics of highly-charged ion beams Proposal: to use REC linear polarization as a probe for ion spin polarization. Established theory from the polarization transfer in atomic photoionization. U. Fano et al., Phys. Rev. 116 (1959) 1147; R. Pratt et al., Phys. Rev. 134 (1964) A916. Calculations performed for the REC into (initially) hydrogen-like bismuth Bi82+ ions (I = 9/2) for the energy Tp = 420 MeV/u. tan 2 = P2 P1 direction of polarization A. Surzhykov et al., Phys. Rev. Lett. 94 (2005)

25 Linear polarization of emitted x-ray photons: Applications -- Diagnostics of highly-charged ion beams Proposal: to use REC linear polarization as a probe for ion spin polarization. Established theory from the polarization transfer in atomic photoionization. U. Fano et al., Phys. Rev. 116 (1959) 1147; R. Pratt et al., Phys. Rev. 134 (1964) A916. Calculations performed for the REC into (initially) hydrogen-like bismuth Bi82+ ions (I = 9/2) for the energy Tp = 420 MeV/u. P2 I 1/2 tan 2 = ~ F P1 I 1/2 φ S. Tashenov et al., PRL 97 (2006) ; A. Surzhykov et al., PRL 94 (2005) Rotation angle provides information on the degree of ion polarization!

26 Two-step processes: Capture vs. excitation -- Do we get more by following the dynamics of the ions? (initially) bare ion (initially) H-like ion

27 Lyman- vs. K- emission from high-z ions (initially) bare ion (initially) H-like ion Ly- 1 is strongly anisotropic X. Ma et al, PRA 68 (2003) U92+ Tp = 309 MeV/u U91+ Tp = 102 MeV/u K-α1 is isotropic

28 Lyman- vs. K- emission from high-z ions (initially) bare ion (initially) H-like ion Ly-a1 is strongly anisotropic X. Ma et al, PRA 68 (2003) U92+ Tp = 309 MeV/u E1: W E1~1 U91+ Tp = 102 MeV/u 1 A 2 J =1 P 2 cos 2 M2: W M2 ~1 5 A 2 J =2 P 2 cos 14 K-α1 is isotropic

29 K- decay of highly-charged ions -- angular distribution as observed in experiment W K ~ N J =1 W E1 N J =2 W M2 1 =1 N J =1 N J =1, N J =2 A. Surzhykov et al., PRA 73 (2006) A 2 J =1 N J =2 A 2 J =2 P 2 cos 14 2 relative populations of J=1, 2 states N J =1 =N J =2= 1 2 N J =1 = 3 5 N J =2= 8 8 Calculations have been done for L-REC of U91+ with Tp = 100 MeV/u E1+M2 E1 only

30 K- decay of highly-charged ions -- for 220 MeV/u U90+ ions following REC W K ~ N J =1 W E1 N J =2 W M2 1 =1 N J =1 A. Surzhykov et al., PRA 73 (2006) A 2 J =1 N J =2 A 2 J =2 P 2 cos 14 2 Relative populations of the J = 1, 2 levels following REC (IPM model): N J =1 3 = N J = By taking into account P2 -> S1 channel: N J =1 6 = N J =2 7 N J =1 N J =2 N J =1 N J =2 E1 (30 %) E1 theory 0.08 M2 (70 %)

31 K- decay of highly-charged ions -- following the Coulomb excitation of the projectiles W K ~ N J =1 W E1 N J =2 W M2 1 =1 N J =1 A. Surzhykov et al., PRA 73 (2006) A 2 J =1 N J =2 A 2 J =2 P 2 cos 14 2 excitation of He-like U90+ ion Excited states of He-like heavy ions can be produced also by the Coulomb excitation of the projectile in the field of target atoms. Experiments were already performed at the GSI storage ring for He-like uranium ions U90+. Strong anisotropy of the subsequent K 1 radiation has been observed!

32 K- decay of highly-charged ions -- following the Coulomb excitation of the projectiles W K ~ N J =1 W E1 N J =2 W M2 1 =1 N J =1 N J =1, N J =2 1 5 A 2 J =1 N J =2 A 2 J =2 P 2 cos 14 2 relative populations of J=1, 2 states Angular distribution results dominantly from the decay of the J=1 level. Role of electron-electron interactions still unexplored. E1 (30 %) E1 Tp = 217 MeV/u M2 (70 %)

33 Atomic parity non-conservation processes -- Two-photon processes for HCI e- γ q e- q e- Exchange of Z-boson leads to the mixing of atomic levels with different parities. Z q q E n erg y e- s (+ ) p (-)

34 PNC studies with heavy, few-electron ions -- enhancement of parity and time-reversal violating interactions Helium-like uranium U90+ is a perfect candidate for PNC studies: Simple system (only 2 electrons) Large electron-nucleus overlap Small 21S0-23P0 energy splitting 8 6 E (e V ) D rak e P la n te In d e l ic C heng a to Still many open questions: How big is the 21S0-23P0 energy splitting? How strong laser fields do we need? n u c le a r c h a r g e, Z What is the role of e-e interactions?

35 There is a need for accurate many-electron calculations! Analysis and interpretation of optical and x-ray spectra (astro physics) Diagnostics of astro physical and laboratory plasmas Development of UV/EUV light sources and lithograhpy many but not so accurate Frequency standards and atomic clocks Spectroscopy on heavy and superheavy elements (actinides, transactinides) Isotope shifts and hyperfine structures Nonradiative (inner-shell) transitions and autoionization Ion recombination and photon emission Multi-photon processes... Complete experiments Parity nonconservation (PNC) Search for electric dipole moments

36 Spectroscopy of heavy and super-heavy elements Atomic Physics : Atomic Levels Nuclear Physics : re u t c ru n! t S ic ow om nkn t A u Atomic Structure Ionization Potentials Nuclear Spins, Moments Lr Lr No Md Fm Es Backe, Lauth, Sewtz (Mainz) Theoretical challenges: strong relativistic and QED effects systems with open d- and f-shells many overlapping and nearly degenerate configurations large number of electron

37 M. Sewtz et al., Phys. Rev. Lett. 90 (2003) Optical spectroscopy of atomic Fermium (Z = 100) First observation and classification of atomic levels Determination of hfs and isotope shifts Atomic Physics: Atomic Structure Ionization potentials Nuclear Physics: Nuclear spins Moments Changes of charge radii Theoretical request: Energies, lifetimes, transition rates Scan Distance : 1800 cm-1 5G o 5f12 7s 7p, Jp = 6-, 5 6,5 12 p 3 ES : 5f 7s 7p, J = 6, 5,7 H6,5,7o (?) Breeding in High Flux Reactors NFm< 1012; 255Fm; t1/2= 20.1 h

38 M. Sewtz, W. Lauth et al., private commun. (2005) Experimental proposal: Optical spectroscopy of nobelium (Z=102) Laser Ground-state configuration: [Rn] 5f14 Dipole Magnets 7s2 Target Wheel Low-lying excitations: [Rn] 5f14 7s 7p 5f13 6d 7s2 5f14 6d 7s 5f14 7s 8s 5f13 7s2 7p } Quadrupole Triplet 254 No Beam Quadrupole Triplet Beam Dump Buffer Gas Cell Condenser Plates for Electric Field ev 6d shell open 5f shell Configuration interaction No 5f14 7s2 7p shell 1 3 P1 P1 S. Fritzsche, EJP D33, 15 (2005)

39 Zhou & Froese Fischer., Phys. Rev. Lett. 88 (2002) Low-lying resonances of (super-) heavy elements... for lutetium (Z=71) and lawrencium (Z=103) RCC: Eliav et al.., Phys. Rev. A52 (1995) 291; DFT: Vosko & Chevary, J. Phys. B26 (1993) 873

40 Zhou & Froese Fischer., Phys. Rev. Lett. 88 (2002) Low-lying resonances of (super-) heavy elements... oscillator strengths in different gauges Good accuracy of the (atomic) energies is a necessary, but not a sufficient criterion!

41 S. Fritzsche, JESRP (2001) 1155; Phys. Scr. T100 (2002) 46 RATIP Relativistic Atomic Transition and Ionization Properties (CPC library) Relativistic CI wave functions including QED estimates and mass polarization RELCI, CPC 148 (2002) 103 LSJ spectroscopic notation from jj-coupled computations LSJ, CPC 157 (2003) 239 nc P J M = c r r P J M r Auger rates, angular distributions and spin polarization; level widths AUGER Many-electron basis (wave function expansions) Construction and classification of N-particle Hilbert spaces Shell model: Systematically enlarged CSF basis Interactions Dirac-Coulomb Hamiltonian Photoionization cross sections and (non-dipole) angular parameters PHOTO Radiative and dielectronic recombination; angle-angle correlations Breit interactions + QED Electron continuum; scattering phases Coherence transfer and Rydberg dynamics...

42 S. Fritzsche, JESRP (2001) 1155; Phys. Scr. T100 (2002) 46 Relativistic CI wave functions including QED estimates and mass polarization ; e d a RATIP c148 (2002) 103 RELCI, CPC e d s t Relativistic Atomic Transition e s i t a spectroscopic r llsj notation e e p and Ionization Properties o th frompjj-coupled r (CPC library) d ir ng ncomputations u a LSJ, CPC 157 (2003) 239 d... s e s i d n m Auger rates, angular distribuu e t t tions and spin polarization; s P J M = c r r P J M e s y s level widths s r r a c AUGER he t 0 o 13 er n a Photoionization cross sectsid Many-electron basis (wavethfunctionnexpansions) ions and (non-dipole) angular o e r Construction and classification ofcn-particle Hilbert parameters o o t spaces m r PHOTO n i e Shell model: Systematically enlarged CSF basis d f f e o Radiative and dielectronic Interactions it liz recombination; angle-angle e U Dirac-Coulomb Hamiltonian h correlations c t Breit interactions + QED Electron continuum; scattering phases Coherence transfer and Rydberg dynamics...

43 HFS & Isotope shift measurements for Os- AG A. Kellerbauer et al. MPIK Heidelberg Typical spectrum 192Os-: 2.00 Signal: Neutral atoms as function of laser frequency D 6 o Je J = 3/2 J = 5/ F 4 e (ev) J = 7/2 Os Jg = 9/2 Os ν = (30) THz λ = (14) nm U. Warring et al., Phys. Rev. Lett. 102 (2009)

44 HFS & Isotope shift measurements for Os- Typical spectrum 192Os-: AG A. Kellerbauer et al. MPIK Heidelberg Signal: Neutral atoms as function of laser frequency electric-field detachment ts n u o c two-photon detachment (x10) νcenter (MHz) ν = (30) THz λ = (14) nm 75 U. Warring et al., Phys. Rev. Lett. 102 (2009) MSMS = 4.9 F THz u = 12.4 GHz fm 2 A. Fischer et al., Phys. Rev. Lett. 104 (2010) ) u y ar in im el pr = 16(9) GHz fm 2 16 A ) δvres (T z H MSMS = 2(11) THz u F Theory: A /(1 2 9 Experiment: 1u =0.14 THz u M NMS =ν 0 me Transition for all stable isotopes: A /(192 A ) δ<r2>192,a (fm2 u)

45 Atomic and heavy-ion SPARC collaboration -- Recent developments and progress Key topics of this collaboration: Test of quantum electrodynamics in strong fields for light and high-z ions... two-times Green's functions; 2-photon, 3-photon (??) diagrams; differences with experiment especially for the HFS; systematic QED approach in the MBPT framework Collision & capture dynamics in strong fields at relativistic energies... U28+ electron loss; few-body dynamics; polarization effects; multi-electron processes Atomic physics techniques applied to nuclear physics Multi-photon processes Antiproton physics Test of fundamental interactions and symmetries beside of QED Interaction of ions with intensive (laser) light... dynamics in strong fields, high-harmonics generation... generation of high harmonics in the kev region; interaction with excotic ion. GSI

46 Atomic and heavy-ion SPARC collaboration -- Recent developments and progress Key topics of this collaboration: Test of quantum electrodynamics in strong fields for light and high-z ions... two-times Green's functions; 2-photon, 3-photon (??) diagrams; differences with experiment especially for the HFS; systematic QED approach in the MBPT framework Collision & capture dynamics in strong fields at relativistic energies... U28+ electron loss; few-body dynamics; polarization effects; multi-electron processes Atomic physics techniques applied to nuclear physics Multi-photon processes Antiproton physics Test of fundamental interactions and symmetries beside of QED Interaction of ions with intensive (laser) light... dynamics in strong fields, high-harmonics generation... generation of high harmonics in the kev region; interaction with excotic ion. GSI

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49 Time-independent density matrix theory Initial state S - scattering operator Final state t f t i f = S i S initial state density matrix 1... m f ' 1... ' m = 1, 2... transition amplitudes 1... n ' 1... ' n R ' 1... ' n 1... n i ' 1... ' n 1... n R Measurement of physical properties: 'detector operator' describes the experimental setup: P= probability to get a 'click' at the detectors: W =Tr P f = 1... m P f 1... m 1... m

50 Time-independent density matrix theory Initial state Final state t f t i S - scattering operator f = S i S! e g a t n a v d a t a e r G Using the density matrix, the system can be accompanied through several steps of the interaction which may lead to the emission of photons, electrons,...

51 Weak- vs. strong-field (light-matter) interactions s c i s. experiments',...; cross sections, angular distributions & spin polarization, `complete y s n h o for example: single-photon double ionization i p t c ; ra n s o n nte i o i s t gi i a l c rre atin e r co iol p e lv f e a o f s r o ve n i e l re a o R em im o Current interests and challenges t D and Atomic processes and multipole mixing in strong fields Weak-field photoexcitation and ionization: He (Briggs and Schmidt, 2000) A++ A+ A He (Schneider and Rost, 2003) ity r a Multi-electron coincidences (magnetic bottle) p Second-order emission processes Creation and control of entangled photon pairs Parity non-conservation and time-reversal violation Different mechanisms: shake-off, knock-out Studying fundamental constants (time variations,...)

52 Ion-Atom Stöße langsame Stöße schnelle Stöße Vielteilchenbild Einteilchenbild Besseres Verständnis der Vielteilchendynamik erforderlich. Hochgeladene Ionen sind sehr gut geeignet, um die elementaren Prozesse in (extrem) starken Feldern zu verstehen. Verstärkung des REC bei langsamen Ionen (!) Resonante (dielektronische) Rekombination. Abbremsen und Einfang in Fallen. Wichtig für Ionen-Oberflächen Prozesse <E> [V/cm] s Z = Ionen sind variabel: Feldstärke Zahl der Elektronen 1011 Zeitskala 1010 Z= Nuclear Charge, Z g=1 g=5

53 Supercritical fields in ion-atom collisions strong spin-orbit splitting; swapped `level order' Fricke & Soff (1977) Z~ 173 Mokler & Liesen (1982) Processes during the collision: excitation into higher shells multiple charged ion neutral target ionization ( -electrons) MO radiation characteristic x-rays

54 Laser spectroscopy of MPI-K in Heidelberg (A. Kellerbauer et al.) laser negative ion source D 6 o Je Os J = 3/2 J = 5/ F mass separation 4 e (ev) J = 7/2 Os Jg = 9/2 Measurement principle: Measurement principle: Laser frequency is scanned around transition frequency Laser frequency is scanned around transition frequency Excited state is detached by electric field Excited state is detached by electric field Neutrals detected on forward MCP Neutrals detected on forward MCP

55 FAIR 1x1012 1/s for U28+at 1 GeV/u 90 GeV protons 34 GeV/u U92+ SIS100/300 Stored and Cooled Highly-Charged Ions and Exotic Nuclei from Rest to Relativistic Energies Intense Beams of Radioactive Isotopes High Energy Cave Virtual Photon Sources at X- and -Ray Energies XUV Energies via Lorentz Boost of optical wavelengths FLAIR New Experimental Storage Ring... with Novel Instrumentation Ultracold Electron-Beam Target High Resolution X-Ray and Electron Spectrometers In-Ring Recoil Momentum Microscope Highly Intense Laser Beams Traps

56 Polarization of the K-shell REC photons position sensitive detector U92+ gas jet K-shell ion beam S. Tachenov/T. Stöhlker (2004) Compton effect: Klein-Nishina formula d ℏ ℏ ' sin cos d ℏ ' ℏ polarization dependence ℏ ' ℏ