Relativistic dynamics of (slow) highly-charged ions Stephan - PowerPoint PPT Presentation

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

Highly-charged ions provide a unique tool -- for probing strong electro-magnetic fields ultra-strong E ≈ 1 0 1 6 V / c m E ≈ 1 0 1 6 V / c m I n t e n s e L a s e r

Highly-charged ions provide a unique tool -- for probing strong electro-magnetic fields 1s-Lamb Shift ultra-strong Experiment: 459.8 eV ± 4.6 eV Theory: 463.95 eV E ≈ 1 0 1 6 V / c m E ≈ 1 0 1 6 V / c m 2p 3/2 2s 1/2 Ly α 1 (E1) 2p 1/2 M1 Ly α 2 (E1) 1s 1/2 I n t e n s e L a s e r Decelerated Ions: 520 (our exp. Lamb Shift [eV] ) Cooler 510 U 91+ Gasjet 500 Theory Cooler 490 480 Decelerated 470 460 Ions: Jet 450 440 430 420 1990 1992 1994 1996 1998 2000 2002 Year A. Gumberidze et al., PRL 94 (2005) 223001

Highly-charged ions provide a unique tool -- for probing strong electro-magnetic fields ultra-strong ultra-short 1  = E ≈ 1 0 1 6 V / c m E ≈ 1 0 1 6 V / c m  1 − v / c  2 I n t e n s e L a s e r t ≤ t ≤ 0 . 1 a s 0 . 1 a s I ≈ 1 0 2 1 W I ≈ 1 0 2 1 W 2 2 / c m / c m In contrast to: few-cycle laser pulses decelerated ion beams, HITRAP

Relativistic dynamics of (slow) highly-charged ions Stephan Fritzsche GSI Darmstadt & Oulu University Eisenach, 28 th June 2010 electron-photon electron-electron interaction 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

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

Electron capture into bare high-Z ions ~ ∑ polarization ∫ d ∣ M ∣ 2 So far... total cross sections d  d  ~ ∑ 2 ∣ M ∣ polarization angular distributions

Electron capture into bare high-Z ions ~ ∑ polarization ∫ d ∣ M ∣ 2 So far... total cross sections d  d  ~ ∑ 2 ∣ M ∣ polarization angular distributions New directions ... polarization ~ ∣ M ∣ 2 No summation over Alignment studies polarization states !

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

Capture into the 2p 3/2 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 2p 3/2 1s 1/2  angular distribution (arb. units) U 91+ fitting anisotropy parameter T p = 310 MeV/u W ∝ 1   P 2  cos  beam energy (MeV/u) observation angle (deg) J. Eichler et al. PRA 58 (1998) 2128 Th. Stöhlker et al. PRL 79 (1997) 3270

Capture into the 2p 3/2 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 2p 3/2 1s 1/2  angular distribution (arb. units) U 91+ fitting anisotropy parameter T p = 310 MeV/u W ∝ 1   P 2  cos  Theory:   b =± 3 / 2 −  b =± 1 / 2 = 1 2   b =± 3 / 2   b =± 1 / 2  alignment of the 2p 3/2 state: relative sublevel | j b m b > population beam energy (MeV/u) observation angle (deg) J. Eichler et al. PRA 58 (1998) 2128 Th. Stöhlker et al. PRL 79 (1997) 3270

Effective anisotropy parameter: Multipole contributions W ∝ 1  eff P 2  cos  effective anisotropy parameter  ± 3 / 2 − ± 1 / 2   eff = 1  f  E1 , M2   2  ± 3 / 2  ± 1 / 2  structure function alignment parameter f  E1 , M2 ∝ 1  2  3 〈∣ M2 ∣〉 〈∣ E1 ∣〉 P 1 ~ | φ | 2 2p 3/2 E1 M2 1s 1/2 P 12 = | φ 1 + φ 2 | 2 Double slit screen

Effective anisotropy parameter: Multipole contributions W ∝ 1  eff P 2  cos  effective anisotropy parameter  ± 3 / 2 − ± 1 / 2   eff = 1  f  E1 , M2   2  ± 3 / 2  ± 1 / 2  structure function alignment parameter f  E1 , M2 ∝ 1  2  3 〈∣ M2 ∣〉 〈∣ E1 ∣〉 2p 3/2 E1 M2 1s 1/2

Effective anisotropy parameter: Multipole contributions W ∝ 1  eff P 2  cos  effective anisotropy parameter  ± 3 / 2 − ± 1 / 2   eff = 1  f  E1 , M2   2  ± 3 / 2  ± 1 / 2  structure function alignment parameter f  E1 , M2 ∝ 1  2  3 〈∣ M2 ∣〉 〈∣ E1 ∣〉 2p 3/2 In contrast, contributions to decay rates appear additive: E1 M2  M2 2 ∝ ∣〈∣ M2 ∣〉∣ ∝ 0.008 1s 1/2  tot ∣〈∣ E1 ∣〉∣ 2 even for U 91+

E1-M2 multipole mixing: Alignment of the 2p 3/2 state A. Surzhykov et al. PRL 88 (2002) 153001 W ∝ 1  eff P 2  cos  angular distribution (arb. units) U 91+ T p = 310 MeV/u fitti  eff ng effective anisotropy parameter observation angle (deg) beam energy (MeV/u) Dynamical alignment studies enables one to explore magnetic interactions in the bound-bound transitions in H-like ions !

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

Two-photon coincidence studies Normal (independent) measurement Coincidence measurement Photon-photon correlation functions: W  RR ,  ∝ 1   4  5 ∑ A 2q  RR  Y 2q  Lengthy derivation in the framework of the density matrix theory. q t n n U 91+ o e i m t u θ RR = 0 deg n b g i r i t l a s i d l a r i θ RR = 15 deg θ RR = 0 deg t a n l e u g r θ RR = 15 deg e n θ RR = 90 deg f a f i d θ RR = 90 deg observation angle θ RR observation angle θ

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

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 1 P L =  P 1 cos  2 = 2  P 2 2 P L

Linear polarization of emitted x-ray photons -- Statistical characteristics for photon ensembles photoionization recombination P 1 = I 0 − I 90 I 0  I 90 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

Linear polarization of emitted x-ray photons -- Statistical characteristics for photon ensembles photoionization recombination electric dipole approximation Relativistic effects decrease the linear polarization ! U 92+ 100 MeV/u Cross-over behaviour !! 300 MeV/u 500 MeV/u F. Sauter, Ann. Phys. 9 (1931) 217 800 MeV/u U. Fano, Phys. Rev. 116 (1959) 1156 A. Surzhykov et al , PLA 289 (2001) 213 J. Eichler et al , PRA 65 (2002) 052716

Linear polarization of emitted x-ray photons: Applications -- Diagnostics of highly-charged ion beams P roposal: 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.

Linear polarization of emitted x-ray photons: Applications -- Diagnostics of highly-charged ion beams P roposal: 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 Bi 82+ ions ( I = 9/2) for the energy T p = 420 MeV/u. λ F = 0.0 P 2 = I 45 − I 135 λ F = 0.3 I 45  I 135 λ F = 0.7 P 1 = I 0 − I 90 λ F = 1.0 I 0  I 90

Linear polarization of emitted x-ray photons: Applications -- Diagnostics of highly-charged ion beams P roposal: 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 Bi 82+ ions ( I = 9/2) for the energy T p = 420 MeV/u. P 2 tan  2 = P 1 direction of polarization A. Surzhykov et al. , Phys. Rev. Lett. 94 (2005) 203202