Two-photon transitions in heavy ions:
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1 Two-photon transitions in heavy ions: From relativistic and many-body effects to parity non-conservation phenomena Andrey Surzhykov Physics Institute of the University of Heidelberg and Atomic Physics Division of GSI, Darmstadt Work is supported by Helmholtz association under the project VH-NG-41
2 Two-photon atomic transitions In 199 in her PhD thesis Maria Göppert-Mayer suggested that bound-bound transitions can undergo under simultaneous absorption/emission of two correlated photons. decay absorption For many years two-photon decay/excitation of atoms and ions has attracted much of experimental and theoretical interest.
3 Two-photon atomic transitions Analysis of the two-photon decay requires knowledge about complete spectrum of the: ~ M fi f α ε e ikr E α ε e E i 1 1 ikr The summation in the second-order transition amplitude includes a summation over the discrete part of the spectrum as well as an integration over the positive and negative-energy continuum. 1 i + mc 0 -mc A large number of studies have been performed over the last decades to investigate: Total decay rates Energy (spectral) distributions
4 Two-photon atomic transitions: Novel studies Most recent years interest arises to study angular and polarization properties of emitted photons. A number of interesting applications have been proposed for these studies in high-z domain. Detailed analysis of relativistic and many-body effects. Spin entanglement in relativistic regime, test of Bell s inequality Parity violation in heavy atomic systems = -1 = -1 e e q q
5 Helium-like heavy ions In high-z domain two-photon studies are most likely to be performed with the helium-like ions: There are metastable states even for high-z Can be efficiently prepared in ionic collisions Good candidates for PNC studies R. Dunford, PRA 54 (1996) 380 J. Rzadkiewicz et al, PRA 74 (006) Request for theoretical description of two-photon transitions in helium-like heavy ions with the special emphasis on angular and polarization properties.
6 A little bit of theory To describe two-photon transitions in helium-like heavy ions we make use of the independent particle model which allows to express two-electron matrix elements in terms of single-electron ones. b a b b b a a a b b b a a a J j n j n j n j n J b b a a JM JM j j N ) ( ) ( ) ( ) (, r r r r r r What are the functions? We have used few approximations: Dirac-Coulomb functions with effective charge Dirac-Fock solutions Kohn-Sham solutions (r ) nj 1 1 e e ~ i i i i f fi E E M kr kr ε α ε α
7 Two-photon decay of Helium-like ions We have used independent particle model together with the density matrix approach to analyze properties of the two-photon emission from helium-like heavy ions: Total and energy-differential decay rates Angular correlations between emitted photons Polarization properties of the photons Emission angles and polarization states of the photons remain unobserved
8 IPM versus Relativistic CI calculations Example: Test calculations for the S 0 1S 0 transition in helium-like uranium. IPM s 1 A. Derevianko and W. R. Johnson, PRA 58 (1997) 188 Derevianko & Johnson IPM calculations 1 x 1 energy sharing (reduced energy) Good agreement was found between the IPM and CI calculations!
9 Two-photon decay of Helium-like ions We have used independent particle model together with the density matrix approach to analyze properties of the two-photon emission from helium-like heavy ions: Total and energy-differential decay rates Angular correlations between emitted photons Polarization properties of the photons Both photons are measured in coincidence, polarization states remain unobserved
10 S 0 1S 0 two-photon decay: Angular correlations x=0.1 x=0.5 E1E1 all multipoles Simplified picture s 1 s 1 1s p state z axis M L = -1 M L = 0 M L = +1 p state 1s W( ) 1cos z axis Non-dipole effects significantly affect angular correlation function!
11 S 1 1S 0 two-photon decay: Angular correlations x=0.1 x=0.5 E1E1 all multipoles One may observe significant higher-multipole effects for x=0.1. What happens for the case of equal energy sharing (x=0.5)?
12 S 1 1S 0 two-photon decay: Angular correlations x=0.1 x=0.5 E1E1 all multipoles Similar effect is known for the spectral distribution of emitted photons. It is a result of fundamental symmetry arguments (photons are Bose particles)! Effect is known is particle physics as a Landau-Yang theorem! Energy sharing, x Can one use two-photon decay for probe of possible small violations of the spinstatistics relation for photons?
13 P 0 1S 0 two-photon decay: Angular correlations x=0.1 x=0.5 E1M1+M1E1 all multipoles One may observe significant higher-multipole effects especially for the equal energy sharing. For x=0.5 no parallel ( = 0) emission is possible! E1 M1 P 0 ~ M fi E1( ) E E M 1( ) i M 1( ) E1( ) Interference between two decay channels (double slit-like scheme) suppresses forward emission! E E i 0 M1 E1 1S 0
14 Two-photon decay of Helium-like ions We have used independent particle model together with the density matrix approach to analyze properties of the two-photon emission from helium-like heavy ions: Total and energy-differential decay rates Angular correlations between emitted photons Polarization properties of the photons Polarization states of both photons are measured in coincidence
15 Spin states: S 0 1S 0 versus P 0 1S 0 For 0 0 transitions photons emitted in pure spin states! To explore the degree of polarization correlation, one may use the standard language of the quantum information theory (concurrence measure). 1 S S 0 3 P S 0 x=0.5 1 Bell s state at any geometry!
16 Outlook: atomic PNC effects By performing the two-photon polarization spectroscopy of heavy helium-like ions we might be able to determine accurately PNC mixing parameter. Mixing coefficient for the states with opposite parities: mixing parameter parallel polarizations! orthogonal polarizations! Transition amplitude: ~ M 1 1 M 1 1 i M 3 1 S 1 S S 1 S P 1 S Theoretical work is in progress!
17 Summary We have used independent particle model together with the density matrix approach to analyze properties of the two-photon emission from helium-like ions: Total and energy-differential decay rates Angular correlations between emitted photons Polarization properties of the photons Applications of the two-photon spectroscopy have been discussed for: Accurate analysis of relativistic and many-body phenomena Test of Bose quantum statistics Atomic parity violation studies with highly-charged ions
18 Two-photon transitions in heavy ions: From relativistic and many-body effects to parity non-conservation phenomena In collaboration with Filippo Fratini Thorsten Jahrsetz University of Heidelberg Stephan Fritzsche University of Oulu Thomas Stöhlker Alexandre Gumberidze Christophor Kozhuharov Sergyi Trotsenko GSI, Darmstadt Andrey Volotka TU Dresden Jose Paulo Santos Pedro Amaro Universidade Nova de Lisboa Paul Indelicato ENS, Paris
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