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Higher-order effects in the angular distribution of photoelectrons A. Kövér 3rd Japan-Hungarian Joint Seminar Debrecen, October 9, 2007

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The investigation of the angular distribution of photoionization gives detailed information on Electronic structure of atoms Electronic structure of atoms Correlation between the different ionization channels Correlation between the different ionization channels

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Double Differential Cross Section of photoelectron for linearly polarized photons: σ nl is the cross section of photoionisation, β, γ, δ are the anisotropy parameters of the dipole and non-dipole interactions (for s-shells δ =0) P 2 is the second order Legendre polynomial kE The θ, Φ are the polar and azimuth angle relative to the electric vector and relative to the k, E plane, respectively. E1 dipole E2, M1 quadrupol

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β=2 γ=1 δ=0.5 k (direction of the photon beam) P Polarization vector

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Wuilleumier&Krause PRA 10 (1974) 242. hν=1486.6 eV hν=1253.6 eV hν=132.3 eV hν=108.9 eV In general the dipole approximation gives good agreement with the experimental data when the photon energy <1 keV

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In the last decade: Intensive theoretical investigations were carried out to determine the the non-dipole contributions to determine the the non-dipole contributions at low energies. at low energies. Bechler et al, Cooper et al ill. Derevianko et al: Bechler et al, Cooper et al ill. Derevianko et al: relativistic independet particle model (RIPM). Amusia et al ill. Johnson és Cheng: non relativstic Amusia et al ill. Johnson és Cheng: non relativstic and relativistic random phase approximation (RPAE) and relativistic random phase approximation (RPAE) Gorczyca és Robicheaux: R-mátrix calculations Gorczyca és Robicheaux: R-mátrix calculations It was found that it is very sensitive to the coupling between different ionization channels.

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Wuilleumier and Krause (1974): experimental investigation of non-dipole effects at low photon energy (1 keV and 2 keV) Wuilleumier and Krause (1974): experimental investigation of non-dipole effects at low photon energy (1 keV and 2 keV) Experimental: Hemmers at al (1997): Hemmers at al (1997): Strong non-dipole effect at Ne 2s, 2p photoionization.

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Our investigations: We determined the dipole ( ) and non-dipole ( és ) anisotropy parameters for Xe 5s, (90-225 eV) Xe 5p 1!2,3/2 (100-200 eV) Ar 3p 1/2,3/2 (90-330 eV) subshells.

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ESA-22 electron-spectrometer - Double pass - Double pass - Second order focusing - Two independent spectr. - Built in retardation lens - Second order focusing - Two independent spectr. - Built in retardation lens - High energy resolution 20 channeltrons at every 15 o 20 channeltrons at every 15 o Simultaneous detection of electrons in the 0 o -360 o angular range Simultaneous detection of electrons in the 0 o -360 o angular range The confidence level of the angular distribution is high. 10 cm

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Synchroton: A Max-II Lund, beam line I411

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Xe 5s dipole és non-dipole hν90-225 eV, Δhν=90-300 meV, d mon =120 m E pass =70 eV ΔE spm =170 meV Δhν=90-300 meV hν=90-225 eV, Δhν=90-300 meV, d mon =120 m E pass =70 eV ΔE spm =170 meV Δhν=90-300 meVRIPM: Rel. independet particle model TDDFT:Time-dependentdensity-functionalRRPA:Rel.Random Phase approx. 13 chan 4d, 5s, 5p shells 20 chan: 4s, 4p, 4d, 5s, 5p S. Ricz et al Phys. Rev A67(2003)012712

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A Xe 5p 1/2 and 5p 3/2 subshells dipole ( ) A Xe 5p 1/2 and 5p 3/2 subshells dipole ( ) hν100-200 eV, Δhν=50-240 meV, d mon =100 m, hν=100-200 eV, Δhν=50-240 meV, d mon =100 m, E át =70 eV és ΔE spm =170 meV E át =70 eV és ΔE spm =170 meV 13 channel RRPA: 4d, 5s, 5p 20 chan RRPA: 4s, 4p, 4d, 5s, 5p R. Sankari et al Phys. Rev A69(2004)012707 Difference between the spin-orbit components

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Ar 3p dipole és ,non-dipole Ar 3p dipole és , non-dipole ΔE spm =160 meV Δhν≈100 meV ΔE spm =160 meV Δhν≈100 meV ΔE spm =60 meV ΔE spm =60 meV hν≈50 meV hν≈50 meV S. Ricz et al Phys. Rev A72(2005)014701

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Interference between the direct ionization and the resonance excitation participator Auger decay (REPA) Interference between the direct ionization and the resonance excitation participator Auger decay (REPA) L1L1 L3L3 L2L2 M L1L1 L3L3 L2L2 M E phe E=0 Bound states Continuum states DIREPA

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Participants: H. Aksela S. Aksela M. Jurvansuu Á. Kövér J. Molnár J. Nikkinen T. Ricsóka R. Ricz R. Sankari D. Varga

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The asymmetry parameter σ L, σ R are the cross sections on the left and right side

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k (direction of the photon beam) P Polarization vector The asymmetry parameter: Left Right

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Ar 2p A LR 1/2 =0.015(11) A LR 3/2 =0.0095(90) A LR tot =0.0087(7) Esa-22 A LR tot =0.010(3) Scienta Non zero asymmetry was measured with two independent spectrometer. The agreement between the measured data is excellent

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Parity violation? NO

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