Higher-order effects in the angular distribution of photoelectrons

1. Higher-order effectsin the angular distributionof photoelectrons A. Kövér3rd Japan-Hungarian Joint Seminar Debrecen, October 9, 2007

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

3. Double Differential Cross Section of photoelectron for linearly polarized photons: E2, M1 quadrupol E1 dipole σnl 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) P2 is the second order Legendre polynomial Theθ, Φ are the polar and azimuth angle relative to the electric vector and relativetothe k, E plane, respectively.

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

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

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

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

8. Our investigations: We determined the dipole () and non-dipole ( és ) anisotropy parameters for Xe5s, (90-225 eV) Xe5p1!2,3/2 (100-200 eV) Ar3p1/2,3/2 (90-330 eV) subshells .

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

10. Synchroton: A Max-II Lund, beam line I411

11. Xe 5sdipole ésnon-dipole hν=90-225 eV, Δhν=90-300 meV, dmon=120 mmEpass=70 eVΔEspm=170 meV Δhν=90-300 meV RIPM: Rel. independet particle model TDDFT: Time-dependent density-functional RRPA: Rel.Random Phase approx. 13 chan 4d, 5s, 5pshells 20 chan: 4s, 4p, 4d, 5s, 5p S. Ricz et al Phys. Rev A67(2003)012712

12. AXe 5p1/2and5p3/2subshellsdipole (b) hν=100-200 eV, Δhν=50-240 meV, dmon=100 mm, Eát=70 eV és ΔEspm=170 meV 13 channel RRPA: 4d, 5s, 5p 20 chan RRPA: 4s, 4p,4d, 5s, 5p Difference between the spin-orbit components R. Sankari et al Phys. Rev A69(2004)012707

13. ΔEspm=60 meV • hν≈50 meV Ar 3pdipole és, non-dipole • ΔEspm=160 meV Δhν≈100 meV S. Ricz et al Phys. Rev A72(2005)014701

14. Ephe • Interference between the direct ionization and the resonance excitation participator Auger decay (REPA) Continuum states DI REPA E=0 M M L3 L3 Bound states L2 L2 L1 L1

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

16. The asymmetryparameter σL,σR are the cross sections on the left and right side

17. k(direction of the photon beam) Right Left The asymmetryparameter: P Polarization vector

18. ALR1/2=0.015(11) ALR3/2=0.0095(90) ALRtot=0.0087(7) Esa-22 Ar 2p ALRtot=0.010(3) Scienta • Non zero asymmetry was measured with two independent spectrometer. • The agreement between the measured data is excellent

19. Parity violation? NO