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![Page 1: Higher-order effects in the angular distribution of photoelectrons A. Kövér 3rd Japan-Hungarian Joint Seminar Debrecen, October 9, 2007.](https://reader035.fdocuments.net/reader035/viewer/2022070307/551a756d5503463e778b617e/html5/thumbnails/1.jpg)
Higher-order effectsHigher-order effectsin the angular in the angular distributiondistribution
of photoelectronsof photoelectrons
A. A. KövérKövér3rd Japan-Hungarian Joint 3rd Japan-Hungarian Joint
Seminar Seminar DebrecenDebrecen, October 9, 2007, October 9, 2007
![Page 2: Higher-order effects in the angular distribution of photoelectrons A. Kövér 3rd Japan-Hungarian Joint Seminar Debrecen, October 9, 2007.](https://reader035.fdocuments.net/reader035/viewer/2022070307/551a756d5503463e778b617e/html5/thumbnails/2.jpg)
The investigation of the angular The investigation of the angular distribution of photoionization distribution of photoionization gives detailed information ongives detailed information on
Electronic structure of atomsElectronic structure of atoms Correlation between the different Correlation between the different
ionization channelsionization channels
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Double Differential Cross Section of photoelectron Double Differential Cross Section of photoelectron
for for linearly polarizedlinearly polarized photons photons::
)}sin()cos()](cos[)(cos1{4
22
Pnlnl
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
The θ, Φ are the polar and azimuth angle relative to the electric vector and relative to the kk, EE plane, respectively.
E1dipole
E2, M1quadrupol
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β=2
β=2γ=1δ=0.5
k (direction of the photon beam)
PPolarization
vector
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Wuilleumier&Krause PRA 10 (1974) 242.
hν=1486.6 eVhν=1253.6 eV
hν=132.3 eVhν=108.9 eV
EE
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:In the last decade:
Intensive Intensive theoreticaltheoretical investigations were carried investigations were carried outout
to determine the to determine the the non-dipole the non-dipole contributions contributions
at low energies.at low energies.
Bechler Bechler et alet al, Cooper , Cooper et alet al ill. Derevianko ill. Derevianko et alet al: : relativisrelativistictic independet particle modelindependet particle model (RIPM). (RIPM).
Amusia Amusia et alet al ill. Johnson és Cheng: ill. Johnson és Cheng: non relativsticnon relativstic and and relativisticrelativistic random phase approximationrandom phase approximation (RPAE)(RPAE)
Gorczyca és Robicheaux: Gorczyca és Robicheaux: R-mátrix R-mátrix calculationscalculations
It was found that it is It was found that it is very sensitivevery sensitive to the to the coupling coupling between different ionization between different ionization channels.channels.
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WuilleumierWuilleumier and and Krause Krause (1974) (1974):: experimental experimental investigation of investigation of non-dipole effects at low photon non-dipole effects at low photon energyenergy (1 keV (1 keV andand 2 keV) 2 keV)
Experimental:Experimental:
Hemmers Hemmers at al (19at al (199797):):
Strong non-dipole effect at Strong non-dipole effect at
Ne 2s, 2pNe 2s, 2p photoionization photoionization..
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Our investigations:Our investigations:
We determined the dipole We determined the dipole (()) and non-dipole and non-dipole (( és és ))
anisotropy parameters foranisotropy parameters for
XeXe 5s5s, , (90-225 eV) (90-225 eV)
XeXe 5p5p1!2,3/21!2,3/2 (100-200 eV) (100-200 eV)
ArAr 3p3p1/2,3/21/2,3/2 (90-330 eV (90-330 eV))
subshellssubshells
..
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ESA-22 electron-spectrometer
- - Double pass Double pass
- Second order focusing - Second order focusing - Two independent spectr.- Two independent spectr.- Built in retardation lens- Built in retardation lens
- High energy resolution- High energy resolution
20 channeltron20 channeltronss at every 15 at every 15oo
Simultaneous detection of Simultaneous detection of electrons in the 0electrons in the 0oo-360-360oo angular angular rangerange
The confidence level of the angular distribution is high. 1
0 c
m
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Synchroton: Synchroton: A Max-II A Max-II Lund, beam Lund, beam line I411line I411
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Xe 5sXe 5s dipole dipole ésés non-dipolenon-dipole hhνν=90-90-222525 eV eV, , ΔΔhhνν=90=90--303000 meV, d meV, dmonmon=120 =120 mm
EEpasspass=70 eV=70 eV ΔΔEEspmspm=170 meV =170 meV ΔΔhhνν=90=90--303000 meV meV
RIPM:RIPM:Rel. independet Rel. independet particle modelparticle model
TDDFT:TDDFT: Time-dependentTime-dependentdensity-density-
functionalfunctional
RRPA:RRPA:Rel.Random Rel.Random Phase approx.Phase approx.
13 13 chanchan4d, 5s, 5p4d, 5s, 5p shellsshells
20 20 chanchan: : 4s4s, , 4p4p, , 4d4d, , 5s5s, , 5p5p
S. Ricz et al Phys. Rev A67(2003)012712
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AA Xe 5pXe 5p1/21/2 andand 5p5p33/2/2 subshellssubshells dipole (dipole () )
hhνν=10100-0-220000 eV eV, , ΔΔhhνν=50=50--240 meV, d240 meV, dmonmon=100 =100 m, m,
EEátát=70 eV és =70 eV és ΔΔEEspmspm=170 meV=170 meV
80 100 120 140 160 180-0,4
0,0
0,4
0,8
1,2
1,6
2,0
80 100 120 140 160 180-0,4
0,0
0,4
0,8
1,2
1,6
2,0
80 100 120 140 160 180
-0,3
-0,2
-0,1
0,0
0,1
0,2
0,3
0,4
1/2 saját mérés
Krause et al mérése 13 csat RRPA 20 csat. RRPA
1/2-
3/2
Fotoelektron energia (eV)
13 13 channelchannel RRPA: RRPA:4d, 5s, 5p4d, 5s, 5p
20 20 chanchan RRPA: RRPA: 4s4s, , 4p4p,, 4d4d, , 5s5s, , 5p5p
R. Sankari et al Phys. Rev A69(2004)012707
Difference between the spin-orbit components
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Ar 3pAr 3p dipole dipole ésés ,, non-dipolenon-dipole ΔΔEEspmspm=160 meV =160 meV
ΔΔhhνν≈100 meV≈100 meV ΔΔEEspmspm=60 meV=60 meV hhνν≈50 meV≈50 meV
S. Ricz et al Phys. Rev A72(2005)014701
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Interference between the direct ionization and the Interference between the direct ionization and the resonance excitation participator Auger decay (REPA)resonance excitation participator Auger decay (REPA)
L1
L3
L2
M
L1
L3
L2
M
Ephe
E=0
Bou
nd
sta
tes
Con
tin
uu
m s
tate
s
DI REPA
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Participants:Participants:
H. AkselaH. AkselaS. AkselaS. AkselaM. JurvansuuM. JurvansuuÁ. KövérÁ. KövérJ. MolnárJ. MolnárJ. NikkinenJ. NikkinenT. RicsókaT. RicsókaR. RiczR. RiczR. SankariR. SankariD. VargaD. Varga
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The The asasyymmetrmmetryy paramparameeterter
σL, σR are the cross sections on the left and right side
RL
RLLRA
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k (direction of the photon beam)
PPolarization
vector
RL
RLLRA
The The asasyymmetrmmetryy paramparameeterter::
Left Right
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Ar Ar 2p2p
Ar 2p, h =461.2 eV
Electron energy (eV)
206 208 210 212 214
Nor
mal
ised
inte
nsit
y (a
rb.u
.)
0
1000
2000
3000
4000
3P0,1,2 LMM
2p1/2
2p3/2ALR1/2=0.015(11)
ALR3/2=0.0095(90)
ALRtot=0.0087(7)
Esa-22
ALRtot=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? NOParity violation? NO
Atomic mass (au)
0 20 40 60 80 100 120 140
(L-
R)/
(L+ R
)
0.00
0.02
0.04
0.06
0.08
0.10
Th.
( L
-R)/
(L+ R
)
0
1e-12
2e-12Exp. in February
Exp. in September
Exp. after 180O rotation in September
TheoryH2
He
NeAr Kr Xe