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

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

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

β=2

β=2γ=1δ=0.5

k (direction of the photon beam)

PPolarization

vector

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

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.

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..

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

..

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

Synchroton: Synchroton: A Max-II A Max-II Lund, beam Lund, beam line I411line I411

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

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

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

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

Participants:Participants:

H. AkselaH. AkselaS. AkselaS. AkselaM. JurvansuuM. JurvansuuÁ. KövérÁ. KövérJ. MolnárJ. MolnárJ. NikkinenJ. NikkinenT. RicsókaT. RicsókaR. RiczR. RiczR. SankariR. SankariD. VargaD. Varga

The The asasyymmetrmmetryy paramparameeterter

σL, σR are the cross sections on the left and right side

RL

RLLRA

k (direction of the photon beam)

PPolarization

vector

RL

RLLRA

The The asasyymmetrmmetryy paramparameeterter::

Left Right

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

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