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EFFECT OF EXITING PHOTON INELASTIC SCATTERING

IN PHOTOIONIZATION OF ATOMS

V.A. Kilin, R.Yu. Kilin

Tomsk Polytechnic University

In collaboration with Prof.Dr. M. Amusia (S.-Petersburg, Russia)AG Prof.Dr. H. Schmoranzer (Uni Kaiserslautern)AG Prof.Dr. K.-H. Schartner (Uni Giessen)

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1. Multi-step physical models in theoretical studies of atomic processes and properties

2. Model physical processes studied in our previous works as “elementary” steps in multiple ionization of atoms

3. Post-photoexcitation fluorescent photons as inelastic scattered exciting photons

4. PT approach to inelastic photon scattering

5. Conclusion

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1. MULTI-STEP PHYSICAL MODELS IN THEORETICAL STUDIES OF ATOMIC PROCESSES AND PROPERTIES

Externalperturbation

(EM field, accelerated charged particles, etc.)

Reaction products

(excited atoms, ions, photons)

Isolatedatom

?What we have in reality:

1. Probably, not all the reaction products observed2. Experiment uncertainty3. Interpretation of experimental data

We study scattering processes

Limit cases: - Complete Absorption (Esc.particle=0)- Absolute Elastic Scattering (Esc.particle=Eincoming)

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1. MULTI-STEP PHYSICAL MODELS IN THEORETICAL STUDIES OF ATOMIC PROCESSES AND PROPERTIES

What we imagine (modeling) :

To understand physics (main physical mechanisms) and to carry out necessary evaluation of physical properties we need, in many cases, to decompose a complicated many-electron process into “elementary” steps, of which each could be explained in terms of “single-particle events”

KrI+res KrI 3d9 np (b) KrII 4s14p4 n’l’ np +e1 (2) KrIII 4s24p3 np + e1 + e2 KrIII 4s24p3 ns/d+ e1 + e2 + fl

KrIII 4s24p4 + e1 + e2 + fl + vis

EXAMPLE: Multi-step Double Photoionization with excitation

res

Photoexcitation of the resonant state KrI 3d9np and its furtherdecay pathways

vis

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2. Model physical processes as “elementary” steps in multiple ionization

1. Many-electron Auger effects

Three-electron(doubled)

Auger effect

Double Augereffect

Satellite Auger

transitions

“deepening” and “countermotion”of vacancies

i1 i2 → f1f2f3 +eq

i1 → f1f2f3 +(e1, e2) i1 → f1f2f3 nl+eq

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3d-1→4s-14p-2[4P,2D] nl[LS] +q 3d-1→ 4p-3[4S,2D, 2D] nl[LS] +q

n=1,2,…,9; l=0,1,2,3;ε~2-35 eV

Calculated superposition of the continuous spectra of double Auger transitions and discrete spectra of satellite Auger transitions in Kr

0 5 10 15 20 25 30 35 40

200

400

600

800

1000

1200

1400

Kr ×10-6

Background of double Auger electrons

3d-1→4s-14p-2[4P,2D] +q1+q2

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2. Model physical processes as “elementary” steps in multiple ionization

2. Autoionization transitions

Double autoionization decay of a resonantly excited state

Autoionization decay of a doubly excited state

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5 10 15 20 25 30 35

150

300

450

600

1750

2000

2250

Пло

тнос

ть в

ероя

тнос

ти

x 10

5

Энергия (эВ)

B

C

A

Calculated total electron spectrum of Double Autoionization transitions from KrI 3d95p resonantly excited state

5 10 15 20 25 30 35

5

10

15

20

25 C

B A

Плот

ност

ь ве

роят

ност

и

x

10

5

Энергия (эВ)

Сумма

4s -2 [1S]

4s -1 4p -1 [1P]

4s -1 4p -1 [3P]

KrI 3d95p KrIII 4s0[1S]

KrIII 4s14p5[1,3S]

+(e1,e2)

+(e1,e2)

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i1i2i3 nli1,2,3 f n'l'

2. Model physical processes as “elementary” steps in multiple ionization

Two-electronradiation

transitions

3. Many-electron radiation transitions

Three-electronradiation

transitionsSingle-photon decay of a two-hole stateSemi-Auger transitions (e + photon)Etc.

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2. Model physical processes as “elementary” steps in multiple ionization

4. Multiple photoionization (PI)

Direct double PI

Two-stepdouble PI

Triple PI

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60 90 120 150 180 210 240 270 300 330

0.05

0.10

0.15

0.20

0.25

0.30V

Chang & Poe

VL

Carter & Kelly

V

++(, {qmin

})

++(, {qmin

()})

L

++(, {qmin

})

Энергия фотона (эВ)

- [104] - [196] - [178] - [182] - [187] - [197] - [189] - [190]

Ne++А

бсо

лю

тно

е с

ече

ни

е (

Мб

)

Calculated and experimental DPI total cross sections of Ne

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3. Post-photoexcitation fluorescent photons as inelastic scattered exciting photons

Principal possibility of an irradiation transition in a multi-step sequence, Slide 4, as well as the observation of resonant and background photons in PIFS experiments demonstrates that the effect of inelastic exciting photon scattering (IEPS) takes place in photo-

ionization/excitation. (s): 2s2 2p6 +1 2s1 2p6 +ep

(s’): 2s2 2p6 +1 2s1 2p6 +es,d +2

Examples

(Ne) :(p): 2s2 2p6 +1 2s2 2p5 + es,d

(p’): 2s2 2p6 +1 2s2 2p5 + ep,f +2

- The IEPS effect influences, in a measure, on both the measured and calculated PI cross sections and photoelectron angular distribution, especially in the region close around the resonant energy.

- One may expect to observe and explain new features in fluorescence and photoelectron

spectra as well as in photoelectron angular distribution taking into account the IEPS.

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3. Post-photoexcitation fluorescent photons as inelastic scattered exciting photons

PIFS spectra of Kr

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4. PT approach to Inelastic Photon Scattering

ke

k

k

n

N

nnN ptrA

ctrrrH ˆ),(

1),,...,,(ˆ

121int

( ) * ( )

, ,,

( , ) ( )i t kr i t kr

k k kk

A r t e a e a e

( , )A r t

Conventionally, the photoionization (PI) of atoms is considered as a process of driving an atomic electron out because of interaction of a N-electron atom with EM field

. Here the vector potential is a superposition of monochromatic plane waves of, (ω=с ), and polarization

In case of low EM field intensity, atoms are able to absorb a single photon. Therefore, only one component k = k1, ω = ω1 can be taken into account in calculation of PhI cross sections.

Consider the influence of inelastic exciting photon scattering (IEPS) on PI cross sections. Then the exciting photon energy ω1 satisfies the following equation: ω1 = ω2 + If + εq,

where ω2 is the scattered photon energy, If is the ionization potential of a f-shell,

and εq is the photoelectron q energy. Note, that the transition energy Etr = ω1 - If = ω2 + εq

can be continuously distributed (shared) between photoelectron q and scattered photon ω2. This is very similar to the continuous energy distribution between two electrons

in such processes as double PI, double Auger transitions, double autoionization of resonantly excited states, and so forth, considered in our previous works. Therefore, the contribution 1( , )sc f of IEPS to total PI cross section is the integral

01 2

1 1 2 220

( , , , )( , ) ( )sc q

sc f q q

d ff I d d

d

frequency ω, wave vector

,

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4. PT approach to Inelastic Photon Scattering

To develop the theory of IEPS within the framework of perturbation theory (PT), one needs to take into account two terms with ω1 and ω2 in the vector potential.

This leads to the formula for differential IEPS cross section 3

21 2 1 21 2 1 24

2

( , , , ) 4( , , , ) ( )sc q

sc q f q

d fM f I

d c

In the lowest non-vanishing PT order the IEPS amplitude 1 2( , , , )sc qM f could be presented as the sum of the following two partial amplitudes:

1M1 2

( ) 1( )

ˆ ˆ

2k F q kk F

q d k k d f

i

2M 2 1

( ) 1( )

ˆ ˆ

2k F f kk F

q d k k d f

i

=

=

+

+

PT

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4. PT approach to Inelastic Photon Scattering

It is seen that the partial amplitudes M1 and M2 can contribute significantly in cases :

(a) , i.e., if an intermediate state k is a hole or discrete excited one and (b) , i.e., if an intermediate state k is a state of continuum. In case (a) the two opportunities of IEPS with PI of f-shell may be held via two steps, of which the first step is: (1)   photoionization of intermediate k-shell followed by the second step irradiation transition k-1 f-1 + ω2, left top in figure above,

(2)   excitation of intermediate hole-particle discrete spectrum state (f-1 k) due to the interaction with electromagnetic field and irradiation of the photon ω2, which then followed by

photoionization of (f-1 k), right top in figure above. Both in (1) and (2) the second step transition changes the photoelectron energy because of correlation interactions, which are not included yet within the considered order of PT. In case (b) the left bottom figure corresponds and describes the photoionization of f-shell with the ejection of intermediate photoelectron k on the first step. Then photoelectron k gives out a part of its energy irradiating the photon ω2.

1 0k q 1 0k f

1M1 2

( ) 1( )

ˆ ˆ

2k F q kk F

q d k k d f

i

2M 2 1

( ) 1( )

ˆ ˆ

2k F f kk F

q d k k d f

i

=

=

+

+

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4. PT approach to Inelastic Photon Scattering

Higher PT order amplitudes

, and so on

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4. PT approach to Inelastic Photon Scattering

RPAE higher order PT diagrams

RPAE higher order PT diagrams accounted through calculationof photoelectron WF in the field of vacancy i

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Conclusion

1. Background photoelectrons and fluorescent photons observed in PES

and PIFS experiments could be related, at least partly, to the IEPS effect.

2. To accurately calculate the photoionization cross section nearby

a resonance one needs take the IEPS effect into account.

3. Photoelectrons of “unusual” orbital momentum can be observed in PI

superinducing new features in their angular distribution.

4. The second term in vector potential of EM field responsible for irradiation

of the secondary photon allows new Interchannel Interactions

in Photoionization and Photoexitation.

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