Inner shell photoexcitation of atoms with correlation effects on autoionization : application to the argon 2p shell

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Submitted on 1 Jan 1993

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Inner shell photoexcitation of atoms with correlation effects on autoionization : application to the argon 2p

shell

A. Hopersky, V. Yavna

To cite this version:

A. Hopersky, V. Yavna. Inner shell photoexcitation of atoms with correlation effects on autoionization : application to the argon 2p shell. Journal de Physique II, EDP Sciences, 1993, 3 (9), pp.1319-1329.

�10.1051/jp2:1993203�. �jpa-00247909�

Classification Physic-s Abstiacts

32.80F

Inner shell photoexcitation ^of atoms with correlation effects

_on

autoionization

_:

application to the argon 2p shell

A. N.

Hopersky

and V. A. Yavna

Rostov

Railway Engineers

Institute, Chair of Mathematics, 344017 Rostov-on-Don, Russia (Received 30 December f992, revised 23 April f993, accepted 25 May 1993)

Abstract. For _atoms with closed shells in their ground state, a Hartree-Fock (HF) equation is obtained for the electron moving ^{in the field} of _an inner shell vacancy which decays

through

autoionization. In this

equation,

the

following

processes are taken into _account I) change of the HF field of the

remaining

atom _{as a} result of autoionization decay of the inner shell vacancy 2) interaction of the

photoelectron

with _a virtual Auger electron, thus the radial correlation in their

movement is accounted for. The

developed

method is

applied

to

study

the

Lu, ui-photoexcitation

ⁱⁿ

Ar atom.

1. Introduction.

Theoretical studies of

photoabsorption

near the ionization threshold of atomic inner shells have

shown that in order _to obtain _a 85-95 §b accuracy between theoretical and

experimental

spectral

features one has _to include :

I) Monopole

rearrangement ^{of electron} shells

(MRES)

within the field of _an inner shell vacancy

[1-3].

MRES is the most

important

correlation effect in inner shell

photoabsorption.

It describes the radial

restructuring

of electron shells after the creation of _a vacancy. Inclusion of MRES when

calculating,

for

example,

^the

Ljj nj-photoabsorption

in Ar

[3]

decreases the theoretical

photoabsorption

cross section calculated in _{a «} frozen _{core »}

approximation by

two orders and _even within the Hartree-Fock

single-configuration approximation (HFSA)

it leaves

only

^25-30 §b

disagreement

^{with the}

experiment [4]

2)

Correlational reduction

(CR)

of the outer Shell electron

density

within the final state of

photoabsorption [5]

_;

3)

Vacuum correlations

(VC) [6].

CR and VC effects may be described within the frame of the Hartree-Fock

multiconfiguration approximation.

Thus it _was shown in references

[5, 6]

that the main correction _to the total wavefunctions of initial and final States of K- and

Ljj jjj-photoabsorption

of Ar _are

given by

the

configurations

of virtual _outer

3p-shell excitationslionizations

of the

Kj~

=

3 p~ ^~ n

~p, d)

_n~~p,

d) shake-type

(fi

j ~ ~ F -Fermi

level).

Within this

approach

the initial and final _states of

photoabsorption

_are built _on different sets of radial

orbitals,

and the MRES effect is included via the methods of the

theory

of _non-

orthogonal

orbitals

[71. According

to

[51,

the

mixing

of the

photoabsorption

final _state

configuration

with the

Kj~-configurations

leads _to atomic electron

density

delocalization _as

compared

with HFSA situation

(the

CR

effect). Taking

CR into _account leads to the

growth

of the

photoabsorption

_cross section _near the ionization threshold

(by

20-25 §b in _case of Ar

Ljj iii-spectrum).

Construction of the initial state function _as a

Superposition

of

configuration

functions makes it necessary ^to include the

absorption

of the

photon

both

by

vacuum

configuration

and

by

the

Kj~-configurations

of _vacuum excitations

(the

VC

effect).

Inclusion of

VC decreases

photoabsorption

_cross sections in Ar

La,

iii-spectrum ^{obtained within} the

MRES ₊ CR

approximation by

5 §b _;

4) Multiplet

effects in order _to calculate the spectrum ^fine structure.

Thus, taking

the

spin-

orbit

Splitting

of Ar

2p-shell

into account when

calculating

Ar

Ljj, ju-photoabsorption [3,

51 makes it

possible

to describe the details of the

experimental

_spectrum of reference [41 well

5)

The autoionization of _atoms and related correlations in the motion of

photo-

and

Auger-

electrons in order to describe the

photoabsorption

cross section

shape

_{as a} function of the

photon

_energy. The method of

taking

this correlation

angular

_part into _account has been

developed

in reference

[81. However,

the

problem

^{of the} modification of the

photoelectron

wavefunction radial part ^{in the field}

changing

due to autoionization is still unsolved.

Therefore, the aim of the present ^{work is} :

I)

to obtain the HF

equation

for the

photoelectron moving

in the field of _an inner vacancy which

decays through

autoionization _;

2)

to

explain

the influence of radial correlation in the

movement of the

photo-

^and

Auger-electrons

_on the characteristics of the spectrum ^and

3)

to

explain

the still

remaining discrepancies

between

theory

and

experiment.

2. Theoretical methods.

2. I THE _{ENERGY AND THE} WAVEFUNCTION OF THE FINAL STATE PHOTOEXCITATION. Let _us

consider the final _state wavefunction

(E)

_as the

superposition

of the function of the state

Eo)

= no 11 ^n/

having

the inner no

to-vacancy

and of the

Ej )

= n~

Ii

^' _n~

Ii

^' _ei

Ii

nI

channel of atom autoionization

(nI

is the discrete spectrum

photoelectron

_{; ej}

Ii

is the free

Auger

electron _n, ej ~ F where F is _a Fermi level

[91)1

[El

~ "E

llE0l

^~

^d~l

^PET

^{[Eli (l)}

lElE'l

=

6(E E'), iEjiE~)

=

&(ei e~) lEolEol

= i,

lEolEil

= °

Let _us request ^that

[E)

be the

eigenfunction

of the atomic non-relativistic Hamiltonian

ji

fi(E)

=

E(E)

N N

fi= £ (-A~/2-r/~Z)+ z [r,-r~[~~; ₍₂₎

1=1 <»j

where Z is _a nuclear

charge,

N is the number of electrons in _an atom, _r, is the I-th electron radius-vector.

Let _us

assign

(Eo(fi( _Eo)

₌

Eo

_;

(Eo(fi( Ej)

= vi.

The

general

structure of the

(Ej (fi( E~)

^{matrix element when}

^{using (2)}

^is :

(Ej (fi( E~)

=

E~i (pi e~)

+ pi

Ii Ii

e~

Ii

₊

Ail. (3)

In

(3) E~i

is the energy of the

[E~i)

=

(n~ Ii

_n~

Ii

nI -state and it does _not

depend

_on the

e/j-function.

The bound orbitals stay ortho-normalized

during

the autoionization process.

Ail

=

(aj~

+

all

_{is the term}

_describing

_the electrostatic interaction of the

Eli-Auger

electron with the atomic residual shells

(aj~)

and with the

nt-photoelectron (al'[)

;

j

^I

^{d~ I(/}

^{+ I}

⁾

_{__} i z

2

dr~

^~ ₂

r~

^'

In reference

[81

the

theory

of autoionization has been

developed assuming

that

lEj (h( _E~)

=

Ej &(ej ~~). (4)

Representation

of

(3) by (4)

is

possible

^{if the PI}

j-Auger

electron function satisfies the

equation

lej Ij)ii~

e~

lj)

₊

^All

_{= ej}

&(ej e~)

_ej

=

Ej E~i (5)

I-e- if it is obtained in the field of the

[E~,i)

core. The solution of

equation (5)

with respect to the

Eli-function

in its _tum supposes that the _set of one-electron states of the _core

[E~,i)

^{is known.}

Specifically,

it is

suggested

that the

nl-photoelectron

function is obtained

within the _core field which has

changed

because of autoionization.

The

problem

of

obtaining

the

n/-photoelectron

wavefunction _{was not} studied in reference

[81.

However,

without

solving it,

it remains unclear how radial correlations in the motion of

photo-

and

Auger-electrons

affect the

photoabsorption

spectrum characteristics.

We propose to solve the

problem

of

obtaining

the wavefunction of

n/-photoelectron

in _two steps

1.

Equation (5)

is

being

solved with _{a « zero}

approximation

_» n/

-photoelectron,

I-e- the state which is obtained within the n~

Ii

^' _n~

Ii

^' _core field.

Introducing

_{a « zero}

approximation

_»

?-photoelectron

_allows

us to write instead of

(3)

lEj (fi E~)

=

Ej (ej e~)

+ q7 j~ q7_j~ =

ail al'l

_;

(6)

2. An HF

equation

for the

nl-photoelectron

is

being

constructed under the condition that the

photoexcitation

_{resonance energy} reaches _{an extremum}

(the

value E at which the term

[«e[~

in the

photoexcitation

_cross section reaches its

maximum).

Let _us

perform

the described steps.

Calculating

the matrix element

(Ej (ji E)

^and

_(Eo (ji E) by taking (1, 6)

into considera-

tion,

_we obtain

integral equations

for the

mixing

coefficient of the

configurations

~E,

~ PI

~l

~

dF2 #E~ '12)

(7)

and for the total energy of the _state

(1)

E=Eo+ldejvjpe,, ⁽⁸⁾

where

~j

=£P(E-Ej)~' +ze&(E-Ej);

iJ' is the

principal

part

symbol

_{; ze} is the real function which will be determined in the

iollowing.

Since

u~ = VI>, the

conjugation sign

is omitted

everywhere. Expression j~), by using (7),

is reduced _to the form

«

1,,

E

=

Eo

+

Fe

+ ze Uel~ +

I

_4~,,

fl

_~,

dei

,

(9)

,,=~ i=>

where

,<-1

4~~=uju~flq7,,,+il Ue"Ui(e,=e'

i=1

the value

Fe

₌ ^iJ°

ldej ^[vi

[~

(E Ej)~

describes the autoionization

photoabsorption

resonance energy shift relative _to

Eo [81.

From

(9),

Since the values of _q7~

, ~ are small and if the additional condition for the

ze-function

IZE 9'<,

i

+1(

~ l

(10)

is introduced, it follows that

E=Eo+Fe+Ae+ze([ue[~+Ce); ₍₁₁₎

w n

Ae

=

£

iJ' 4~,,

fl (E

_{E~ )~}

de~

,i=2 1=1

Ce=2M dejvjueq~je(E-Ej)~'m2ue&ve,

ze can be obtained from

expression (I I).

The

normalizing

factor _«e in

(I )

_may be obtained from the condition of normalization of the

E)

state

(E E')

= (E

E')

= «e «e, l +

dej pe pe,) ⁽¹²⁾

Using

the

expression

of reference [81 ^for a

product

of

singular

terms

~~, ~l~~

~~~

^-

^{~~, ~~}

^{~ ~ ~}

~~

^{+ ST~}

6(E E) lE i _iE

+

Eii

after

introducing (7)

into

(12)

with the condition

(10)

we

get

(«e(~ («2

₊

z[) ((ve(~

₊

Ce)

=

(13)

Expressing

_ze from

(I I)

_we

have,

instead of

(13)

(«e(~

=

(Ye/«) ((E _{Eo Fe} Ae)~

₊

Yi)~ (14)

In

(14)

_ye

=

re/2

= ar ve ^~ + C

e and the value

re

describes the width of the no

lo-vacancy Auger decay,

With the condition

(&ue/ue)~

« l, the

expression

for

re

is reduced _to the form

re

= 2 _«

(Ue

+ &Ue)~

(15)

In

(15),

the matrix element ue is calculated with the function of

Eli-Auger

electron obtained within the field of the _«

zero-approximation

_»

?-photoelectron,

and

&ue

describes the

correction _to ue,

2.2 HARTREE-FOCK EQUATION FOR THE PHOTOELECTRON.

According

to

(14)

the energy

Fe (shift

of autoionization _resonance which is calculated with the

Eli-Auger

^electron

wavefunction obtained in the field of _«

zero-approximation

_» nl

-photoelectron)

is

changed by

_a

value

Ae,

^As a

result,

the

photoexcitation

_{resonance energy} is determined from the condition of the denominator in

(14)

to be

minimal,

I-e-

by solving

the

integral equation

E-Eo-Fe-Ae=0. (16)

To solve it

approximately,

let _us express

Fe

and

Ae

as

Taylor

series around the value

E=E,,i+P,

where E~,i = (E~~i

(fi _E~,i)

and P is the

Auger

electron energy

during

the real

Auger-decay

of the

nolo-vacancy-

Since

Ae

_~

Fe

in the _sense of order of

magnitude,

then

keeping

the first

derivative in the

decomposition

of

Fe,

we preserve

only

the first _term in the

expansion

of

Ae

Fe>Ft+ ((Fe)[~~t.(E-E); _{AemAt. (17)}

Determining

the

spectroscopic

factor [91 of the

[Eo)

-state in

(I)

_as follows

s =

1

_~

iJ'

~~ ^dej(uj(~ (E-Ej)~') ^e t) ^~,

~E

o

we obtain from

(16, 17)

E=s(Eo+Ft+At)+ (I -s)E. (18)

We shall obtain the HF

equation

for the

photoelectron by

variation of the functional

(18)

_over

P~,i(r)m (nl

the radial part ^{of the}

nl-photoelectron

wavefunction

~~

iii

~ ~

"l, n'l

(ni

_n i

)

= o

,

l

9)

where the _sum contains the term n = n' _{; A~,1,}

~, i are the

Lagrange

terms [91 ^which account for the

orthogonality

of the

photoelectron

wavefunction _to the _core wavefunctions of the _same

symmetry. ^{One has}

(n/

n' i

1«

=

P,,i (r

P

~>i

(r)

dr

o

For the _atoms with closed shells in the

ground

_{state vi} does not

depend

_on the wavefunction

of the

nl-photoelectron,

and

(19) gives

the needed

HF-equation

Ill

^~

ⁱ (~l'~'Yl'n'(~)

^~

i ~l Yl'i,'(~)) ^11111~i

^~

^SDr

^"

,i l'wf L>0

"

I bl YIn'(")

~

i')

_~

z

A

nl, n'l ~ i

(2°)

n'l'<F n'#n

L~0

In

(20)

F is the Fermi level _; ~~i is the

photoelectron

_energy

' j-i j w

~ L+

Y~ii'(r)

=

dr'Pn'l'(~~) Pnl (~')

₊

d~'Pn'l'(~~)

m

Piil

(~~ l

1' ~ ^l" j

"

Nl'~'= sNl'~'+ _(I s)Nl'~'; (21)

a)

=

sa(

₊

_(I

_s

a(

_;

b)

=

sb(

₊

(I

_s

b(

_;

where

Nl'~'

and

Nl'~'

_are the

population

numbers of the n'l' shell. The

angular

al-, b(-

and

al-, b(-coefficients

_are obtained within

[Eo)-

and

[E~i)-configurations, correspondingly, According

to

(20, 21),

the

nl-photoelectron

_moves within the field of the _core with the effective

population

numbers

Nl'~'

of the n'l'-shells.

Thus,

for the Ar atom

Ljj,uj-photoexcitation

studied below for

[Eo)

=

[2p~' nd)

and

[Ej)

=

(3 p~~

_ej

pnd)

_we

have

Nf~=N[~~=2; m=1,2,3;

N)P

= 5 ₊

(1- s)

_;

N(P

=

6

2(1- s). (22)

In

(20)

the _term D~ is obtained

by

variation of the functional

At

over the nl radial part ^of the

nl-photoelectron

wavefunction. We

keep only

the first _term in the series for

At.

^We have then

iW

^{u v}

~' l~

^~'

^{~~l d~2}

j~

~/

^(~~

^~~2(~)

^{~~) ~~~~}

^n(")

^~2

^{ii ))}

>

(23)

o 0 10 20

where the energy denominator is written in

Koopmans

^theorem

approximation [101

~10

_{~ ~ ~l ~}

~no

~n~n~ ^~l ~ ~n~l~ ⁺ ~,>~j _~nolo ~l

E~~~ and

E~~_~,~ ^{are the total}

energies

of the no 11 ^and n~ 11 fi~ 11 states ; the

angular

coefficients a~ and b~ _are obtained for the

configuration

^{of the}

[Ej)-autoionization

channel.

2.3 ASYMPTOTIC _{BEHAVIOUR OF THE POTENTIAL FOR THE} PHOTOELECTRON. if i'W i"o

(io

^{is the atomic}

radius)

it follows from

(23)

that

D~ r~ ^'

d(r) (nl )

°~ Vi U~

I'

^~,

~~~~

~

~0 ^{~~~ ~~~} _{~10 ~20}

0

~~ ~~~~~~~

~~~~~~~'

Using

the determination of the

principal

_part of the

integral (in

the _sense of

Cauchy [I11),

the rule for

taking

derivatives

(prime

means the derivative _over the parameter

x)

(ii

^b

~,i~ dY ~

b' 4',ih ^~'

~l~

+

4'If

dY

a

and Dirac's delta-function property

&(xj -x~)

+«

=

~-« dy &(xj -y) &~y-x~),

one may show that the function

d(r)

satisfies the relation rim

(i

₊

d(,-))

~ s- ^'

(24)

r - W

As _a

result, according

to

(21, 24),

the

asymptotic

behaviour of the

potential

for the nl-

photoelectron

function determined

by solving

the HF

equation (20)

still is of Coulomb

(~ lli)

_type when

going

from HFSA _to the wavefunction

(1).

2.4 PHYSICAL INTERPRETATION OF

N]"~'

AND

D,.

The autoionization

decay

of the

no

lo-vacancy, according

to

(21)

for

Nl'~'

and _to

(23)

for

D,

at s _~ l, is

equivalent

_{to a} virtual redistribution of the part ^of n~

I~-, n~I~-shell

electron

density

between the

nolo-shell

^and

El

j-Auger

electron. As _a result of such _a

redistribution,

the interaction of the nl

-photoelectron

with the

nolo-vacancy (N)°~°~N(°~°)

becomes weaker, while its interaction with

n2/2-,

n~

/~-vacancies

(N)~~~~~~~~~ ~ N(~~~~~~ ^~~) and with the ~l

j-Auger

electron appears,

It is convenient to state the

physical meaning

of the electron correlation described

by D,

within the

representation

of

Feynman's graphs [91.

Here, ^{unlike the} case of the standard

graph technique,

the

integrals

_over the continuous spectrum are meant

only

to be in the _sense of

principal part.

According

to the HF

equation (20)

the value

s.(nl(D~)

is the contribution of nl ~l interaction _to the

photoelectron

~,~i-energy. The

graphs describing

the matrix element

(nl (D~)

_are shown in

figure

I.

According

to

figure lay,

the no

lo-vacancy decays

into the n~

l~-,

_n~

I~-vacancies

and the

~Ij-Auger

electron _at the time ii, ^At t~ ~tj ^the

Eli-Auger

electron interacts with the

nI-photoelectron

and _at t~~t~ ^it

disappears together

with

n~l~-

and

n~l~-vacancies, restoring

the initial

nolo-vacancy,

The

graphs describing

the

exchange

related _to

the

processes of

figure lay

_are in

figures la~-la4.

The

change

of the HFSA

potential

due _to no

lo-vacancy

autoionization must lead to a

change

of the features of the theoretical

photoexcitation

_spectrum calculated within _a HFSA. This

change

_may be

interpreted

_as the effect of the autoionizational redistribution of electron

density (ARED)

of the atomic residue,

From the

point

of view of the classification of multi-electron processes in atomic inner shell

photoabsorption,

the

predicted

effect of ARED adds to the

hierarchy

of correlations described in the Introduction.

L mt~) _{L L} m(~) _L L L L L

i(m) n(m)

i~

⁾

~ / _, K '

K K ~ K K

j it~) ^{j j}

^{J J}

^{j j}

8~ 82 ~5 ~4

Fig. I. (nl

(Di)

matrix element

represented

by Feynman graphs. The wavy line is _a Coulomb

interaction. The direction of time is tj _~ t~ _~ t~. ^The arrow in the left hand direction is _a vacancy, the

arrow in the

right

hand direction is _an electron. See the text for aj a~. The functions have been obtained

as follows I

= no lo ^and _m (n )

= n~12, n~

1~-within

the field of _no lo-vacancy k

=

et j-Auger electron within the field of

(n~11

n~ it ^'

nl)

_-core with _{a « zero}

approximation»

nI-photoelectron j

=

nI-

photoelectron

through

solving

equation (20).

2.5 PHOTOEXCITATION cRoss SECTION. The calculation of the no

lo-nl photoexcitation

cross section which goes

together

with the creation of the final _states of type

(I)

has been

performed

within _a

dipole approximation

via the formula _:

~

12

" (~°

)

"

j ^"~ "~l

~°n "W l~ ^~ ~

~~l Pwj ^{Ml (25)}

M

=

(Eo(fi O)

;

Mj

=

(Ej (b( O)

_{w~~ = E,~~}

E((O)

_{+ e~i,}

In

(25)

_« is _a fine structure constant ao is Bohr's radius

(O)

is the atomic initial state ;

b

_is

a

dipole

transition operator ; w is the energy of the absorbed

photon (in atom.un.).

The matrix element M for the closed shell _atom in _a

ground

state has the form _: j

p/~o

^lo 1/2

(no I~

^{~° ~ nI}

b O)

₌ ^~

Rii

; /~~ = max

(/

o, /

(26)

2

lo

₊ °

In

(26)

the radial part

Rii~

^{of the matrix element M is determined with inclusion of MRES}

by

means of the

theory

of

non-orthogonal

orbitals [71 _up to the first order terms _:

(ni

ml

(ml iii nolo) (ni iii mio)(mio

_no

lo)

~~~° ^{~ ~'~~} '~° ~°~

~~~j~

(ml

ml ^~

(niio mio

^{' ~~~~}

where ml

)-, mlo)-,

_no

lo )-orbitals

have been obtained

by solving

the HF

equations

for the

configuration

O

),

F is the Fermi

level,

I.is _a one-electron operator ⁱⁿ a

length

form and N is _a

product

of the

overlap integrals

for the functions of electrons not involved in the transition. One has

w

(ml ii

_no

lo

)

=

P~i (r P~

i

(r )

_I dr

0

° °

In the calculation of the

Mj

matrix element the

principal

autoionization channel has been considered

(with

vacancies

appearing

in _one electron

shell)

Mj

=

(n~ ^/(~?

ej

ii

nl

(b _O) (28)

3. Results of calculations _: Ar

Lij, u~~photoexcitation.

The theoretical results described above have been

applied

to the calculation of

2p-3d

photoexcitation

of the Ar _atom, The choice of the

object

of

investigation

is due to a great

sensitivity

of the spectrum to small

changes

in

HF-potential [5, 121.

In reference

[5]

the _near

Ljj, jjj-photoabsorption

_cross section of Ar _was calculated

including

relativistic

(spin-orbit splitting

of the

2p-shell)

and multi-electron

MRES-,

CR- and VC- effects. As _a result, within the

region

of

2p~(~P~/~)3s~3p~ 3d-photoexcitation

_resonance

(theoretical

resonance energy w =

246.64

eV, experimental

value is _w

= 246.90 eV

[4, 131)

the

disagreement

between theoretical and

experimental

[41

spectra

^did not exceed 5 percent

(«~~

~ «~~P~. In the present ^work we do not

perform

_a direct

comparison

between calculation

and

experiment.

We

just

intend _to demonstrate the

possibility

to

decrejse

the value of the above mentioned

disagreement betiveen

_the

_theory

_{[51 and the}

_experiment

_{[41 if}

one includes the interaction of the _state with the inner

2p-shell

_vacancy with the dominant channel of its

virtual

Auger decay producing

two vacancies in the

3p-shell [13, 141.

In _a first step, ^{the MRES has been} included

by solving

the HF

equations

for the

configuration

s~

2s~ _2p~ 3s~ _3p~

_{3d. When}

determining

the

amplitude (28)

^the

ls~2s~2p~3s~3p~3d ep-autoionization

channel has been included which

gives

a 65§b contribution _to the total

Auger decay

^{width of}

2p-vacancy

r

= 0.13 eV

[5, 15].

The function of the

ep-Auger

electron _was obtained within the field of the

ls~ 2s~ 2p~ 3s~ 3p~

^{3d-core. To}

account for the

remaining

35 §b contribution _to the total width

by

other autoionization

channels,

the

2p~

^' 3d

3p~

^~ _{~p 3d} interaction matrix element has been increased 1.24 times.

In the determination of the

amplitude (26)

_we have included the condition that the

Is~

2s~ 2p~ 3s~ 3p~

3d-state be

orthogonal

to the lower

(in energy) lying

state Is~

2s~ 2p~ 3s~ 3p~

3d of the _same symmetry, ^{which eliminates the} sum in

(27).

The calculated

cross section

(25)

for the

3d-photoelectron

function with inclusion of MRES and

only

the

angular

correlations in the _movement of

photo-

and

Auger

-electrons is

presented

in

figure

2 with _a dashed line

(multiplet

effects _are

omitted).

In _a second step,

equation (20)

has been solved upon the basic functions of the

s~

2s~ _2p~ 3s~ _3p~

_{3d-core with inclusion of D~ to obtain the} radial function of

3d-photoelec-

tron. The function of the _{« zero}

approximation

_»

R-photoelectron

_was obtained within the

field of the Is~

2s~ 2p~ 3s~ 3p~-core.

The function of the

~p-Auger

electron was obtained within the field of the

ls~?s~ 2p~ 3s~ 3p~ )-core.

_The calculation of the

spectroscopic

factor has

given (I s)

_~

10~~ _which

_allowed

us to use

N)P

=

5, N(1'

= 6 instead of

(22).

It has been obtained

thit

the direct part ^{of the}

electr~static id

ep interaction in D~ ^dominates over the

exchange

one. This leads to additional localization of the

I-state

near the nucleus. Thus the mean radius of the 3d-function decreases _as

compared

^with the HFSA

by

^0.03 a.u, which leads to _a 3 §b increase of the

2p

^3d resonance cross section. The additional _to

Fe

~

0.020 eV

(shift

of the HFSA

photoexcitation

resonance towards the low energy

side)

is

A~

₌ ^{0.004 eV. The calculated}

2p I photoexcitation

cross section is shown in

figure

2

with _a solid line

(multiplet

effects _are

omitted).

The additional localization of 3d-state near the nucleus and the additional to the low energy shift

Fe

^{of the} autoionizational resonance may be

interpreted

as the effect of the autoion- izational redistribution of electron

density (ARED)

of the atomic Is~

2s~ ?p~ ^3s~ 3p~

^residue. In

JOLRN~L DE PH~SIQLL II -T W9 ~EPTEXIBER 1993 ,1

~(k~/tia

z

~

21?0 24T4 tillev

Fig.

2. The Ar _atom

2p

3d

photoexcitation

cross section (the present theory) ^included are I

F~,

A~, D~ and 2 F~. ^The

2p-level

width r 0.13 eV is that from the

experiment

[4, 15].

Multiplet

effects _are omitted. _w is the energy of the absorbed

photon.

this _case the ARED effect may also be

thought

_as the effect of the correlational

«

pressing

down _» of the

I-photoelectron

_{into the}

_vicinity

of the nucleus

by

the «fast

moving

_»

ep-Auger

electron. Our results show that the

remaining discrepancy

^{of the calculated}

[5]

and the measured [41 cross sections in the

region

of

2p-3d

resonance may be decreased if _one takes into account the influence D~ on the

3d-photoelectron

radial function.

4. Conclusion.

This

study

has shown that the correlation effects connected with the

change

of the HF

potential

because of inner shell vacancy autoionization may

play

_a noticeable role in

obtaining

more accurate values of the

photoexcitation

cross section and _resonance line

energies.

It is

interesting

to

generalize

_our method to

study

the

photoexcitation

of

heavy

atoms, the

atoms of transition elements and

photoexcitation

of _rare earths into the

collapsing [12,

131

d-,

f-,

-symmetries

of

photoelectron.

One may suppose that,

together

with inclusion of CR- and VC-effects, the modification of HF

potential

in

equation (20)

for the

photoelectron,

the presence

if Ae

^{and the}

change rj°1=

2

vi ue(~

for 2

once

in

(14)

will make the theoretical

spectral

features of these elements

noticeably

_more

precise.

Acknowledgments.

The authors _are

grateful

to Dr A. G.

Kochur,

DrI. D. Petrov and DrB. M.

Lagutin

for

discussions _{on our} results.

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