REARRANGEMENT OF INNER SHELL IONIZED ATOMS

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REARRANGEMENT OF INNER SHELL IONIZED ATOMS

M. Krause

To cite this version:

M. Krause. REARRANGEMENT OF INNER SHELL IONIZED ATOMS. Journal de Physique Col-

loques, 1971, 32 (C4), pp.C4-67-C4-75. �10.1051/jphyscol:1971415�. �jpa-00214616�

JOURNAL DE PHYSIQUE Colloque C4, supplkment au no 10, Tome 32, Octobre 1971, page C4-67

REARRANGEMENT OF INNER SHELL IONIZED ATOMS (*) M. 0. KRAUSE

Transuranium Research Laboratory, Oak Ridge National Laboratory, Oak Ridge, Tennessee U. S. A.

RBsum6. -

Les divers processus de rearrangement des electrons orbitaux dans un atome ionise en couche interne sont exposb et discutes

a

la fois du point de vue experimental et du point de vue theorique. Dans le rearrangement electronique suivant I'ionisation primaire, c'est le processus appele

⁽⁽ shake-off))

qui joue le r81e principal pour l'excitation multiple de l'atome, quelle que soit la particule ionisante incidente (photon, electron, ...). I1 est montre que ce phenom&ne est la cause directe de la production de satellites dans les spectres

X

et Auger, aussi bien par excitation primaire que par excitation secondaire. Les taux relatifs de processus shake-off sont donnes en fonction

: a)

de l'energie du photon ou de 1'6lectron incident,

b)

du nombre quantique de l'electron orbital et c) du numero atomique. L'importance de la correlation electronique est soulignee pour le cas oh les electrons concernts viennent tous deux de la meme couche.

Le rearrangement de l'atome

a

la suite d'une ionisation simple ou multiple est discute, en parti- culier la cascade de vacances provoquees par les series de transitions radiatives ou Auger et qui peut conduire finalement

a

une distribution de charge ionique et, dans le cas de mol6cules.

a

une violente fragmentation coulombienne. I1 est aussi fait mention du processus Auger double et du processus Auger radiatif.

Abstract.

- The various processes by which orbital electrons of inner shell ionized atoms rearrange are discussed on the basis of experimental evidence and theoretical concepts. In the electronic rearrangement concomitant to the initial ionization event, the shakeoff process is reco- gnized as playing a predominant role in multiple excitation of the atom by the incident ionizing photon or particle. Shakeoff events are shown to be the direct cause of the occurrence of satellites in X-ray and Auger spectra in both primary and secondary excitation. Relative transition rates of multiple processes are given as a function of a) energy of incident photon or electron,

b)

quantum number of the orbital electron, and

c)

atomic number. The importance of electron-electron corre- lation is pointed out for cases where the electrons involved come from the same shell.

Readjustment of the atom following initial single or multiple ionization is discussed in terms of

a

vacancy cascade in which a series of radiative and Auger transition takes place ultimately leading to an ionic charge distribution and, in cases of molecules, to violent coulombic fragmentation.

Reference is also made to the double Auger process and to the radiative Auger process.

Photoionization processes involving a single elec- tron were described in the opening session of this conference by T. M. Zimkina [l]. Ionization processes involving two and more electrons will be the subject of this talk. These multiple processes as they come about by the rearrangement of the atom comprise multiple, especially double, ionization in the initial ionization act by photons, particles or electrons, Auger electron cascades in the subsequent readjust- ment, double Auger processes and, last but not least, the semi or radiative Auger process. I shall illuminate the experimental and theoretical aspects of these pro- cesses as well as the various consequences and mani- festations, and in doing so, the historical development will :become apparent as a matter of course.

Regardless of the particular atomic potential used, whether hydrogen-like, Herman-Skillman or Hartree- Fock, theoretical treatments of photoionizatio~ have

(*)

Research sponsored

by

the U.

S.

Atomic Energy Corn- mission under contract with the Union Carbide Corporation.

Recount of Invited Talk at this Conference.

in general allowed for only one electron to interact with the incoming photon and, in the usual frozen- structure approximation, have allowed the remaining electrons t o stay in their old orbits, those of the neu- tral atom, even after the photoelectron has been emitted [2], [3]. In reality, however, electrons adjust rapidly to the new situation and assume new statio- nary states in the atom ionized in one of its shells [4]- [6]. This rearrangement takes place in 10-l6

S

or less provided the energy of the incident photon lies somewhat above the ionization threshold of the orbi- tal electron to be ejected. Since threshold regions, constitute only a small, though important, portion of the continuous energy range of photon-electron interactions, such sudden rearrangement, or relaxa- tion of the atomic core will be a common event.

In fact, it has significant and sometimes spectacular consequences.

Much in the same way as a molecule, t o quote a more familiar case, can be thrown into various states of vibrational excitation upon interaction with radiation

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971415

C4-68 M. 0. KRAUSE

or particles, the atom following innershell ionization may find itself in various states of excitation, which excitation may arise from discrete-discrete transitions and discrete-free transition of a second electron. If we were to record a photoelectron spectrum we should, therefore, see a number of lines, with different intensi- ties, indicating different excitation states. Just as the Franck-Condon overlap integrals determine the spec- tral intensities in the molecular case, overlap inte- grals between the wavefunctions of the initial and final states of the atom determine the intensity distri- bution in the photoelectron spectrum. We have a quantum statistical distribution of singly ionized atoms in their ground state or various excited states and of multiply ionized atoms in ground or excited states. This way of looking at the problem arises from a re-examination of Koopman's theo- rem [7]. We shall see later that a different approach will prove more practical, though more restrictive, for actual numerical calculations.

Which are the experimental manifestations of multiple excitation, inclusive ionization

?

Table I gives a summary of the observables using the neon atom as an object of illustration.

X-ray satellites have been known for almost as long as the characteristic lines themselves

:

M. Sieg- bahn [8] described them first in 1916, and there is hardly a classical X-ray spectroscopist who has not added a few more satellites and knowledge to the understanding of their origin. In fact, it was realized very early that double hole configurations were res- ponsible for their appearance. Recently, detailed corre- lations between specific satellites and specific hole configurations have been established mainly through the efforts of the Helsinki group [g], [10]. The type of satellites referred to in Table I appears on the high energy side of the parent line.

Auger electron satellites, the counterparts to the X-ray satellites, have been observed and correctly assigned only in the recent past at several laboratories, namely in Miinster [ll], Uppsala [12], Oak Ridge [13], [l41 and Nebraska [15]. In contrast to the X-ray

satellites, Auger satellites appear generally on the low energy sides of the parent lines or at least below the highest-energy diagram Auger line.

Ion charge distributions, another manifestation of initial creation of multiple hole-states, have been reported almost exclusively by investigators at Oak Ridge [4], 1161, but others have started to utilize this method. Let me point out, however, that a clear picture evolves from ion charge spectra only if, fol- lowing initial ionization, competing and cascading reactions occur with low or negligible frequency.

Photoelectron spectra are by their very nature the most direct evidence of multiple photoionization events. They provide specific data on the type of transitions and on the spectra of the emitted elec- trons. Most of this sort of ionization has been inves- tigated in Oak Ridge [17], [l81 and in Uppsala [12].

Other possibilities, not listed in Table I, of studying multipIe excitation are photoabsorption studies, per- formed with the aid of synchrotron light, discharge tubes or conventional X-ray sources, and energy loss spectra of incident monochromatic electrons or ions. While double excitation, in the narrower sense of the word, is essentially a threshold phenomenon which requires a different treatment than given here, the energy loss spectra show promise of being another fruitful source of information, especially if these electrons are placed in coincidence with the ions crea- ted

[19].

Needless to say, coincidence studies between appropriate pairs of the various observable quantities, Table I, could pin down exact assignments where otherwise ambiguities or doubts might exist.

On the theoretical side, several proposals were made in the early thirties about the origin of the X-ray satellites and the formation of the initial mul- tiple vacancies. As we know nowadays Bloch's appro- ach [20] of utilizing the sudden approximation in perturbation theory proved to be the most fruitful.

For many years the field had lain fallow. Recently, in rapid sequence, workers in Kiev [21], Helsinki [22f and Oak Ridge [l71 succeeded in interpreting quanti- tatively the origin of double ionization. But the real

Consequences of K Ionization

and KL Ionization or Excitation of Neon as Recorded

by

Selected Experimental Methods

Observed Quantities Photoelectron(s)

Initial event photon impact Photons Auger electrons Ion charges

(")

- - - ^-

K + o o Discrete line Ka lines K-LL lines 2 +

Two continua Ka satellites K-LL satellites (KL-

3

+

L + c o

K - r m 1 ^LLJJ)

K + W I Discrete lines Satellites of Klines K-LL and K-LX 2 +

L

+

M N, ... satellites

(")

By nonradiative readjustment.

breakthrough had come before from a different direc- tion, from the theory of atomic ionization during nuclear p decay. Here Migdal, Feinberg, and Levinger satisfactorily predicted the electron shakeoff [23]

caused by a sudden change of the nuclear charge, and thus together with the experimental evidence [24]- [26], coming mainly from Oak Ridge, provided the basis for our present understanding of multiple ioniza- tion by atomic rearrangement. What is the essence of the theory

?

Perturbation theory, in the sudden appro- ximation, gives the following expression

for the transition probability of some electron

nl

going to n'

1 when the effective charge changes suffi-

ciently rapidly from

Z to Z

+

AZ. Transitions are

governed by the selection rule A1

= 0 ;

they are mono- pole transitions. Perhaps the most important implica- tion of this treatment, sometimes called shakeoff theory, is the fact that no mention is made of the specific cause of the change in effective charge or screening. Therefore, it should be applicable to the ionization of an electron from any shell by either photons, electrons, or heavy particles, or by nuclear transformations, provided these processes occur in periods of time that are small compared with the orbital periods of the electrons that undergo shakeoff excitation [22]. If we construct wavefunctions for all possible discrete and continuum states and include n l

=

n' I the expression will yield an intensity spectrum of the states of the ion, and, for the case of photoioniza- tion, it will yield the corresponding photoelectron spectrum. Since, even with modern computer t:chni-

ques it is rather cumbersome and difficult to pro- duce all the necessary excited state wavefunctions, numerical calculations are commonly restricted to the case

nl =

n' I, that is to the case of the electrons remai- ning in their orbitals. Then the probability of vaca- ting is simply

and no distinction is made between transitions to .discrete and to continuum states. In this equation, N is the number of like electrons and P, is the usually small transition probability to filled states. Comparison of theory with existing experiments shows that the wavefunctions + can be single electron wavefunctions if the two electrons promoted come from different principal shell, but must be correlated wavefunctions if the two electrons come from the same shell [18],

[27l, 1281.

Typical results [29] are displayed in figure 1 where shakeoff probabilities are plotted as a function of

Z

for the case of

/?-

decay. Since P- decay is nearly equivalent to K electron loss as far as electrons in the shells

n 2

2 are concerned these curves apply

20 ^{ORNL-DWG 67-32405}

I I I I I I I l I I

FIG. l.

-

Calculated shakeoff probabilities per electron in shells I S to 4 S as a function of atomic number. Calculation refers to

8-

decay, but can also be used as a good approximation

for K ionization (Ref. 29).

also to ionization in the K shell to a good approxima- tion.

Let us now review the experimental data. Figure 2 shows a recording by Graeffe et

al. [30] of the Ka

X-ray satellites of silicon. Satellites a', a, and a, are the consequence of KL hole states, a, and

a6

of KL2 states, and al0 and a l l probably of KL3 states. Spectra of this kind reflect multiple ionization regardless of the type of ionizing agent. In fact, figure 2 indicates the relative amounts of multiple vacancies to be independent of the type of incident radiation or particle, at least under conditions to be discussed below. Note also the

^t< bunching

of the satellite groups, each designating a different number of holes created.

Figure 3 illustrates the equivalent situation by way of Auger electron satellites [31]. Again, satellite intensities are shown to be independent of the excita- tion mode. A complex structure is seen which allows detailed analysis 1131 of the initial collision mecha- - - - nism and specifics of electron shakeoff. However, initial KL2 and KL3 hole states are masked by the many possible final states into which KL holes decay.

In a more complex atom, like Si, whose K Auger spectrum is shown in figure 4, the satellites due to various KL, KL2 states again appear to be bunched together according to a preliminary analysis. The K spectrum of argon [32] exhibits the same feature even more clearly.

Figure 5 presents the photoelectron spectrum of

neon excited by Mg Ka X-rays. In this very direct

C4-70 M. 0. KRAUSE

I ^*2 l

1 ,

^{- -- --}

observation of the interaction of a single photon with

^{c *} - - -- - -7- -

I-'

-

- - - - .L$

E

T

more than one orbital electron. discrete ~ e a k s and an

, - ^-- - , - - . ^- - - ^- - ^-

--~-Fe::,

-

2e (UPPER CURVES)

continuum appear on the low energy side of the main line, which is the photoelectron line of single electron emission. The discrete peaks are shifted by the energy required to lift an electron to an excited level of the

134" 136" 138" lLOe ern

$m

E ^{W -}

5 2 20

5

FIG. 5. -The K photoelectron spectrum of neon excited by.

Mg Ka X-rays. Main peak NeK (MgKa) indicates single electron emission, discrete peaks between- 37 and

-

47 eV indicate shakeup processes, 1 sZ 2 sz 2 p6 -t 1 s 2 sZ 2 p5 np, and adja- cent continuum shakeoff processes, 1 s2 2 s2 2 p6 + 1 s 2 sz 2 p5

(Ref. 18).

(,,,( , , 1 , , 1 , , 1 , , 1 1 , 1

-

IlLiDOM

i

IlLllNE X LL II""s8

- i ^{i i}

- ' D f . d 2 r >

1

' 0 -

T i

^{, % ' h}

/ ' / l 1

^{$ p}

i ^i&,i' *'W

k&\l/h*"

^'ih

~ I I I I I I I I I I I ~ I ~ I I I I ~ ~ ~ ~ ~ I I I I , ~ I I I I I I , I I ~ , , I I I I I I I I ~ I I I ~ ~ ~ , ~ ~ ~ ,

After presenting the pertinent theory and experi-

,MW **a ,%m ,530 ,520 ,330 ,540 I S 3 0 ,560 ,,,Q a s 0 ,,a, ,m

XIXLIIC ENTRrn car,

FIG. 4.

-

The K Auger spectrum of silicon excited by electrons.

Lines labelled m, j, h, and a are the normal Auger lines. Another diagram line is located in region of peaes b and c. A preli- minary analysis suggests that line b corresponds to initial sha- keup excitation, lines c, n and k to single shakeoff ionization,

and lines f and e to double shakeoff ionization (Ref. 14).

inner-shell ionized atom. The adjacent continuum is indicative of the ionization of a second electron.

A bonus is obtained with these photoelectron spectra

:

the lines on the high energy side of the main line are indicative of the X-ray satellites that have been genera- ted in the anode material of the X-ray tube. We have, indeed, used the electron spectrometer not only to disperse electrons but also to disperse X-rays after their conversion into photoelectrons. Satellites of the anode element, usually excited by electrons, and satellites of the target element, excited by photons, appear at the same time in the same spectrum. Photo- electron spectra have been measured and successfully interpreted [12], [14],

[17],

[27] for a number of atoms,

-2e (LOWER CURVES)

molecules, shells and photon energies

;

more

FIG. 2.

-

The Kal,z line of silicon and its high energy satellites,

details will be given in another presentation at this

excited by photons (upper curve) and by electrons (lower curve).

conference [18].

Note similarity of the two spectra (Ref. 30).

O R l L LlVr m ,,ioa

I , ! , , ,

mental data we are ready to ask several questions

:

a) What does the energy spectrum of the shakeoff electrons look like ; b) Are the various satellites we

FIG. 3.

-

The K Auger spectrum of neon consisting of diagram

lines K-LL and satellite lines KL-LLL, excited by both photons

ascribe to multiple-hole states in the correct energy

and electrons. Note similarity of the two spectra (Ref. 31).

positions

; c)

How do and

A more detailed spectrum is discussed in Ref. 13.

intensities compare with one another, and d ) HOW

close to threshold does the validity criterion of the hv

=

E,,, + ^{EB(K) (3)}

sudden approximation hold

?

The energy distribution of shakeoff electrons must for process and be obtained from spectra similar to that of figure 5

hv

=

ELin +

&(K) f

E:,,(2 p

-,

np) (4) or from coincidence measurements. Analyses of

photoelectron spectra reveal that shakeoff electrons for ionization plus excitation. Thus carry away predominantly small energies, as shown

in figure

6 . Although the spectrum presented drops

AE

=

Ekin - ^ELin

⁼

^{Ed,,(2 p}

^-,

^np) . (5) off somewhat too steeply because in the early inter- This excitation energy is to be calculated for an ion pretation several discrete transitions were not reco- with another electron lacking, in this particular case, gnized as being hidden near the onset of continuum the K electron. The energies of the Auger satellites transitions, satisfactory accord can be noted for the accompanying the normal K Auger lines of neon have general shapes of the curve derived from photoioniza- been found [131 to be in excellent agreement with tion and the curve calculated for P decay. calculations using optical data for the final states

150

and reliable evaluations or measurements for the

initial states. Similarly, the energies of satellites of

6 m

other spectra support the concept of their origin in

initial multiple ionization. Several highly resolved

q 50

spectra [l81 bear out the selection rules of theory

e

which require the transitions of the shakeoff electrons

to be monopole transitions. I will not dwell on the

0 -03 0 0 5 40 l l 2 0 2 5 3 0

W/<. RELATITIVE ENERGY

correct energy assignments of X-ray satellites since

Comparison of Theoretical Spectrum ILevngerI ~ 8 t h of Neon with K-Phololon~2ation D8strlbulmon Anseng from Shakeoff of L Electrons

this Seems t o be a well-proven point [l()]. Actually, several decades ago the nature of those satellites was

FIG. 6. -Energy spectrum of L shakeoff electrons of neon

recognized almost solely on energetic grounds.

concomitant to K electron ionization. Theoretical curve, refer-

ring to corresponding

B-

decay, is composed of 2 s, 2~ and

If, as I have pointed out at the beginning, the

2 p 2 p contributions (Ref. 17).

various satellites mentioned have a common source

and, in addition, are generated with intensities Jnde- The discrete satellite lines in figure 5, are indeed, pendent of excitation mode, results of the various in the right energy position relative to the single- studies should be identical, barring a few minor, second electron emission line in accordance with the energy order, differences.

conservation relation Table I1 gives a summary of data for neon, the

Simultaneous bxcitation of K and

L

Electrons in Neon.

Intensities in % Relative to All Processes Excitation

2 ~ + 3 ~ Others -

6.1 (7)

2 (1)

Ionization Total

+

13.8 (8)

Source

("j

-

Auger

;

e

;

mostly double processes

Auger

;

e Auger

;

e Auger

;

hv

PE

;

hv

;

moderate resolution PE

;

hv

;

high resolution PE

;

hv

;

high resolution X-rays

;

e

;

extrapolated X-rays

;

e

;

interpolated X-rays

;

hv

;

extrapolated X-rays

;

hv

Ion charge

;

hv

p- decay

Theory

;

K ionization Theory

;

K ionization Theory

;

P- decay

Ref.

(")

Listed are

:

I ) quantity observed, i. e., PE photoelectron

;

2) excitation mode, i. e., hv

^E

photons

;

and 3) pertinent remarks.

C4-72 M. 0. KRAUSE

element studied the most thoroughly [Ill-[13], [16]-

[18], [33]-[37]. Satisfactory agreement can be noted among the experimental results obtained by widely varying apparatus and methods in several laboratories of different countries. Even though agreement is not perfect partially due to the difficulty of separating ionization and excitation processes, we readily see that rearrangement associated with K shell ionization of neon leads to the promotion of one or more L electrons in 21 to 22 % of the events with about 213 going into the continuum and 113 into discrete bound states. Theory, using uncorrelated single-electron wavefunctions, agrees nicely with experiment, though we note a slight underestimate. I have also entered in the Table data 1251, [29) on shakeoff probabilities associated with p- decay to show that the change in nuclear charge by one positive unit is nearly equiva- lent to removal of one K electron as seen from the L electron level. Experience with other systems 1171, [18], [27], [35] yields as similarly good results as those noted for neon with the following important qualifi- cation

:

if electrons come from the same principal shell, theory is in error, sometimes grossly, when relying on uncorrelated electron wavefunctions, but again restores agreement when using correlated wavefunctions. More details on such cases will be reported at the Conference by Carlson

et

al. [18].

The final question, I wish to put forth, concerns the range of validity of the sudden approximation or shakeoff theory. According to the approximation employed, the shakeoff probability as given by relation (1) should be attained only somewhat above threshold and then should be independent of energy.

How much is

⁽⁽ somewhat >> ?

Is a plateau being rea- ched

?

In figure 7 results of an experimental test [5]

of the validity criterion are presented as well as calcu- lations by Sachenko and Demekhin [21]. The ratio of multiple-hole to single-hole production reaches a constant value at higher energies for both electron and photon excitation. In the cases studied so far, the breakdown point of the sudden approximation appears to occur at (E,,, -

Ei

-

^{E,,)/E, w}

10, where the numerator represents the excess energy of the incident particle,

E,,,, over the ionization energy

of the inner shell electron,

E,, plus the ionization

energy of the shakeoff electron, E,, which refers to an ion with a hole in an inner shell. The nature of the overshoot in figure 7a is not completely understood, but it may indicate either or both of the following mechanisms

:

under electron bombardment a complication such as direct collision ionization beco- mes active or, as the data on helium [27], [28] might suggest, a weak electron-electron correlation becomes visible. The limited number of data point in figure 7b, referring also to neon, do not rule out a possible slight overshoot under photon impact.

Phenomena near threshold, expecially those reso- nance structures of double-excitation processes obser- ved in abundance with the aid of synchrotron light

NEON

1.00

-

--- THEORY (All

0 0 4 0 Q EXPERIMENT 1N1)

4 LL

8 ( E ~ - ~ I R - ~ O 8 l 6 24 32 4 0 48 5 6 64 72 80 88

- d 5

: :

:

; /

0 6 0

0 4 0 TITANIUM

0 2 0

(E~-E,I/E~% 8 16 24 32 4 0 48 5 8 64

I I I I I

E,/(<<I-:o 2 0 3 0 4 0 5.0 6 0

I , ,

E, .heV

-

^{5 5 10 I S 2 0 25 3 0 35}

FIG. 7. -double ionization as a function of energy of incident electron or photon. The intensity ratio of double-to- single ionization is normalized to unity in the plateau region. (a) shows the result under electron bombardment, (b) under photon bombardment, including the theoretical prediction, and (c) the results for another element again under electron impact.

Ee and E" are incident energies, Ei is the binding energy of the innershell electron, i. e.,--Ne K, and E. the binding energy of

'the shakeoff electron (Ref. 5).

at NBS in Washington [38], require a more sophisti- cated treatment than outlined here.

A review of these

processes has been gi en by Fano and Cooper [2].

Here, withpgure 8, I merely wish to present evidence for double excitation in the actual X-ray region as demonstrated by Wuilleumier [39].

p/p opparents

: : :

^I

i

j d'obsor~tim Lm.N

i

8 4

:

^{du KRYPTON}

: ^:S : : :

I , I S , I

0 * , I

: ^,I : : : : : I a I'

I I'

I S '

.

^{0 '}

I I'

S ( I : ^EeV

4 2 0 2 4 6 810 6 % , 7 8 , 7 ' \ 2 ~

-

30 386.40 FIG. 8.

-

Photoabsorption spectrum near the LIII edge of krypton, showing discrete peaks, namely B and C. which are due to simultaneous excitation of two electrons (Ref. 39).

Up to now, I have only discussed those multiple processes that occur in the initial ionization act and have treated subsequent events, such as Auger and radiative transitions, only as corollaries, as indicators of the initial event. Let us look briefly at the second phase of electronic rearrangement, the de-excitation of the innershell ionized atom or molecule. Suppose a K electron were removed from an element such as Xe, then the next most likely step will be a K

+

L,,, radiative transition, as illustrated schematically in figure 9, which in turn will be followed by a

A VACANCY CASCADE I N X e

X-X-X-X X X-X

; :

* X

X y 7 : :

^{X-X I} M, ^{L I I}

X-X L1

FIG. 9. -Typical vacancy cascade in Xe following K shell ionization with ultimate loss of all electrons of the 0-shell.

L,,, - MIv,vMIv,v Auger process leaving two vacancies in the M,,,, level. These vacancies will multiply in yet more Auger processes until all vacancies have reached the outermost shell, which in the example chosen will be completely depleted of electrons. Normally, there are many different routes possible within a so- called vacancy cascade and the end result will be a distribution-in-charge which we can portray if we chose to examine the ions produced. Many systems have been investigated in the past I5 years, especially at Oak Ridge [4j, [40]. An actual charge distribution is plotted in figure 10 and compared with the results of a model calculation [4], which considers all possi- ble paths of readjustment, in series and parallel, by radiative and radiationless transitions and which takes into account shakeoff and double Auger proces- ses. Gratifying agreement between experimental and calculated spectrum can be noted, giving support

I I m EXP

4 2 3 4 5 6 7 8 9 4 0 4 4 4 2

CHARGE OF ION

Charge Spectrum Resulting from Photo~onization in the K-Shell of Krypton.

FIG. 10. - Charge distribution resulting from photoionization in the K shell of krypton. Comparison of experiment with cal- culation which is based on vacancy cascade model (Ref. 4).

to the vacancy cascade model in which readjustment takes place in sequential steps.

About 10-l5 seconds elapse from the time of the original ionizing event to the ultimate termination of the cascade. Effects on molecular systems must, therefore, be devastating [41], [42]. Suddenly, the molecule following innershell ionization finds itself devoid of all bonding electrons consisting merely of a conglomerate of positively charged ions. Under the force of coulombic repulsion the molecular cons- tituents, often highly charged, fly apart gaining considerable recoil energies. Carlson and White 1421 have demonstrated the complete disintegration of molecules as big as C,H,I or Pb(CH,),.

This review would not be complete if I were not to mention the double Auger effect as well as the semi or radiative Auger effect.

Evidence for the existence of the double Auger process has come from measurements of charge states of ions of rare gases 1431-[46]. If, for example, we succeed to produce one and only one vacancy in the NI,,, shell and in no other shell of xenon, then xe2' will arise from a single Auger process NI,,,-00, and Xe3+ must arise from a double Auger process NI,,,-000. The emission of a second electron in an Auger process can be likened

[47],

roughly speaking, to the emission of a second electron at the time of initial ionization in a shakeoff process. Thus shakeoff theory can provide us with a rough estimate of the probability of a double Auger event by using the appropriate electron wavefunctions in equation-(2).

Relative intensities of the double Auger processes that

G-74 M. 0. KRAUSE

have been identified so far, are compiled in Table 111.

The astonishingly great intensities of transitions invol- ving the outermost shells of Kr and Xe are probably due to a strong correlation among these outershell electrons.

Intensities of Known Double Auger Processes Relative to All Radiationless Transitions (in percent)

Rel.

Element Transition Intensity Ref.

- - -

Ne K-LLL 8 (1) [433

Ar

LII,III-MMM

10 (2) P41

Kr

MIV,V-NNN

31 (4) [45!

Xe -N~v,v-ooO 30 [461

By a radiative Auger process or semi Auger process we mean a radiative transition with the simultaneous emission of an electron obeying the energy relation h v ( Z + X ) + E k i , ( Y + ~ ) = E ( X - YZ) (6) where the photon energy of a transition Z

-,

X is degraded by the amount of kinetic energy that is acquired by the electron ejected from the shell Y.

Since Ekin(Y

-,

W) can assume any arbitrary value, hv(Z

+

X) will vary correspondingly with the restric- tion that the sum of E,,, and hv will always be equal t o the energy E(X - YZ) of the corresponding Auger process. Figure 11 presents the experimental

o L 2 1 L 21bo ^{I I l} 1

2050 2000 1950

-

^{ENERGY (eV)}

3

2

X

Q LL1 l- Ln 'm

B 1 -

(3

Z Q

z

I:

W a

FIG. 11.

-

Satellite structure on low energy side of Ku line of sulphur giving evidence for the radiative Auger effect (Ref. 48).

evidence for this effect, measured by Aberg and Utriainen

[48].

Earlier, satellites on the low energy

side of diagram lines had been observed by Bloch [49], Hulubei [50] and collaborators and ascribed to a radiative Auger effect. The previous notion was that such a process would only occur in order to

⁽⁽

by-pass a forbidden quadrupole transition, but very recent experiments point to its appearance concomitant with allowed dipole transitions. In Mg, Al, Si, and S the effect occurs [48] nearly 1 % of the time, relative to the KE line intensity, and in Ar and KC1 an unusually high intensity of more than 10 %,

relative to the L,,, parents, has been found by Cooper and LaVilla 1511.

1 ^{. .- - - -}

-

I/lm8.(COUNTS PER

-

^{O1HIN AND} W ~ S T E P ) 1

K m"y'

Although Bloch [207 made an early attempt to interpret the simultaneous emission of an electron and a photon by 1. order perturbation theory and was moderately successful a complete theory of the radiative Auger effect does not exist.

Viewing the material once again and as a whole we see a fairly complete and consistent picture emerge from the evidence gathered up to the present. We have established a common origin for a variety of pheno- mena, such as satellites in Auger, X-ray, and photo- electron spectra, ion charge, etc., which origin is multiple ionization

;

and we have found the sudden approximation or shakeoff theory to be a reliable model to account for this multiple ionization. We know the criteria and limits of the theory, both for electron and photon ionization, but we should be prepared for surprises when more data will have become avai- lable for ionization by heavy projectiles [52], ionic or neutral, and perhaps, ionization by electrons in shells with high quantum numbers.

I

2i00 2i50 p23kJ A 5 0 0 A 0 -

( b l

' We have identified the rearrangement processes

that take place subsequent to initial ionization and we have a fair understanding of most of the processes.

However, data on double and semi Auger processes are scarce and theoretical treatment of these pheno- mena is, at most, spotty. Needless to say, further investigations of these types of Auger effects would be desirable. They are not only interesting per se but also can affect so-called first order properties such as level widths and intensities of diagram lines.

Note added in proof.

- Since the time of the Conference a new developpment in theory, the appli- cation of the Brueckner-Goldstone many-body per- turbation theory to photoionization and especially to multiple processes, is showing great promise.

CHANG (T. N.) et al. (Phys. Rev. Letters to be published) partition the various contributions to multiple ioniza- tion into core rearrangement, virtual Auger transitions, initial state correlation, and direct collisions and get excellent agreement with experiment for outershell photoionization of neon. For background informa- tion, see KELLY (H. P.), Phys. Rev. (1963) 131, 684

;

KELLY (H.) and RON

(A.) Phys. Rev. Letters (1971)

26, 1359

;

and Pu (R. T.) and CHANG (E. S.) Phys.

Rev. (1966) 151, 31.

References

111

ZIMKINA (T. M.), ⁽⁽ Atomic Shell Primary Photoioni- zation ^D. This issue.

[2] FANO (U.) and COOPER (J. W.), Rev. Mod. Phys., 1968,40,441.

[3] BETHE (H.), in Handbuch der Physik, edited by S. Fliigge (Springer Verlag, Berlin, 1957), Vol. 35.

[4] KRAUSE (M. 0.) and CARLSON (T. A.), Phys. Rev., 1967,158,18.

[5] CARLSON (T. A.), MODDEMAN (W. E.), and KRAUSE (M. O.), Phys. Rev. A, 1970,1,1406.

[6] PARRATT (L. G.:, Rev. Mod. Phys., 1959, 31, 616.

[7] MANNE (R.) and ABERG (T.), Chem. Phys. Letters, 1970, 7, 282.

[8] SIEGBAHN (M.) and STENSTROM (W.), Z. Physik, 1916, 17,48 and 1916,17,318.

[9] UTRIAINEN (J.), LINKOAHO (M.), RANTAWORI (E.), ABERG (T.) and GRAEFFE (G.), Z. f. Naturf.

1968,23a, 11 78.

[l01 ABERG (T.), Thesis, University of Helsinki, 1966 (unpublished). See also DEMEKHM (V.

F.)

and SACHENKO (V. P.). Bull. Acad. Sci. (USSR), and BAUN (W. L.),' ~ ' e c t r o c h i m . Acta, 1965, 21, 1471. An earlier review is given by BLOCHIN (M. A.) in Physik der Riir?tgenstrahlen, VEB Verlag Technik, Berlin ( 3 957).

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[l41 MODDEMAN (W. E.), Thesis, issued as report ORNL- TM-3012 (1970), Oak Ridge National Laboratory, Oak Ridge, Tennessee.

[l51 EDWARDS (A. K.) and RUDD (M. E.), Phys. Rev., 1968, 170, 140.

1161 CARLSON (T. A.) and KRAUSE (M. O.), Phys. Rev., 1965,140, A 1057.

1171 KRAUSE (M. O.), CARLSON (T. A.) and DISMUKES , (R. D.), Phys. Rev., 1968, 170, 37.

[l81 CARLSON (T. A.), KRAUSE (M. 0 . ) and MODDEMAN (W. E.), This issue, p. 76.

[l91 VAN DER WIEL (M. J.) (personal communication) ; see also VAN DER WIEL (M. J.), EL-SHERBINI (Th. M.) and BRION (C. E.), Chem. Phys. Letters, 1970, 7, 161.

[20] BLOCH (F.), Phys. Rev., 1935, 48, 187.

[21] SACHENKO (V. P.) and DEMEKHIN (V. F.), Zh. Ekspe- rim. i Teor. Fiz., 1965, 49, 765 [Engl. Transl.

Sov. Phys. JETP, 1966,22,532].

[22] ABERG (T.), Phys. Rev., 1967, 156, 35.

1231 MIGDAL (A. B.), J. Phys. USSR, 1941, 4 , 449 ; FEINBERG (E. L.), J. Phys. USSR, 1941, 4, 424 ; LEVINGER (J. S.), Phys. Rev., 1953,90, 11.

[24] SNELL (A. H.) and PLEASONTON (F.), Phys. Rev., 1957,107, 740.

[25] CARLSON (T. A.), Phys. Rev., 1963, 130, 2361.

[26] See also, ANDRA (H. J.), 2. Physik, 1968, 215, 279.

[27] CARLSON (T. A.), Phys. Rev., 1967, 156, 142.

[28] BYRON (F, W.) and JOACHAIN (C. J.), Phys. Rev., 1967, 164, 1.

[29] CARLSON (T. A.), NESTOR (C. W.), TUCKER (T. C.) and MALIK (F. B.), Phys. Rev., 1968, 169, 27.

[301 GRAEFFE (G;, SIIVOLA (J.), UTRIAINEN

(J.),

LINKOAHO (M.) and ABERG (T.), Phys. Letters, 1969, 29A, 464.

[31] KRAUSE (M. O.), STEVIE (F. A.), LEWIS (L. J.), CARL-

SON (T. A.) and MODDEMAN (W. E.), Phys.

Letters, 1970, 31A, 81.

[32] KRAUSE (M. 0.) (to be published).

[33] PARRATT (L. G.), Phys. Rev., 1936,50,1.

[34] FISCHER (F. W.) as quoted in Ref. 9.

[35] ABERG (T.), Phys. Letters, 1968,26A, 515.

[36] NESTOR (C. W.), TUCKER (T. C.), CARLSON (T. A.), ROBERTS (L. D.), MALIK (F. B.), FRCESE (C.), Report ORNL-4027 (1966) (unpublished), Oak Ridge National Laboratory, Oak Ridge, Ten- nessee.

[37] KESKI-RAHKONEN (0.) and ABERG (T.) (personal communication). The value quoted is a prelimi- nary result.

[38] EDERER (D. L.), LUCATORTO (T.) and MADDEN (R. P.), Phys. Rev. Letters, 1970, 25, 1537 ; CODLING (K.), MADDEN (R. P.) and EDERER (D. L.), Phys. Rev., 1967, 155, 26 ; MADDEN (R. P,) a n 8 CODLING (K.), Astrophys. J., 1965, 141, 364.

[39] WUILLEUMIER (F.), Thesis, Paris (1969) and this issue, p. 88.

[40] SNELL (A. H.) and PLEASONTON (F.), J. Phys. Chem., 1958, 62, 1377 ; CARDON (T. A.),

HUNT

(W. E.) and KRAUSE

(M.

O.), Phys. Rev., 1966, 151, 41.

1411 WEXLER (S.), J . Chem. Phys., 1962, 36, 1992.

[42] CARLSON (T. A.) and WHITE (R. M,), J. Chem. Phys., 1966,44,4510 and 1968,48,5191.

[43] CARLSON (T. A.) and KRAUSE

(M.

O.), Phys. Rev.

Letters, 1965, 14, 390.

[44] CARLSON (T. A.) and KRAUSE (M. O.), Phys. Rev.

Letters, 1966,17, 1079.

[45] KRAUSE (M. 0.) and CARLSON (T. A.), Phys. Rev., 1966,149,52.

[46] CAIRNS (R. B.), HARRISON

(H.)

and S C H ~ N (R.

I.),

Phys. Rev., 1969,183,52.

[47] WOLFSBERG (M.) and PERLMAN (M. L.), Phys. Rev., 1955,99,1833.

[48] ABERG (T.) and UTRIAINEN (J.), Phys. Rev. Letters, 1969, 22, 1346.

[49] BLOCH (F.) and Ross (P. A.), Phys. Rev., 1935,47,884.

1501 HULUBEI (H.), CAUCHOIS (Y.) and MANESCU (I.), C. R. Acad. Sci., 1948,226,764.

[51] COOPER (J. W.) and LAVILLA (R. E.) Phys. Rev.

Letters, 1970, 25, 1745.

[52] KHAN (J. M.) (private communication) is presently preparing

a

review on innershell ionization pro- cesses in ion-atom collisions. In the present context, the following papers are of interest ; RUSSEK (A.) and MELI (J.), Physica, 1970, 46, 222 ; KAVANAGH (T. M.), CUNNINGHAM (M. E.), DER (R. C.), FORTNER (R. J.), KHAN (J. M.), ZAHARIS (E. J.) and GARCIA

(J.

D.), Phys. Rev.

Letters, 1970, 25, 1473 ; and VOLZ (D. J.) and RUDD (M. E.), Phys. Rev. A, 1970, 2 , 1395.