RECENT DEVELOPMENTS IN AUGER SPECTROSCOPY OF FREE ATOMS

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RECENT DEVELOPMENTS IN AUGER SPECTROSCOPY OF FREE ATOMS

H. Aksela, S. Aksela

To cite this version:

H. Aksela, S. Aksela. RECENT DEVELOPMENTS IN AUGER SPECTROSCOPY OF FREE ATOMS. Journal de Physique Colloques, 1987, 48 (C9), pp.C9-565-C9-577.

�10.1051/jphyscol:1987995�. �jpa-00227416�

JOURNAL DE PHYSIQUE

Colloque C9, supplement au n012, Tome 48, dbcembre 1987

RECENT DEVELOPMENTS IN AUGER SPECTROSCOPY OF FREE ATOMS

H. AKSELA and S. AKSELA

D e p a r t m e n t of P h y s i c s , U n i v e r s i t y of Oulu, SF-90570 Oulu, F i n 1 and

ABSTRACT

T h e recent progress in the Auger electron spectroscopy of free a.l.oms is discussed. lligh resolution spectra of open shell atoms from high tcmpera.tnre va.pours have become experi~-nenla.lly availa.ble, and thus offer an elegant method to test the 1a.test theoretical MCIIF models. Sa.tellite structure accompaning the main lines displa.ys the mn.ny electron effects, and thcir a.na.lysis ca.n be used to study electron correlation phenomena.. Irr~proveci possibilities to use synchrotron radia.l.ion for selective excitation of normal and resona.ncc AII r r spcctra can bc used as probes for the electronic structure and a s a further test of theorclicaf bevelopment.

INTIEODUCTION

When a.n atom is ionized in a n inner shell by electron, ion or photon impact, the resulting hole state can be filled by means of X-ray emission or a nonra.diative Auger process. In the 1a.tter case a n outer-shell electron fills the hole and another outer-shell electron is c:jected leaving the atom in a doubly ionized state. Auger electron spectra. show a. complicated f i ~ ~ e structure because the spectra. display the electronic structures of single vacancy a.nd double vac:a.ncy states of a n a.lom.

T h e Auger emission is very sensitive for testing the qua.ntum theory. Forl.hermore, the a.na.lysis of the spectra ca.n result in a better understanding of the electronic s t r u c t i ~ r e of the atoms. On the other ha,nd Auger spectroscopy has been found to have itnpor1a.nt applic:a.tions e.g. in studies of solid surfaces and chemical compounds.

This work deals with recent experimental and theoretical invesligations of detailcd line- structure in Auger electron spectraof free atoms. 'rhos, the main concern will be the intensities and energy-splittings of the lines, which determine the detailed line-stucture of the Auger spectra. In addition, a short summary of the relativistic theory of the Auger e h c l is forwarded. For discussion, that goes beyond the present perturbation-theory, the reader is referred to ref. 1. T h e postcollision interaction effects in Auger spectra and anisotropic a r ~ g ~ ~ l a r distributioll of Auger electrons will not be included; for treatment of these topics, s r c e.g. rcfs. 2 and 3. '1 he material used in this report has mainly been collected from the literature; but some unpublishccl resulls o b t a i n ~ d by our research group are also discussed. T h e most activr roups in the area of erpcrimrrrlal atomic Aogcr spectroscopy have been a t Freiburg, Hamburg a n d Berlin in West Germany, Berkeley California,

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987995

C9-566 JOURNAL DE PHYSIQUE

Oak R i d g ~ 'l'ennesee, Uppsala Sweclen and Paris I'rance, in addition to O I J I group i n Oolu, I~inland.

Remarkable contributions to the t h ~ o r y of Artgrr dcrny have come front Ilelsirtki, Finland, from Ellgene, Oregon and from Tasmania, Australia (Larkins) and frorrt A l l ~ ~ t q u c r c l ~ ~ r , New Mrxico (hlcGuire).

We will first discuss some Auger spectra for which a. dcla.iled corrtpa.rison between experi- menta.1 and ca.lculated line-structures has been possible. Reca.usc the thcorctica.1 ca.lcuIal,ions ha.ve been done for free a.toms, n~easuremerits of atorrtic: spectra which a.re riol, a.Kectcd by rnolccular or solid-state effects should be used when c?ntpa.rir~g theory with cxperimc*rtt. T h e influence of I.he molecular a.nd solid states on the spectm. IS, however, srna.11, a.s long a s At~ger tra.nsilions involving only inner shells are investigaied. T h e lines arc broadened due to the rr~olecular splitting, a,nd the kinetic energies are shifted by a consta.nt arnotlnt due to chemical sl~ifts a.rtd extra.-a.lorrric rela.xation phenomena. T h e energy shifts are usu;~lly considerably smallcr for gas-phase molecules than for the same solid species.

Experirnerital arra.ngements

T h e 11sua1 experimenta.1 procedure is as follows. T h e primary inner-shell ioniza.tions is pro- duced by a n electron, ion, or X-ra.y beam. T h e kinetic energy distribution of the ernitted Auger electrons is measur,ed using a high-resolution e1cctrosta.tic a.na.lyzer. As an exarr~ple of high tern- pera.ture Auger electron spectrorrieters the rnc;l.suring system 4 * 5 11sed by our resca.rc:h group a.1 the University of Oulu is shown in Figure 1. It comprises a.n ir~ciuclively 11c:lted sa.rnple oven, a, four element retarding lens6 between the va.pour sample and a. double-pass sirnulated7 spherical-field electron energy analyzer.

T h e experimentally observed &ectrum is always a ror~vol~ltiori of irtltcrent spccl.rurn c n t i l t ~ d by the sample and the instrument function reprcsrnling the 1)roadcning cattscd by the spectrorncl.er used. T h e resolution of energy analyzers shonld Ors11d1 that the line 1)roadening caused by the analyzer is typically smaller than the inherent lik. time wiclrti of the Augrr lines. In practise this

S I M U L A T E D S P H E R I C A L DOUBLE- PASS ANALYZER

P

INDUCTIVELY

- - - - I

~ h l

^{HEATED OVEN}

E l

^EL:CTRON

Fig. 1. Schen~at~ic of the experimental set-up used to ~ncasure Auger elerl.ron spectra a t the Uni- versity of Oulu.

11sua.1ly means that the energy resolution should b(! betl,er lha.r~ 0.05% of t h c inilia.1 kinetic energy of Auger electrons. T h e energy resolution of eleclror~ energy a.na.lyxcrs ca.n I)c irnproved by rel.a.rding the electrons before they enter into the ana.lyxing electric field, beca.nse the energy resolution of the a.na.lyser is a give11 percenta.ge of the kinetic: energy of the electror~s in the ana.lyzing field.

T h e rel,arda.tion ca.n be done either by means of special electron lensesR, which a.re a.lso focusing the divergent incoming beam of electrons or by homogenous electric fielcls genera.ted by grids in diKerent volta.ges.

At room 1empera.tore only ra.re gases a.ppca.r a.s free a.torns. A very 11sefu1 method to produce free &oms is the vapouriza.tion of solid sa.mples. Most solid ele~nents vn.pouriae mainly as free a.t,oms and only a few form molecular clusters (Sl)4, 're2). T h e typical v;l.pour pressure used in a.

source volume is a,bout torr. T h e tempcra.l,ures needed to genera.l.c: these vaporlr pressures vary from some hundred centigmdes up to 3000°C. Jlcsislive hca.ting applying bililar hca.ling wires can be done conveniently until around 1200°C. For higher tempcr;~.tures mainly two kinds of heating are used, namely inductive l ~ e a . t i n g ~ ~ ~ - " or electron bombard~rlent h e a . t i r ~ ~ ' ~ . Auger tra.nsition in a n energy diagram

Let us consider the Ne atom as a n exanrplr. 'I'hc grour~d stat(. configuration of Ne is 1.922s22p6. Figure 2 displays the energy levels of neutral Ne and the itlitis1 and final states of the KLL Auger transitions predicted by the MCI>F calculations. The verlical lines connecting the energy levels of the initial and final states represrnt, the Auger transiliorls, and the correspor~ding spectrum is depicted on the right hand side of t h r figure.

Fig. 2.

C9-568 JOURNAL DE PHYSIQUE

For a long lime, the KLJ, Auger spectra of several periodic t,nblc r l e r n c ~ ~ t ~ s a r ~ d I,he oul.er- shell spectra of the rare-g.1~ atoms were studied most Ihoro~ighly. During I IN last, fiftecr~ gears, the Auger spectra of closed-shell metal atorr~s have also been investigated ~ i ~ r c f u l l ~ " , ' ~ - ~ ~ . In recent years interest has more turned to the studies of the transiliorls in ope11 shell atoms and to I.he spectra that display pronounced many-electron e f ~ ~ ~ t s ~ ~ ~ ~ - " . Next we will consider some selected examples.

Auger spectra, of open shell atorns

In a closed shell a.tom the energy levels a r e tl~le l o the hole sta.les ca-~rsed by the Auger dcca,y.

The spectrum of a n open shell atom is more con~plicatccl a.nd revea.1~ rriore fine strucl.ure due 1.0 the coupling of the pa.rticipa.ting hole states to tlic outermost open shell ~vhere I,he vacar~cies stay passive during the deca.y. This causes the splitl,ir~ of the pa.rcnt levels Lo tIa.ughters, a s ca.rl be seen from figure 3, where the final state energy levef struclt~res oC rol'd, 47Ag and rsCd, gredictecl by the single-manifold. Direc-Fork calcnla.tions, are prcscr~l.cd (a ma.nifoltl is defined as the sel, of jj-coupled sta.les which reduce to a, single nonrcli~tivislic configura.tior~ n.il,hirt t,he r~onrcla.~,ivistic litnit,). Since the open-sheJl elements ma.ke up the Iilrgcr pa.rt of the periodic: ta.ble ail t~nderstar~cling of their speclra will be important lor the iri~itful progress in electron spc~ctroscopy.

ENERGY LEVELS

Fig. 3. Energy levels of l'b, Ag and Cd with two :!d va.ca.r~cies.

Auger satellite transitiorls due to rnany-electrorr c!Kecls

T h e correlation elferts may cause large energy shifts arltl the redistril)ution of inhensily, as is nicely clemonstrated in the case of ns hole states o f rcnl gases a.nd their r~ciqhbour element^^^-^^.

Figure 4 shows a corriparison between calculated single-rnaniloltl and rr~lllt~confi uratiort profilcs and the experiment for the M 4 , 5 N l N 2 , 3 tmnsitions In j r K r The singlcparti% picture is not able to provide a good dcscriptlon for the k f 4 , 5 N 1 N 2 , 3 trarlsiliorls. 'The ~ a l c u l a t i o r ~ s carried or11 by taking inbo accou~it the correlatio~l between I.he 4s~17,"nr~d 4s2JpB4d 1ina.l-s1nl.c configural.io1ls repro(1uce the experinlent fairly well, although [.hey sligl11.y ovcrcstitnal.c the sllifl betwccrl t l ~ c main (1-4) and the satellile (5-8) structures. 'I'tlc anagololrs sa.tellite sl.rc~cl~ire is less pronounced in the l,z,nh41Mz,3 s l ) e c t r ~ ~ m of IeAr but even nlorc 1)rorlouncecl in the N d , ~ 0 1 0 2 , ~ s p e c t r ~ ~ m of 54,Ye"7-3". By comparirlg with photoelectron sltltlics, a sl.rong irlcreimc i l l the illter1sit.y of these correlation sa.tellitcs, in oir~g frorrl the single-hole sta1.c to the dollt)le llole state (final stale or Auger decay), is o b t a i n e t This clearly indicates that t l ~ e correlation salcllites are very se~lsitive to t,he degree of the iorlizntion and the states or I.hc otllcr elcclrons in tllo atom.

(a) M45N1Nt3. J - I SINGLE CONFIGURATION PROFILE OF Kr

25 27 29 31 33 35 37 39 L 1 L3 K l N E l l C ENERGY (.V)

M45N,i\1t3. J-1 MULTlCONFlGURAllON

6 PROFILE

27 29 31 33 35 37 39 L1 L3 KINETIC ENERGY (eV)

(c) EXPERIMENTAL M45N1N2,3 AUGER i4 SPECTRUM

1 '"!

25 27 29 31 33 35 37 39 L 1 L3 K I N E T I C ENERGY (.V)

Fig. 4 Comparison betrvecr~ calculated and expcrirner~tal Auger spectra or Kr".

C9-570 JOURNAL DE PHYSIQUE

T h e intensities and energy spittings of the Af4,sN4,s N 4 , 5 Augcr lincts a.re only sligl~t~ly varied a.s a. function of in going from 54,ye to sGRn, if ark intlcpcndcnt partic:lc tlcscriI)tion is a s s ~ ~ m c d ~ ~ . In the experimental spectra, however, a drastic cha.nge irl the fine struc:tnre of the Auger spectra is observed, when the spectra. of Xe a.nd B:I. a.re corrtpa.red with cac.11 otherg0. This is a clear indication of the fa.ilure of the single paxticle picture to describe the s t r u c t ~ ~ r e in the spectnirn of Ba..

In the multiconfiguration calculations for the 3d-'(6s'

+

8s5d+ 5d2) + Itl-2(Gs2

+

G s 5 d + ~ d ~ ) ~ S 0 transitions four peaks, lying a.bout 2 eV frorn ench other were observetl instead of orre 'So line found in the single configuration picture. By gencra.ting a sum profile of four normal spectra. of Xe shifted by 2 eV from ea.ch other the structure o\)served cxperimcnlally ca.n be reproduced fa.irly well. This clea.rly indica,les tha.t the result 01)tn.ined by the mulliconliguration cn.lcola.tions [or the transitions to the 'So final states and extcr~tled semicrnpirica.lly, is ca.pable of predicl.irig t.hc observed ma.nifold structure fairly well. The strong mixing of the config~~ra.l,ions in the initial and fina.1 ionic states of Ba is connected to the collnpsc. of the 5d orbil.a.1 that fa.kes place in going frorr~

the neutral atom to the ionic states. AnaIogously, the coH;rpse of the :$d a.nd I d orbita.1~ in Ca.

a.nd Sr results irl a strong mixing of configura.tiorls tha.t procl~lces rr~anyfc~ld spcctra.1 structorcs".

MCDF cacula.tions with a limited number of configurations incl~ldcd in tlle expa.nsion, nsl~a.llj! fail to reproduce the observed energy splitting. On t l ~ e other hand, cornpnl.:t.tions wil.11 a.n exl.entied basis set a.re extremely time consuming and 1a.borious.

In a.ddition to the electron correlatior~ also the thcrrna.1 popula.tion o f the energy levels lying in close proximity to ea.ch other may result in n.n anonla.lous spcctra.1 strnc:ture. The free iron group atorris a t the end of the 3d tra.nsition elcnicnts a.re good e x a . r r ~ ~ l c s : ' ~ - " - ~ ~ . Single-n~a.nifoId predictions of the energies of the ground state and of the initial a.rld 1ina.l sta.1.e conlig~ira-t.ior~s of

zp-'

^-+ 3d-2 Auger transitions of Ni a.re showr~ in figure 5(n). Duc. Lo the r1ca.r degcn?ri~.cy of the configura.tions, a. mixing between t.hern is expect,ctl. 'I'he nrulticc~nfiguration calcula-l.ions do not predict a.ny strong mixing, however. T h e near degeneracy ma.kcs the thermal popnlation of the two- lowest-lying configura.tions possible in the ground state of thc- a.torn, cspecia.lly a.t the experinlent tempera.tures, which results in the two-Cold spectral structure:. T h e calculated profile assurning GO:4O popu1a.tions for the 3ds4s2 and 3d944s ground sta.te config~~rations a.grees fairly well with the experiment a s shown in figure 5(b).

T h e calculated KLL Augcr spectrum of Ne potra.+~cd in f i g ~ r e 2 was obtair~ed by ta.king the configuration mixing belween the 2sF2 and 2p-2 hole sl,a.tcs into account. 'l'he theory was rr~odilied to better agree with the experiment by introducirlg t,hc i n tercha.nnel mixing i r ~ the fina.1 sta.l,c in ref. 42. Experimenta.1 spectrum, however, conta.irls rich fine struc:turc thiat ca.r~not be reproduced by the normal KLL Auger tra.nsit,ions a.lone. 7'11~ ot)scrvc:d sa.l.ellite sI.rl~cture is mn.inly due to shake processes 1ha.t ta.ke pla.ce before the hrigcr decay"3. 'J'he Auger process thus ta.kes pln.c:e in an a.tom with an outermost electron excited to n 11yclbcrg Sta.tc (sha.ke-11~)) or into the c o n t i r ~ u ~ ~ ~ n (shake-off). It is a.lso possible 1ha.t shake proccsscs take place during t t ~ ( % Augcr transition. 'l'heir contribution is rather srna.11 in the ca.se of the norrna.1 K1,1, s ~ ) e c l ~ r ~ l r r ~ of Nc.

Auger studies with the use of svnchrotron ra.diation

Synchrotron radiation provides a, very elega.111, a.~ld uniq~te excit,a.tiort rnethod for Augcr spec- troscopy. T h e photon flux frorn modern storn.ge rings a.flcr cfrcctivc morlochromn.l,ors (e.g. toroic1il.l gra.ting monochromators) is so high t11a.t gasco~is sa.nlplcs a.r~d also {.heir A~igcr spcctra. ca.n be sric- cessfully studied. Syr~chrot,ron radiation ca.n be used to excite the initiitl electron to a. Ryclberg sta.te, which then ma.y sta.y as a specta.tor durirlg the Allgcr-type decay or pa.rticipate into (.he process. This selective excita.tion is done by the rrlortochron~a.ti7,ed syr~chrotron rn.dia,tion tuned 1.0 correspond to just the excihtion energy desired. There is, however, a. possibility for the excibed electron to be sha.ken up or OK during the decay. 'I'he energy levels of Kr :id9 + ,Ip4 decay with 5p or 6p specta.tor electron a.re shown in figure ~(a.)". Due to the occurrenc.c of a. process where the spectator electron is sha.ken up during the decay, extra. s t r ~ i c t ~ i r e a.ppea.rs in the spectrurn (figllrc G(b)). T h e eKect is rnost pronounced in the casc of 12r4". When the elvctron is excit,ed to a. 3d R.ydberg sta.te, the collapse of the 3d orbital during the clccay (figure 7) makes it likely that the excited electron will jump to the next Rydberg sl.a.te.

T h e resonance Auger spectroscopy is still a very new field of resrarc 11 and therefore the rrurn- ber of rarefully studied systcrns is rather lirnited Ilesonancc Auger spy( Ira of rare gas~s87n"-50 are best known experimentally and also their theoretical inlcrprrl,ation 1s on a rather sound tmsis.

Ilowevcr, high resolution data and a drtailed corrlparisotl with theoretic nl estirt~atcs for cascade processes as well a s for correlation and shake-olls;~tellilc s t r l l r t ~ i r ~ s is neetlrd before the low cnergy part of the resonantly excited spectra can be analyzed s~~ccessfnlly

Ni ~ ~ - ' 3 d ' & s

-

3 d ' ~ s

L

I 815 825 835 EL5 855 ⁷ ENERGY lev)

2p-'3d8&s1-r 3d64s1

-41260

-41270 -

ENERGY leVl

22 2p-' $do& s2 + 3dqt s) ,

3ds6s'+ 3 d ' ~ s

ENEROY IeVI

E I P E I I ~ N E O ~ R ~ Auorn srrctttuu

$,

5

^-41310

8 c

Z "

0 2 2

0 a

I- 13

-41320

Fig. 5. (a,) Energy level diagra,m of Ni.33

(b) Cornparison between ca.lculated a.nd experimental Auger spcc1.t-a. of Ni.33

C9-572 JOURNAL DE PHYSIQUE

. ,

. .

K l H E I l C ENERGY ( * V )

15

\

\

\ \ I

\ \

\ \

-

¹

\EEz

h-; 50 52 5L 56 58 60 62 6L 4 ~ ~ 5 ~ K l H E l l C ENERGY ( e V )

I

Fig. 6. (a) Energy levels of ~ rVertical lines dcpicl thc iollowir~g transil.ions. . ~ ~

@

3d9(2D512)+ 4p6('D2).

@

3d9(21)512)5p + 4p4(l U)5p resulting in peak '1) of Fig. B(b).

@) 3d9(2US12)5p -+ 4p4(' D)Bp resullil~g in 1)cak ( ' I ) ) or tile dasllctl line in Fig. G(b).

(b) Upper part: Experimenlal h15N2,3NZ,B rcsonnncc A11gcr sprcl.rllrn or l ~ r . ~ ~ Lower part: Calculated 3dZl25p -+ 4p45p (solid linc) and 3&2,,5,, ⁺ 4p4fip (dashed linc) profiles.

d wave functions of Ar

U)

r(aU.1

_Fig. 7. ILadial wave runctions of Ar 1tytll)erg or1)ilals in tllc initial and final slates of Auger-likc

'I'lle unique advantnge of the synchrotron ratliation is that the energy o f t h c cxc:itirlg racliat.ion can be selected to hillfill optirnal conditions. 'J'hl~s c.g. excitation of a dcscper core le\scl than l l ~ e one considered can be avoided. A high energy (1-5 kcV) electron bearn ofl.c!n causes ionization with some probability also in dcepcr levels. These cnltse Auger cascaclcs ant1 corresj)onding satellite lines. As a.n exa.mple of this the L M M Auger spectra of Ar excited by two pl~oton energies of synchrotron radiation are displayed in figure 8. 'I'ltc 350 cV photons call ionize also 2s electror~s causing additional structure to the spectrum and higher corllinuo~~s background.

RELA'I'IVISTIC TlIE'OlLY OF AUGER 'rltANSl'rJONS

In this work the inner-holc state is a s s ~ ~ n ~ c * d to be crcaletl I)y art ionization process with energy well above the io11iza.tion tltrcsl~old. A brief su~nrnary of the rclillivistic theory of Auger decay will be given here, for further details the rcatler is rcrcrred to refs. 51-57.

Auger energies

'I'hc energies of Auger transitions can be obtninecl t)y t.hc cnercy dilkrrncr between scparaLclg optimized total energies of the singly ionized ir~ilial and dollbl ~onizetl final stale levels or the emitting system (the ASCF approach). T h e total energies in e i r t r o n i c slates can be calculaled e.q. with the rn~~lticonfiguration Dirac-Fock (h1CI)F) code of Grarlt e l a1."*57

Atomic-state uravc function ASF) for t l ~ c MCDF 1nrl11od is prrsentrcl asa linear cornl,inntion or configuration-slate functions (

I

^{SF). Tlte ASF of} the vllt electronic s t i ~ t c of all atom with total angular momentum J M is thus given by

Fig. 8. L M M Auger spectra of Ar excited by 350 cV and 255 eV photons.

900

- ARGON

^{i a}

720

-

v,

2

^540-

3

8

^360-

180

-

0

. .

%.

. . .

. _{. ..} ^...

. . .. .. .

. .!.

^:

.

^.:

^:.

hv = 350 eV _{a ,}

. ^{. .} _.'.

_':-

:

. . ' . '

. _. ^{< i} ... - ^{. ..}

^:

^{.. .}

. E : c

$

u

2i\?

24 ia*G. j

. ..

^{? ii $ ;}

- .

%-

*hp.

-

740- h v - 2 5 5 e v

.

^I

0 -

l70 175 180 185 190 195 200 205 210

KINETIC ENERGY (eV)

C9-574 JOURNAL DE _PHYSIQUE

where 11 is the number of CSF included in tlrc e.ul)arlsion aud cZp arc t11e rr~ixir~g coc~llicicr~ts for stnte v. T h e CSF a r e corlslructed from antisymmctric proclucts of Dirnc c.entral-licltl follr-spittors.

For t l ~ e MCDF method the mixing coellicicr11.s nncl the spinors arc cjctcrrrrir~ctl Oy applyin the variational method to the expe(:tation val~te of the llatnillonian \vitl~ respect to Al'S d a ( J h l t subject to orbital orthogonality constraints. Tllc llnrrliltoninr~ ~~sccf in the variationnl princ:iplc is taken to consist of a sum of single-particle Dirac Ilnrniltonians p l ~ ~ s the pllrely Coc~lonlb interelec- tronic repulsion

N N .

'I'hc Breit interaction, a.long with other quantum-clectrody~~nrnic (QEC)) c.ontribcltions, arc added to the llamiltonian matrix once the orbitals have 1)ecn clctermirlcd, al~tl the con~plete rrlatrix of IIarniltonian diagonalized to deterrnine the corrected encrgy levels and t ~ ~ i x i n g coellicicnts.

T h e A ~ ~ g e r transition probabilities are c n l c ~ ~ l a t c d frorn the pcrturbiition theory. 'l'he trarlsi- tion rate in frozen orbital spproxirnation is giver1 by

where

Jli

and are the wave functions of the initial and final slates or the Auger decay i n arty nonclosed-shell atom. Pirlal state also contains the cor~tinuum elrctror~ wave function whiclt is assumed to be normalized per unit energy range. V,& is the two-electror~ opcrntor, thal is taken to be the surrl of the Coulomb and generalized Breit ol)ernlors ill the Co~llornb gauge5'

where w is the wave number of the excl~angcti v i r t ~ ~ a l pltoton anti starlclard notations have been used elsewhere.

l ' h e wave function of the vth singly ior~izcd initial state is given I)y equation (1) arld the wave function of the qtll doubly ionized final state, havir~g total angular trlorr~ertturn .I'h.l', by

By usin jj-coupling between the qtll final state arltl tllc crr~ittrd Auger r l r r t r o r ~ (ar~gular mornen- turn j,mq we obtain for the Auger component transition prolal)ility tl~ill n singly io~~irecl initial state (nllljl)-';3 decays into any of the doubly ioniecd final slatcs ( n 2 / ? j z ) - ' (1z:+~j3)-';.1' wiLh the emission of an electron with energy E

'I'he matrix elernents of the two-electron operator betwcrrl two CSF's call be scparatrcl by tensor algebra into angr~lar parts multiplied by rhlial ir~lrgrals. 'She anglulnr factors can be evaluated by using computer code MCP ^and MCBP routincs frorrl Grarit's MCDF I)rograrrl"l".

T h e radial integrals in frozen core approxirrrat,ior~ can be c a l c ~ ~ l a t r t l wi1.h t h r use of bound state Virac-Fock wave functions that correspond lo the initial one hole-stale configamlion. T h e contin~ium wave functions can be obtained by solving tlre Dirac equalions in the inil.ial slale potential w i t h o ~ t ~ l - ~ ~ or t,he exchange conCribution. T h e conlirt~ium wave funclior~s arc then orthogonalized to the bound state wave funcl.ions.

EIfects of relativity on Auger transitions

Theoretical profile for the 1144,5N4,5N4 5 Auger (1eca.y of Ag predict.(-d by reln1,ivistic ca.lcula- tiorts is shown in figure 9. T h e importance

01

the Hreil intrea.ction wa.s tesled by producing proliles without and with it.. T h e introduction of the Rreit opera.tor did not improve visibly the resiilts obtained by the Co~ilomh operator only. T h e transition probabilities ol)la,ined in the Coulomb g i i ~ g e ( ~ q . 4, a.nd in the Lorcnz auge (with the hilflller operator) were f4~11nd to a.gree very well.

Pure Coulomb opera.tor yieldecf the profile (a) when ol)ta,ined with relnlivistic wave functions, whereas nonrela.tivistic wave functions gave the profile b). An ex~)erime~tl~al spectrum is depicted

I

in figure 10. Relativistic single-manifold ASCP calcu a.tions used l l ~ r o ~ t g l ~ o u t to predict Auger energies overestimate the splitting between final s1a.t~ energy levels, which ca.uscs the main tlis- a.grcement between experiment and theory. T h e intensity distribution obtained with McC:nirels ri.dial integrals5' is also shown for comparison.

SILVER M~,5N~,5N,,5

A U G E R S P E C T R U M

332 334 336 338 340 342 344 346 348 350

KINETIC ENERGY (eV)

Fig. 9. Intensity distribution of the 3d95s1 + 4d85.9' transitions of Ag c a l r ~ r l a t ~ d with the Coulomb operator and I)F or IIF wave functions. Lower part shows the. profile obtainccl using McGuires radial i r ~ t e g r a l s . ~ ~

C9-576 JOURNAL DE PHYSIQUE

T h e relativistic efrects on AII er transitions ca.n arise frorrl cllar~gcs i l l cncr ics shifts i r l wave

f,

^.',:

functior~s and Rreit corrections in

%k

two electro~l operator. Systerr~atic sl~~clics abe reser~t.ly 1)ccn published by Crasernan~t and co-workers; for f11rt.Ilcr details, tttc rcacicr is referred to a.11 cilrlicr review of the topic (ref.55) artd references tlterein.

-

M',5NL,5NL.5

z ^{Z = L 7}

3

t

^{I AUGER SPECTRUM}

I I

332 336 Y O 3LL

ENERGY (eV)

Fig. 10. Experimental spectrum of Ag.

ILEFERENCES

1. T. Kberg, and G. llowat, pp 469-619 in llandbucl~ der IJhysik, \'"I XXXI, editcd I)y W.

Mehlhorn, Springer Verlag, IIeidelberg, 1982.

2. W. Sandner, in the XV Interrlational Cor~fcrence or1 Lhc I'hysics or Eleclrorlic and Atolrlic:

Collisiort - XV ICI'EAC, Brighton, U K , 22-28 July, 1987.

3. W. Mehlhorn, pp 55-73 in X-Ra.y and Atorrlic Inrlcr-Shell IJtlysics - 1982, All' Confercnct:

Proceedings No. 94, edit-d by £3. Craserrlcnn, Arrlcricnrl Irlstilulc: of Pllysics, N e w York, l9ea.

4. S. Aksela, M. llarkoma, M. l'ohjola, and 11. Akscln, .I. Phys. R17, 2227 (1984).

5. S. Aksela, M. Ilarkonia, and 11. Akseln, Phys. 1l.c~. 1229, 2915 (108.1).

6. H. Wannberg and A. Skiillernlo, J. Elcctror~ Spccl.rosc. 10, 45 (1977).

7. K . Jost, J . Phys. E12, 1006 (1979).

8. E.1I.A. Grnnnernart and M.J. Vnr~ tier Wicl, [>I). 367-462 i r ~ lli~r~clbook on Syr~chrotron lladiation, Vol. 1, edited by E.E. l<oclt, North Ilollnrltl, 1088.

9. A. Morris, N . .Jonathan, J.M. Dyke, IJ.I). I:rnticis, N. ICeddar, a l ~ t l J.1). Mills, 1l.e~. Sci.

Instrum. 55, 172 (198.4).

10. V. Schrriitit, Comment. At. Mol. I'hys. 1 7 , 1 (1!)86).

11. R. Malutzki and V. Schmidt, J . Phys. B19, 1035 (1986).

12. T. Prescher, M. Richter, B. Sonntag, and 11.E. \\'elzel, N I I ~ : ~ . Irlstr. Phys. llcs. A254, 627 (1 987).

13. H. F3reuckn1a.n and V. Schmidt, Z. Phys. 268, 235 (1974).

14. J. Vayrynen, S. Aksela, and 11. Aksela, Phys. Scr. 1 6 , 452 (1977).

15. B. Rrellcknlan, J . Phys. R12, 1,609 (1979).

16. 11. Aksela and S. Aksela, .J. Phys. H7, 1262 (1974).

17. S. Aksela, J. Viyryncn, and 11. Akscla., P l ~ y s . Ik v . Lctl. 33, 999 (1 974).

18. S. Aksela and 11. Aksela, Fhys. Lett. 4 8 A , 19 (1971).

19. 11. Aksela, S. Aksela, J.S. Jcn, and T.D. 'l'l~ornas, Phys. Rev. 1115, 985 (1!177).

20. S. Aksela and 11. Aksela, Phys. Ilcv. A27, 3129 (1983).

21. 11. IIilIig, R. Cleff., W. Mehlhorn, and W. Schmits, Z. I'hys. 268, 225 (1974).

22. B. Hreuckman, Ph. I). Thesis, Univcrsitat Vreiburg, 1978, unpublisl~cd.

23. S. Aksela, M. Kellokumpu, 11. Aksela, arid J . Viyrynen, Phys. Rev. A23, 2374 (1981).

24. W. Mengel and W. Mehlhorn, pp 319-322 in Inner-Shell and X - R I I ~ Physics.of Atoms and Solids, edited by D.J. Fabian, 11. Kleinpoppcn, and L.M. Watson, J'lenum Press, New York, 1981.

25. J. Viiyrynen, S. Aksela, M. Kellokumpu, arid 11. Aksela, Phys. R e \ . A22, 1610 (1980).

26. 11. Aksela, T. Makipaaso, V. Halonen, M. Pohjola, and S. Aksela, Phys. Itev. A30, 1339 (I 984).

27. S. Aksela and JI. Aksela, Phys. Rev. A31, 1540 (1985

.

28. 11. Aksela, T. Makipaaso, and S. Aksela, Phys. Rev.

1

31, 499 (1985).

29. S. Aksela and J . Sivonen, Phys. Rev. A25, 1213 (1982).

30. 11. Aksela and S. Aksela, Phys. Rev. A27, 1503 1983

.

31. 11. Aksela and S. Aksela, Phys. Rev. A28, 2851 [L983].

32. S. Aksela, T. Pekkala, 11. Aksela, M. Wallenius, and hl. IJarkorna, Phys. Itev. A35, 1426 (1987).

33. 11. Aksela, S. Aksela, T. Pekkala, and M. Wallenius, J'hys. Rev. A35, 1522 (1 987).

34. E. Schmidt, Ph. I). Thesis, Hamburg, 1985, ~lnpublished.

35. M. Meyer, T h . Proscher, E.V. Raven, M. Richter, E. Schmidt, B. Sorintag, and 11.-E. Wetxel, Z. Phys. D2, 247 (1986).

36. E. Schmidt, 1%. Schroder, B. Sonntag, 11. Voss, arid 11.-E. Wetzel, J . I'hys. H17, 707 (1984).

37. 11. Aksela, S. Aksela, 11. Pulkkinen. G.M. Hancroft, arid K.11. 'l'an, Phys. Rev. A33, 3876 (1986). ^'

38. K.G. 1)yall and F.P. Larkins, J. Phys. B15, 2793 (1982).

39. 11. Aksela, S. Aksela, G.M. Bancroft, K.11.

'hn,

and 11. Plllkkinerl, Phys. Rev. A33, 3867 (1985).

40. M. Kellokumpu and 11. Aksela, Phys. JLv. 1\31, 1540 (1985).

41. W. Weter, Diplornarbeit, Freiburg, 1984, unpi~blislicd.

42. G. IIowat, T . !iberg, 0. Goscinski, S.C. Soong, C.P. Bhalla, and hl. Ahrncd, Phys. Lett.

60A, 404 (1977).

43. V. Schmidt. un 548-558 in Proc. Intern. Conf. on Inner-Shell Jonizalion Processes and Future ~ ~ p h c a t i o n s , Atlanta 1972, edited by R.W. Fink, S.T. i'vlanson, J.M. Palms, and P.V. Itao, Oak Ridge, 1973.

44. 11. Aksela, S. Aksela, H. Pulkkinen, G . M . Rancrofl, and K.11. Tan, lo be published.

45. W. Eberhardt, G. Kalkoffen, and C. Kunz, Phys. Rev. Lcll. 4 1 , 156 (1987).

46. V. Schmidt, S. Krummacher, F. Wuilleumier, and P. Dhex, Phys. llev. A24, 1803 (1981).

47. S. Southworlh, U. Becker, C.M. Truansdalc, P.11. Kobrin, D.W. Lirldle, S. Owaki, and D.A.

Shirley, Phys. 'Rev. ~ 2 8 , ' 2 6 1 1983).

48. U. Becker. T. Prescher, E. Sc

\

imidt. B. Sonntag, a.rd IC.11. 'ran. I'hys. Itev. A33. 3891

(1986).

.,

49. D.W. Lindle, P.A. Iieimann, T.A. Ferret, R1.N. Piancastelli, and 1l.A. Shirley, I'hys. Rev.

II. Pulkkinen, G.M. Hancroft, arid K.11. Tan, Phys. Jtrv. A33, 3876 (1986).

51. M.H. Chen and B. Crasemann, Phys. Rev. 1135, (1579 1987

.

52. M.11. Chen and B. Crasemann, Phys. Rev. A28, 2829 1983 . (1979).

I 1

53. M.11. Chen, E. Laiman, B. Crasemann, M. Aoyagi, and 11. Mark, I'hys. Itev. A19, 2252 54. M.11. Chen, pp 31-95 in Atomic Inner-Shell Physics, edited by B. Crascmann, Plenum Press,

New York, 1985.

55. J. T'ulkki, private communication.

56. I.P. Grant, B.J. McKenzie, P.11. Norrington, D.F. Mayers, and N.C. I'yper, Comput. Phys.

Commnn. 21, 207 (1980).

57. B.J. McKenxie, I.P. Grant, and P.11. Norrington, Cornput. Phys. Cornrnun. 21, 233 (1980).

58. E.J. McGuire, Sandia Laboratories Itesearch Report No. SC-RR-71-0835 (1972) unpublished.