15
PHYSICAL REVIEW A VOLUME 26, NUMBER 2 AUGUST 1982 Autoionizing resonance profi1es in the photoelectron spectra of atomic cadmium P. H. Kobrin, U. Becker, * S. Southworth, C. M. Truesdale, D. W. Lindle, and D. A. Shirley Materials and Molecular Research Division, Laurence Berkeley Laboratory and Department of Chemistry, University of California, Berkeley, California 94720 (Received 23 February 1982) Photoelectron spectra have been taken of atomic Cd with synchrotron radiation between 19 and 27 eV using the double-angle time-of-flight method. Dramatically different energy dependences of the partial cross sections for producing the lowest D5/2 D3/2 S]/p and P3/2 ]/g ionic states of Cd+ were observed for photon energies in the neighborhood of the [4d (5s 5p P)] P, &2 6s 'P, antoionizing resonance at 588 A. Partial decay widths from the excited resonance state have been determined by fitting the resonance line shapes to theoretical expressions for the partial cross sections. Resonance profiles in the photoelec- tron angular-distribution asymmetry parameter for the D5/2 and D3/2 channels are also reported. The 'P3/21/2 satellite is found to decrease slightly relative to the S1/2 main line in the 19 25-eV range. Three new satellite peaks have been detected with intensities enhanced by autoionization. I. INTRODUCTION In recent years considerable effort has been spent elucidating several aspects of Cd I photoionization. Much interest has been focused on the excitation of 4d electrons, which are affected by both intrashell and intershell correlations, and on the inter- mediate-Z nature of Cd, which cannot be treated sa- tisfactorily in either a pure LS or jj coupling scheme. Many-body-perturbation theory' (MBPT) has been used to calculate the absolute photoionization cross-section measurements, ' which could not be described correctly by single-electron calculations. Harrison's early angular-distribution measurements of the 4d photoelectrons using a He I source (584 A) prompted theoretical investigations based on MBPT, ' the Dirac-Slater (DS) approximation, the Dill-Fano angular momentum transfer approach, and Dirac-Fock (DF) theory. Recently new experi- mental measurements with resonance lamps have shown better agreement with the calculations. The role of relativistic effects was investigated by Walker and Waber, who examined the Cd 4d branching ratio by making Dirac-Slater calcula- tions. Their work suggested that most of the varia- tion from the statistical value is due to the differ- ence in kinetic energies of the two spin-orbit com- ponents at a fixed photon energy. Measurements with synchrotron radiation and recent Dirac-Fock calculations' have also addressed this problem. Alignment in the Cd+ D3/2 and D5/2 states produced through photoionization with HeI radia- tion has been detected"' by measuring the degree of linear polarization of the fluorescence to the Cd+ ground state. Comparisons with MBPT, ' Hermann-Skillman' and relativistic (Ref. 7) DF calculations have left some discrepancies. The nature of the satellite peaks in the photoelec- tron spectra of Cd+ and other group IIA and IIB elements has been of interest because of the possibil- ity of using them to study electron correlations. ' ' Agreement of satellite intensities with the initial- state configuration interaction (ISCI) model, using multiconfiguration Hartree-Fock (MCHF) calcula- tions, has not been good. ' An investigation with synchrotron radiation re- vealed resonances in the Cd? absorption spectrum, corresponding to double electron excitations in a single-particle picture. ' These excitations have been attributed to excited-state configuration mix- ing. The effects of autoionizing resonances on absorp- tion spectra were treated in the pioneering work of Fano. ' ' Their effects on the more sensitive pho- toelectron spectrum have also been explored theoret- ically. Most experiments to date on atomic systems have been concerned with the Rydberg states of rare gases between the first and second ion- ization thresholds, where only one final state is pro- duced. More tantalizing data have been obtained beyond the second ionization threshold in atoms 26 842

Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

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Page 1: Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

PHYSICAL REVIEW A VOLUME 26, NUMBER 2 AUGUST 1982

Autoionizing resonance profi1es in the photoelectron spectra of atomic cadmium

P. H. Kobrin, U. Becker, * S. Southworth, C. M. Truesdale, D. W. Lindle, and D. A. ShirleyMaterials and Molecular Research Division, Laurence Berkeley Laboratory

and Department of Chemistry, University of California, Berkeley, California 94720(Received 23 February 1982)

Photoelectron spectra have been taken of atomic Cd with synchrotron radiation between

19 and 27 eV using the double-angle time-of-flight method. Dramatically different energy

dependences of the partial cross sections for producing the lowest D5/2 D3/2 S]/p and

P3/2 ]/g ionic states of Cd+ were observed for photon energies in the neighborhood of the

[4d (5s 5p P)] P,&2 6s 'P, antoionizing resonance at 588 A. Partial decay widths from the

excited resonance state have been determined by fitting the resonance line shapes totheoretical expressions for the partial cross sections. Resonance profiles in the photoelec-tron angular-distribution asymmetry parameter for the D5/2 and D3/2 channels are also

reported. The 'P3/21/2 satellite is found to decrease slightly relative to the S1/2 main line

in the 19—25-eV range. Three new satellite peaks have been detected with intensities

enhanced by autoionization.

I. INTRODUCTION

In recent years considerable effort has been spentelucidating several aspects of Cd I photoionization.Much interest has been focused on the excitation of4d electrons, which are affected by both intrashelland intershell correlations, and on the inter-mediate-Z nature of Cd, which cannot be treated sa-tisfactorily in either a pure LS or jj couplingscheme.

Many-body-perturbation theory' (MBPT) hasbeen used to calculate the absolute photoionizationcross-section measurements, ' which could not bedescribed correctly by single-electron calculations.Harrison's early angular-distribution measurementsof the 4d photoelectrons using a He I source (584 A)prompted theoretical investigations based onMBPT, ' the Dirac-Slater (DS) approximation, theDill-Fano angular momentum transfer approach,and Dirac-Fock (DF) theory. Recently new experi-mental measurements with resonance lamps haveshown better agreement with the calculations.

The role of relativistic effects was investigated byWalker and Waber, who examined the Cd 4dbranching ratio by making Dirac-Slater calcula-tions. Their work suggested that most of the varia-tion from the statistical value is due to the differ-ence in kinetic energies of the two spin-orbit com-ponents at a fixed photon energy. Measurementswith synchrotron radiation and recent Dirac-Fockcalculations' have also addressed this problem.

Alignment in the Cd+ D3/2 and D5/2 statesproduced through photoionization with HeI radia-

tion has been detected"' by measuring the degreeof linear polarization of the fluorescence to the Cd+ground state. Comparisons with MBPT, '

Hermann-Skillman' and relativistic (Ref. 7) DFcalculations have left some discrepancies.

The nature of the satellite peaks in the photoelec-tron spectra of Cd+ and other group IIA and IIBelements has been of interest because of the possibil-ity of using them to study electron correlations. ' 'Agreement of satellite intensities with the initial-state configuration interaction (ISCI) model, usingmulticonfiguration Hartree-Fock (MCHF) calcula-tions, has not been good. '

An investigation with synchrotron radiation re-vealed resonances in the Cd? absorption spectrum,corresponding to double electron excitations in asingle-particle picture. ' These excitations havebeen attributed to excited-state configuration mix-ing.

The effects of autoionizing resonances on absorp-tion spectra were treated in the pioneering work ofFano. ' ' Their effects on the more sensitive pho-toelectron spectrum have also been explored theoret-ically. Most experiments to date on atomicsystems have been concerned with the Rydbergstates of rare gases between the first and second ion-ization thresholds, where only one final state is pro-duced. More tantalizing data have been obtainedbeyond the second ionization threshold in atoms

26 842

Page 2: Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

26 AUTOIONIZING RESONANCE PROFILES IN THE. . . 843

and in molecules where the problem is theoreticallyintractable.

The fortuitous overlap of the HeI line with anautoionizing level of Bar was found to enhancemany of the otherwise weak satellite lines.Synchrotron radiation was subsequently used to ex-cite resonances in atomic barium and more recent-

ly in atomic copper, ' in order to study the struc-ture of the autoionizing levels and their interactionwith the continua.

This experiment on Cd was prompted by a desireto study several final ionic states in the neighbor-hood of a broad autoionizing resonance. Metal va-

pors provide some of the best resonances for such astudy, and the 588 A feature in the Cd I absorptionspectrum was chosen as an especially promisingcase. We report here the largest set of partialcross-section and angular-distribution profiles yetobtained for an atomic autoionizing resonance. Inparticular, the partial cross-section profiles for

4d105s 2g 4d95s22D4d' Sp P3/p and 4d' Sp P&/q ionic states, as well

as the angular-distribution asymmetry profiles ofthe 4d 5s D5/q and 4d Ss D3/p photoelectrons,have been measured in the region of the 588 A reso-nance. Three heretofore unobserved satellite peakswere also detected at several photon energies be-tween 22 and 24 eV.

Our experimental procedures are described in Sec.II. The nonresonant measurements of the 4d and Ss

photoelectrons are presented in Sec. III. Section IVaddresses the effects of the 588 A resonance, thecorrelation satellite intensities are presented in Sec.V, and our conclusions are summarized in Sec. VI.

II. EXPERIMENTAL

The partial cross sections and angular distribu-tions of the Cd photoelectrons were measured bythe double-angle time-of-flight (DATOF) method,using the pulsed synchrotron radiation fromSPEAR at the Stanford Synchrotron RadiationLaboratory. The vacuum of the SPEAR ring wasisolated from our sample chamber by a 1500 A-thick aluminum window. The light was mono-chromatized [2.5 A full width at half maximumlFWHM)] by the Seya-Namioka monochromator onthe 8' beam line. The two time-of-flight (TOF)detectors were placed at 0 and 54.7' (the "magic an-gle") with respect to the polarization direction ofthe &97% polarized synchrotron radiation, allow-

ing us to make partial cross-section and angular-distribution measurements simultaneously.

Our TOF photoelectron spectrometer has beendescribed previously. ' It is ideally suited forstudying the low-intensity photoelectrons from met-al vapors because of its high efficiency and excellentsignal-to-noise ratio. Without retarding, theanalyzers have a resolution equal to -3% of the ki-netic energy. The standard gas inlet was replacedby a new stainless-steel effusive oven with a 1-mmdiameter orifice, noninductively wound heater ca-bles, and alumina insulation. To do quantitative ex-periments with the TOF spectrometer it is necessaryto admit calibration gases through the oven's ori-fice. A potential problem with having a passage forthe calibration gas is that the metal vapor may con-dense in and eventually clog the passage. Thisproblem is most acute for those metals which formlow-density solids upon condensation (such as bari-um). To circumvent the problem an active valvewas designed to close the gas passage when it wasnot in use.

The oven (Fig. 1) consists of an outer stainless-steel cylindrical piece which includes the orifice andonto which are fixed the Semco heating cables andalumina heat shields. Except for the orifice, theouter structure is gas tight. The inner stainless-steelstructure consists of the sample cup, which isscrewed to a long rod that extends outside thechamber. The valve seal is made between the top ofthe sample cup and the outer oven wall, thus con-

fining the metal vapor to the sample cup and oven

orifice. This design also allows the sample cup tobe removed for refilling without changing the align-ment of the oven with respect to the analyzers and

photon beam. It was not necessary to refill the Cdoven during the work reported here, as the 3.5 cmcapacity of the sample cup was adequate for 24 h ofoperation. An oven temperature of approximately300'C (corresponding to a Cd vapor pressure of-0.1 torr) was monitored by two thermocouples,one mounted on the exterior of the outer structure,the other near the base of the sample cup. It was

necessary to use the thermocouple readings to makesmall pressure corrections to the partial cross sec-tions. The angular-distribution and branching-ratiomeasurements do not require corrections for pres-sure or photon flux when the DATOF method isused.

The synchrotron light intensity was monitored bya sodium salicylate scintillator and an optical pho-totube separated by a 300—SOO-nm bandpass filter.With the sodium salicylate fluorescence maximumat 420 mm we were able to filter out enough of theoven s black-body radiation to continue monitoringthe synchrotron radiation while the oven was hot.

Page 3: Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

P. H. KOBRIN et al. 26

Qi;.C:Qi

C'C:

Oa'.:,

0;0;0'Cj'0„'

~ 0'C!'0'

Q//0'

Qe,g /' /

Q/'/

Qi,

Q',c'Qi/

~ 0i;0"0//'i C)

:;3'~O/pi3:~~0r/8&

//Qe

Qg

;00:0

'0:0:,0

'0'0;0:0

Qo

Qe

:,0

Kinetic energy (eV)I5 IO 5!11 I I !E I I I I I

4d5 Cdhv =22.9l eV

Ar

0—I

IOO

!

A

I i i i i I i i » I i i i i I i i i i I

I 50 200 250 300 350

Time of flight (ns)

400

FIG. 2. TOF photoelectron spectrum of Cd+ takenwith the "magic angle" detector. The accumulationtime was 1000 sec. The photoelectron peaks are listedin Table I.

and 4d3/q main lines but could be significant for theweaker satellite lines. Systematic errors in both the"magic angle" analyzer transmission function usedto derive branching ratios and partial cross sections,and in the relative analyzer transmission functionused to derive the angular-distribution asymmetryparameter, P, should be small and should vary slow-

ly with photoelectron energy.

III. ASYMMETRY PARAMETERSAND BRANCHING RATIO OF THE 41 PEAKS

FIG. 1. Metal vapor oven (1). Stainless-steel samplecup. (2). Rigid stainless-steel outer stucture. (3). Heatingcables. (4). Alumina heat shields. (5). Stainless-steel foilheat shields. The inner diameter of the sample cup is 10mm.

From the work of Mansfield' we know that the20.S —24.5-eV region of the absorption spectrum ofCd? is densely populated by autoionizing features.At these resonances large variations can be expectedin the 4d branching ratio and the angular-

The main chamber was pumped by a 1000 l/seccryopump and a 500 l/sec turbomolecular pump,which was valved off while the oven was in use toavoid metal vapor contamination. The chamberpressure was 1X10 torr when no calibration gaswas flowing and below 1&10 torr whenever gaswas flowing. For internal calibration many of theCd+ spectra were taken with a small amount of ar-

gon present. The Ar+ P3/p f/Q peaks do not over-

lap any of the Cd+ peaks, as shown in Fig. 2.The error bars on our results represent counting

statistics only. Uncertainties arising from back-ground subtracting are negligible for the 5s, 4d&/z,

Ionic State

41' 5s S~- p:,",,

4d Ss Ds/24d 5s D4d' 6s S,4d 5d D5/2 3/2

41 6p P3/2, 1/2

'From Ref. 35.

5s

5P 1/2

5P3/24d 5/2

413/2

6s516p

8.9914.4614.7717.5918.2819.2820.1220.77

TABLE I. Cd+ Photoelectron peaks.

Abbreviation Binding energy (eV)'

Page 4: Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

26 AUTOIONIZING RESONANCE PROFILES IN THE. . . 845

distribution asymmetry parameters, which would

otherwise be slowly varying functions of energy.The values observed experimentally for these

parameters are thus dependent on the excitationbandwidth, which will determine the extent of theaveraging over direct and resonant processes. Cal-culations which do not include any resonant effectsshould be more directly comparable with measure-

ments outside of the 20.5 —24. 5-eV region.The angular distributions of the 4d5/2 and 4d3/2

photoelectrons have been calculated and measure-

ments have been made previously at several rare-gaslaboratory-source energies between 21.22 and 40.81eV. We report here the first measurements of these

angular distributions using continuously tunable

synchrotron radiation. Our results are shown in

Fig. 3.Figure 3 is divided into three panels for clarity.

The parameters p14dq~2) and p(4d3/2) are presentedin panels (a) and (b), respectively, with a common

photon-energy axis as abscissa. Identical curveshave been drawn in Figs. 3(a) and 3(b). Thesecurves have no theoretical significance but are given

to guide the eye. The data fall into two sets: thoseoutside the 588 A resonance region which followthe curve to a fair degree of accuracy, and thosenear resonance, which depart sharply from thiscurve. To compare the two asymmetry parametersfurther, we have deleted the "resonance" points and

replotted the rest in Fig. 3(c) with a kinetic energyabscissa. The 588 A resonance region is discussedin Sec. IU of this paper.

Before proceeding, it is useful to state a caveat re-

garding this type of separation of photoemissiondata into resonant and nonresonant energy regions.The separation is, of course, arbitrary, but this is

only a numerical problem. For example, a reso-nance energy "region" can be defined as extendingsome number of resonance bandwidths. Of morepractical concern, the observation or nonobservationof a resonance depends on the bandwidth of the ex-

citation radiation. Care is thus needed in compar-

ing data from different laboratories. More vexing isthe residual doubt about whether a data point "offthe curve" represents a resonance or just a bad mea-

surement. The data sets presented in this paperoften show scatter which appears to exceed the sta-tistical errors. While we always tend to suspect un-

known errors, which are difficult to rule out in syn-

chrotron radiation studies because of possible fluc-tuations in the beam position, there is also the pos-

sibility that some of the deviant points arise fromweak resonances.

From Fig. 3(c) we note that our data show good

1.5 q(,1

~

i™~

4d r/z

- o~ ~-+-~-+~—pi-+-+-$-+-+ ~

(b1

4d 3/2

W 05'—

—0.5' I !20 22 24

Photon energ y (eV)

26

T ]T W T

1.5— (c) 3

~ 05MBPT

Q~-g Dept, DSe~0 5L

2l i t t l

4 6 8

K Inetic energy (eV)

10

agreement with the six points given by Schonhense,which are, on the average, slightly lower than ours.From Figs. 3(a) and 3(b), comparison at equalphoton energies gives, on the average,

FIG. 3. The Cd 4d photoelectron asymmetries. Thepresent 4d5/2 and 4d3/2 measurements are shown inpanels (a) and (b), respectively. The identical solidcurves in (a) and (b) are for visual comparison only. In(c) the filled and open circles represent our 4d~/2 and4d3/2 measurements. The filled and open trianglesrepresent the 4d 5/2 and 4d 3/2 measurements ofSchonhense, Ref. 8. The theoretical calculations arefrom MBPT, Ref. 1; DS, Ref. 5; DF, Ref. 7; and x's,GIPM, Ref. 36.

Page 5: Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

846 P. H. KOBRIN et al. 26

P(4d3/2 ) ) I-I(4d5/2) However, this is a small effectwhich disappears when the comparison is made atequal kinetic energies, as shown in Fig. 3(c). Thetheoretical curves predict the P values qualitatively,but deviate systematically in a quantitative compar-ison. The increase in the experimental P values atlow energies is stronger than predicted by any of thetheories. The data do not confirm the differencebetween p(4d, /z) and p(4d3/3) predicted by theDirac-Fock theory in Fig. 3(c). Finally we note, butdo not show, that Schonhense's data at kinetic ener-

gies above 10 eV rise well above the Dirac-Fockcurves.

The Cd 4d branching ratio o(4d5~2)/0(4d3/2) has

been calculated by the Dirac-Slater and Dirac-Fock' methods and has been measured previously

at 21.22, 40.81, and 48.37 eV with resonancelamps' ' and between 19 and 30 eV with 6 Abandpass synchrotron radiation. Our measure-

0

ments with a 2.5 A bandpass are shown, along with

the previous results, in Fig. 4. Our results show theeffect of the 588 A resonance for the first time in

some detail. Outside the resonance region our datatend to confirm the earlier synchrotron radiationwork. The scatter in our results in theh v=22 —24-eV region may arise in part from addi-

tional resonances, as discussed above.Both calculations fail to predict the continued

rise in the branching ratio below 20.5 eV, while

above 24.5 eV the DS curve is a little too high and

T t '1 T T I +T T~ P~ I

4d5/2 4d3/2

the DF curve is a little too low. The poor agree-ment of the DF calculations at the low kinetic ener-

gies has been attributed to the use of jj coupling forthis intermediate-Z atom. The DF calculations forHg show better agreement. ' Inclusion ofcontinuum-state configuration interaction (CSCI)between the various jj channels should also improvethe agreement in Cd.

Johnson et al. have calculated the Cd Ss partialcross section using the relativistic random-phase ap-proximation (RRPA) ~ In order to put our relativecross sections on an absolute scale we have scaledour total cross section to the measurements ofCairns et al. over the 20—26-eV range. TheRRPA calculation is then a factor of 2 larger thanour measurements between 19.5 and 27 eV. We canaccount for two of the major deficiencies in the cal-culation. One is that Johnson et al. overestimatethe total Cd cross section due to the absence of corerelaxation in their calculations. To account for thiswe can compare branching ratios instead of absolutecross sections. The other problem is that theRRPA calculations neglected the effects of two-

electron excitations which are responsible for the

appearance of the 5p satellite. To account for this

we can compare the RRPA Ss cross section to thesum of the Ss and Sp cross sections. In Fig. 5 we

compare our ratio of the Ss plus Sp cross sections tothe total cross section together with the Ss to the to-tal ratio from the RRPA calculations. While theRRPA calculation is still —10% higher than ourpoints it appears that we have accounted for mostof the major discrepancy.

0LK

20~ tl

I.8 PcO

I 6,—Q3

I 4—I I I I . I I I J I I I I I I I I

20 22 24 26

Photon energy (eV)

O.I5—

0C3

O. IO

C:

C3

P 0.05CCI

I I'

I'

II

I

ps+ 5ptotal

FIG. 4. The 4d branching ratio. The filled circlesrepresent our results; the open triangles, the measure-ments of Shannon and Codling, Ref. 9; the open square,the measurement of Siizer et al. , Ref. 14; the measure-ment of Dehmer and Berkowitz, Ref. 37, of 1.75 at21.11 eV is not shown. The DS and DF curvesrepresent the Dirac-Slater and Dirac-Fock calculationsof Tambe et al. Ref. 10.

19 20 2l 22 23 24

Photon energy (eV)

25

FIG. 5. The fraction of the total cross section in thecombined Ss and Sp peaks. The curve from Johnsonet al. , Ref. 38, shows the RRPA calculation of the frac-tion of the total cross section in the 5s state.

Page 6: Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

26 AUTOIONIZING RESONANCE PROFILES IN THE. . . 847

IV. THE 588 A RESONANCE REGION

A. Excitation properties

The most prominent feature in the absorptionspectrum of CdI between 19 and 30 eV is a verybroad asymmetric resonance centered at 588 A.Mansfield' has assigned this resonance as

4d' Ss 'So+hv~[4d (SsSp P)] P3/26$ Pf

the first (n =6) member of the [4d(SsSp P)] P3/2ns series, which has a series limit at522 A. This series of absorptions, which would in-volve the simultaneous excitation of one valence (Ss)and one subvalence (4d) electron, cannot be ex-plained in a single-particle theory without correla-tion. Mansfield has attributed these double excita-tions to excited-state configuration mixing (ESCI)because of the weak appearance or nonappearanceof the 4d 5s 6snp series which would have indicatedISCI. ESCI refers to the mixing of various bound-state configurations. This predominance of ESCI isprobably caused by larger Ss-6s mixing in the effec-tive potential of the 4d 'Sp configuration of the ex-cited state than in the effective potential of theclosed 4d' core of the ground state.

In the ESCI model the states of the Rydbergseries [4d (5sSp P)] P3/2ns, nd (J =1) contain ad-

mixtures of other states with the same parity and

angular momentum. Let us write for the state ex-

cited at 588 A,

0(p) g 2 q +1 22 (q+e)1+@

E —EoI /2

(4)

where q and p are constant over the resonance, Eois the resonance energy, and I is the resonancewidth.

The q parameter, known as the Fano parameter,is given by

q=~X&d I

vI v &&a

I

~ lg &

(5)

f('P, ) =0.07 and f ( P& ) =0.53. Hartree-Fock(HF) calculations suggest that the state usuallycalled P~ at 12.82 eV is actually 85% 'P] and thestate called 'P] at 12.13 eV is only 14% 'P].

While the 588 A feature is by no means an isolat-ed resonance, it appears to have an order of magni-tude more oscillator strength than nearby reso-nances, so that it may be considered alone for mostof the present analysis.

Very little work has been done on the decay of anautoionizing state into several final ionic states. Ifthe outgoing channels reached through the autoion-izing decay can also be reached by direct photo-emission, then the two processes can interfere.Fano' ' showed that the interference in absorptioncaused by a discrete state P, embedded in many con-tinua, denoted by p, causes an absorption lineshapethat has the form

I 06, & =niI[4d'(Ss Sp 'P)l 'P3/26s 'Pi &

+a&I4d Ss Sp 'P~ &+ (2)

and p, which gives the strength of the interference,is given by

X&@ I

l'I p &&sI

~ lg&

where

a =1P=

2&0 Iv

I v &'1/2 1/2

The amplitude coefficient a] of the basis functionnominally characterizing the state is taken to bepositive, and a2 may be one of the smaller mixingcoefficients. The "double excitations" from theground state are primarily due to small admixturesof configurations which are connected to theground state by strong one-electron dipole transi-tions. Because of the strong transitions,

4d 5s So 4d 5s Sp ' P] (3)

at 12.13 and 12.82 eV, the 4d Ss Sp configuration ismost likely to appear admixed in Eq. (2). The oscil-lator strengths for these transitions are

(6)

gf =(0.195)q p o, l ('7)

where g is the statistical weight 2J+1, o., is ex-

where g represents the ground state, 4 is thediscrete state that has been modified by the continu-um, and Vis the Coulomb interaction.

The oscillator strength of the 588 A resonancecan be obtained by fitting the lineshape in Eq. (4) tothe total photoelectron yield from our measure-ments. The oscillator strength, f, is related to theparameters in Eq. (4) by

Page 7: Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

S48 P. H. KOBRIN et al. 26

pressed in Mb, I is measured in Rydbergs and f, q,and p are dimensionless. With q = —0.622=

7

p =0.27, and I =S.1&10 Ry from the fit to ourtotal photoelectron yield, u, =7.3 Mb and J=0, weobtain f=7.8X10 . Using this f value togetherwith those for Eq. (3) yields a 4d Ss Sp 'P corn-ponent a2 ——I g 10 . This small degree of configu-2 —3

ration mixing shows that the strong appearance ofthese "double-excitation" series is due primarily tothe strength of the transitions in Eq. (3) and not tothe magnitude of the mixing coefficient.

B. Partial cross sections

c0(DV)

CAV)O(3

Starace has addressed the problem of the form20

of the expression for each of several different outgo-ing channels in the neighborhood of a resonance.Davis and Feldkamp ' have derived equivalent ex-pressions using a different approach. We shall usethe notation of Starace. His expression for the crosssection of the pth observable photoemission channelat energy E is

o.p(p)o(p, e) = I e +2e[q Re(a ) —Im(a )]

1+@ P P

+ 1 —2q Im(a&)

20I

2I

Photon energy (eV)

22

FIG. 6. Partial cross-section measurements of the

4d5g2 (filled circles), and 4d3/2 (open circles) photoelec-trons. The solid curves are least-square fits to Eq. (l0)convoluted with the monochromator bandpass. Fittingparameters are given in Table II. Dashed curves showfits with monochromator broadening deleted.

—2Re(a&)+(q +1)I a& I

I

0.8—

where ap(p) is the off-resonance partial cross sec-tion for the pth asymptotically observable finalstate of the ion-electron system, e and q are theparameters that are used to characterize the totalabsorption in Eq. (4), and the complex parameter apis taken as constant over the resonance. The aPparameters are given by

'

(PI vIp) 2m„2&g I~

I P & &I I

I'I 0 &

0.6—

0.4—

0-- 0.2—O(DVl

OL

O O.2—

5s

5p

The summation extends over all observable pho-toelectron channels p, so that the term in angularbrackets is common to all channels.

Figures 6 and 7 show the partial cross sectionsobtained in the resonance region for each of the ob-served photoelectron peaks. The solid curves inFigs. 6 and 7 represent least-squares fits to thefunction

O. I—

f

0 20I

2I

Photon energy (eV)22

FIG. 7. Same as Fig. 6, for 5s and (unresolved) 5pphotoelectrons.

Page 8: Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

26 AUTOIONIZING RESONANCE PROFILES IN THE. . . 849

TABLE II. Fitting parameters for the partial and total cross sections. See Eq. (10) for thedefining equation.

Ionic state C2 o.o( e=0 ) (MB)'

4d 5$ S1/24d 5P P3/2, I /2

4d 5$ D5/24d 5$ D3/2

1.8 1(.10)2.89(.30)0.76(.03)0.76(.04)

1.3 1(~ 10)—0.46(.26)—0.35(.04)—0.56(.05)

0.3780.0844.362.5 1

Total 0.83(.04) —0.34(.05) 7.34

'Uncertainty & 1 in last significant figure.'Slope and curvature of oo(e) not given.

C& +Cze+ ecr(e) =Op(e)

1 +@~(10)

convoluted with a function describing the mono-chromator bandpass (a truncated triangular func-

O

tion with 2.5 A FWHM). Here 0p( e ) is a slowly

varying nonresonant partial cross section (we used apower series in e to order e ) and e is the reducedenergy variable of Eq. (4). The resonance widthI =0.07 eV and position Ep ——2 1.10 eV were heldfixed to be consistent for the entire set of profiles.The resonance position is in good agreement withthe 21.09 eV (588 A) value obtained in absorption. '

The 2.5 A ( =0.09 eV at 2 1 .1 eV) monochromatorbandpass is slightly larger than the linewidth (IFWHM =0.07 eV), making an accurate deterrnina-tion of I difficult.

The energy dependence of 0.(e ) in Eq. ( 10) isidentical to that in Eqs. (4) and (8)~ However, Eq.(4) represents the total absorption profile and doesnot apply to a partial cross section. This similarityhas led some experimenters to fit partial cross-section data to Eq. (4) and thus extract an effective

q and p . It should be noted that the treatments ofRefs. 19—21 do not provide a simple theoretical ex-pression for a q or p for each photoionization chan-nel. The fitting parameters are given in Table II.The C

&and C2 parameters for the total absorption

cross section correspond to q = —0.62 and p =0.27as given above.

The 4d 5/2 and 4d 3/2 partial cross sections havesimilar profiles, with the 4d 3/2 showing more in-terference. The total cross section, which receivesover 90% of its intensity from the 4d channels, hasa shape similar to the 4d partial cross sections. Theresonance profile of the 5s channel is opposite thatof the absorption: i.e., the 5s minimum is on thelow-energy side of the maximum while the absorp-tion minimum is on the high-energy side of themaximum. The 5s intensity shows a larger frac-

tional rise (= 1 ~ 2) than do the 4d's. The unresolved5p's have a nearly Lorentzian profile, with a frac-tional increase of 1.9. The 5p profile is slightlyhigher on the low-energy side but a symmetricLorentzian will fit it within experimental error.

What does it mean physically for the Ss and 4dresonances to have opposite phases? From Eqs. (8)and (9) we see that the resonance lineshape for eachchannel is determined by the a„parameter for thatchannel. The a& parameter is in turn a function ofthe amplitude matrix elements describing theresonant (autoionization) and nonresonant (photo-emission) paths from the ground state to the partic-ular ionic state in question. These matrix elementscan, of course, have a wide range of values, depend-ing on the electronic structure of the particularstates under study. Of the four parameters Ep, Ip, and q that describe the absorption process, onlyEp and I carry over to each photoemission reso-nance. The p and q parameters, if they are regard-ed as channel-sensitive quantities, are replaced foreach photoemission resonance by a set of a„param-eters in addition to the absorption q; i.e., two nurn-

bers for each channel p in addition to the integral qvalue derived from the absorption profile.

Now it is clear why Eqs. (8) and (10) cannot becombined to solve for Re(a„) and Im( a„). Theproblem is that several outgoing channels p (where

p specifies the fine-structure level of the core, theorbital and total angular momenta of the continu-um electron and the coupling of the core and con-tinuum electron) are present and unresolved in aphotoemission intensity measurement, which onlyselects the final kinetic energy of the outgoing elec-tron. For example the 4d 5/2 photoelectron peakcontains three outgoing channels:

4d ' 5s 'Sp +h v~4d Ss D5/2 +ep3/2

~4d 5s D,a++f5)2~4d Ss D5&z+sf 7/2 (111

Page 9: Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

850 P. H. KOBRIN et al. 26

o.(5p, @=0)=p 0, (q +1),which is obtained from Eq. (8) in the limit of0.0(Sp)~0. The same result has been obtained in-

dependently by Wendin for a two-channel case.This yields the partial decay width I

&pin the case

of no interaction between the autoionizing anddirect photoemission processes of the Sp channels(see Table III).

For the Ss final ionic state there are only two out-

going channels: the @pi/2 and ep3/2 waves. The di-

pole and Coulomb matrix elements for these twochannels determine two of the a& parameters:

a5„p and a&„p . When the spin-orbit interac-SeP1/2 SeP3/2

tion in the ep continuum is small, which is likelybecause of the diffuse nature of the continuumwaves, and the 'P resonance state shows no singlet-triplet mixing, ' then the partial decay widths of the

(13)

Each observable cross section 0.(j,e) for a particularphotoelectron peak j will then be the sum of several0.(p, e) in Eq. (8). The result is a form similar toEq. (8), in which the cro(p) has been replaced byoo(j), the total off-resonance partial cross section ofthe unresolved channels, and Re(a&), Im(a&), and

~ a& ihave been replaced by Re(a)~, Im(a)J, and

(~

a~ )J, which are averaged quantities that have

been weighted by the 0.0(p). Using the Schwartz in-

equality we know that

(Re(a)J) +(Im(a)i) ((~

ai )J,

so that the modified Eq. (8) is therefore dependentupon three unknown quantities Re(a)J, Im(a)J,and (

~

a~

)J. Because the fitting of experimentaldata to Eq. (10) yields only two parameters, it is im-possible to solve for these three unknown quantities.

While it is not feasible in general to draw specificqualitative conclusions from the photoemission in-

tensity resonance profiles above, there are excep-tions. For example, the Sp partial cross section isnearly Lorentzian which would imply little interfer-ence between the resonant and nonresonant process-es that contribute to its intensity. This point will bediscussed further in Sec. V. In the case of aLorentzian lineshape the height is given by

two channels become equal and the phase differencebetween the two dipole matrix elements becomesnegligible. Under these assumptions Eq. (12) be-comes

(Re(a)5, ) +(Im(a)5, ) =y(~

a~

)5, , (14)

where y depends only on the real ratio of the twodipole matrix elements. To determine y we use theoff-resonance value of the angular-distributionasymmetry parameter, p, for the Ss photoelectronswhich we have measured to be 1.85+0.1. It shouldbe mentioned that because the two dipole matrixelements are not equal off resonance we would ex-

pect P5, to change over the resonance even thoughthe resonance state is LS coupled. Our measure-ments of P&, near the resonance show a scatterdown to P=1.4 that cannot be interpreted in termsof a single resonance. A value of P equal to —1.85agrees with calculations that show a Cooperminimum below threshold and leads to a value of yequal to —1.06 Equations (8), (10), and (14) andthe fitting parameters in Table II may then be usedto obtain Re(a)5„ Im(a)5„and ( ia i )5, . To doso, it is necessary to solve a rather complicated qua-dratic equation for Re(a)q, and pick one of thetwo solutions. We reject the solution correspondingto (

~

a~

)5, ) 1 as implausible, because it would

imply that the Ss channels receive a fraction 13times larger of the resonance decay than of thedirect photoionization. The parameters for theplausible solution are given in Table III.

This analysis of the s channel is considerablymore complicated when the resonance state has in-termediate coupling and lies near a Cooperminimum as does the strong 4d Ss Sp 'P& reso-nance at 12.13 eV. In this case a strong variation ofp„over the resonance is to be expected and addi-tional measurements of the spin polarization arenecessary to obtain the internal distribution of theep&/2 and ep3/2 continuum waves. The spin polari-zation which was recently measured by Schaferset al. shows that the spin-orbit interaction nearthis resonance is strongly influenced and enhancedby the coupling between the discrete resonance andthe continuum states.

TABLE III. Partial decay widths and a parameters.

Ionic state (I;/I )X 100 Re(a) 1m&a)

4d' SP P3/21/24d' Ss SI/24d 5s D5/23/1

9 2

5.86.2

87

1.380.320.25

—0.450.31

—0.380.02

Page 10: Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

26 AUTOIONIZING RESONANCE PROFILES IN THE. . . 851

Information about the a parameters for the 4dchannels can also be obtained. Using the definitionsof a& in Eq. (9) and p in Eq. (6) we find

=p' (15)a, r

where I J is the partial width and oo(j) is the partialcross section for any set of channels. Using a sumrule for the I J,

probably derive their oscillator strength from in-

teractions with the 4d Ss 5p ' P&

states. By eluci-

dating the factors that cause the 588 A resonance tohave a negative q, we may learn something aboutthe other resonances as well.

The sign of the q parameter depends on the signsof the matrix elements in Eq. (5). First we considerthe transition matrix element (q~

~

r ~g) of thedirect absorption which for the 588 A transition is

given by Eq. (2) as

gr, =r, (16) ($6, ~

r~

4d' Ss 'So)

we can also obtain

X 0'f(17)

and

g 0'o(J)lm(a)J =0(18)

which can be derived in a manner analogous to Eqs.(41 ) and (42) in Ref. 20. The results in Tables IIand III are in good agreement with Eq. (18)~

A description of the partial cross-section resultsin terms of the derived a parameters proceeds asfollows. The values of (

~

a~ )J for the 4d, Ss, and

5p electrons show that the partial decay widths aredivided among the three channels in accordancewith their partial cross sections, with the 5p channel

having twice its share. The real and imaginaryparts of (a)q, and (a)4d show the distinct phaseshift between the Coulomb interaction integrals ofthe 4d and Ss channels, which is also apparent inthe profiles of the partial cross sections.

C. Fano q parameter

All of the asymmetric absorptions detected in the20—24-eV energy region displayed negative qvalues. Mansfield showed that the 4d ' 5pns, ndseries as well as the [4d (SsSp P)] P3/ins series

Since we have already found I 5~ and (~a

~ )5, we

can solve Eqs. (15) and {17)for (~

a~

)~, which isa weighted average of the 4d5/2 and 4d3/2 groups ofchannels. This done, we can use the line profile fit-ting parameters C

&and C2 for the 4d channels to

solve for Re(a)~ and Im(a)4d. These results arealso listed in Table III. A check of the results in

Table III can be made using the following relations:

g pro(j)Re(a)J. ——p o,

=a2(4d95s25p 'Pi~

r ~4d' Ss 'So) . 119)

The HF radial integral R~R 5zr dr togetherO

with the corresponding angular part shows that the(4d 5s Sp 'P,

~

r ~4d' Ss 'So) matrix element ispositive.

To calculate the matrix elements in the denomi-nator of Eq. (5) we make use of Eq. (6) and pub-lished calculations of the 4d~ep, ef cross sectionsand radial integrals. The denominator of Eq. (5)represents the indirect photoabsorption amplitudein which an electron is photoexcited to the continu-um and then scattered into the resonance state. Thecalculations for Cd, ' Sn, and Xe (Ref. 46) show

roughly equal cross sections for the 4d ~ep and4d~ef channel in the low-energy region. Becauseonly the calculations on Sn gave radial integralsrather than just cross sections, we have adjusted theSn results to our experimental 4d cross section.These scaled integrals and the values in Tables IIand III were then used to solve Eq. (6) in a nonrela-tivistic framework for the partial decay widths intothe 4d Ss ep and 4d Ss ef channels. Because ofthe quadratic character of Eq. (6), there are twosolutions, one with the p wave as the dominant de-

cay channel and one with the f wave dominant.Without configuration mixing in the excited statethere would be a vanishing I,f due to angularmomentum conservation. We have thus chosen thesolution with the p wave fraction greater than the

f wave which gives r,z/r, f &9 regardless of thesign of the 4d ' Ssep channel contribution. Thus thedenominator of Eq. (5) is positive, which leads tothe final conclusion that the negative sign of the qparameter is due to the negative sign of the mixingcoefficient a 2. The sign of a 2 is relative to certainwave function sign conventions. Since the con-siderations leading to the positive denominatorabove would be generally applicable to all of theCd I resonances in this region, we may expect thatthe corresponding mixing coefficients of the4d Ss Sp 'P

~ state for all of these resonances are

Page 11: Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

852 P. H. KOBRIN et al. 26

negative. We note that, given certain assumptions,an analysis of this kind can yield the sign of theamplitude coefficient when interference with thecontinuum is present. Without interference the signwould be inaccessible.

1.5

4~era(a)g

0.5

D. Resonance effects on the angular distributionand branching ratio

1.5— (b)

Other parameters sensitive to the effects of the588 A resonance are the Cd 4d branching ratio (Fig.8) and the angular distributions of the 4d electrons,expressed as the asymmetry parameters (Fig. 9).Starace has discussed the problem of the branch-

ing ratio of a spin-orbit split pair in the neighbor-hood of a resonance for the case in which no addi-tional final ionic states are accessible. His special-ized branching-ratio formulas are therefore not ap-plicable to the problem at hand. The shape of the4d branching ratio is caused by the 4d3/2 havinglarger percentage variations due to interference thanthe 4d5&2. This is supported by our expectation thatthe p wave is the dominant decay channel from theautoionizing state and that the 4d has morewave contributions than the 4dsr2 from direct ioni-zation.

Kabachnik and Sazhina have derived a generalexpression for angular distribution profiles near au-

toionizing resonances. Angular distributions havedifferent dependences than parital cross sections onthe matrix elements that characterize the excitationand decay of the autoionizing state. Kabachnik andSazhina's expression can be cast in the form

4d5rz 4dsz2& I

O

CO

CQ

L20 21

Photon energy {eV)

22

FIG. 8. The 4d branching ratio measurements nearthe 588 A resonance. The solid and dashed curves areratios of the solid and dashed curves in Fig. 6.

0.5—

20I

21

Photon energy {eV)

22

FIG. 9. Asymmetry parameter measurements of the

(a) 4d5rq and (b) 4d3/2 photoelectrons near the 588 A

resonance. The solid curves are visual fits to Eq. (20)

convoluted with the monochromator bandpass.

A~(j )+A2(j )e+e(g, e)= 0(g)

c,(j)+c2(j)e+e(20)

V. CORRELATION SATELLITES

Through detailed studies of the energy depen-

dences of correlation satellites it is possible to dis-

where e, ci(j), and c2(j) are the same as in Eq. (4),

po(j) is the off-resonant asymmetry parameter, and

A i (j) andA 2(j) are constants.

Our angular-distribution data for the 4d electrons

(Fig. 9) are not adequate to provide very accuratelineshape parameters. In Fig. 9 we have plottedcurves of the form of Eq. (20) convoluted with themonochromator bandpass and with Eo, I, c&(j),and c2(j) taken from the partial cross-section fit.The resonances in Fig. 9 appear asymmetric with

increases in P of over 0.5 unit, which would become1.0 unit in the absence of monochromator broaden-

ing. It can be seen that measurements made at the

21.21 eV Her resonance energy are affected by theresonance.

Page 12: Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

26 AUTOIONIZING RESONANCE PROFILES IN THE . 853

I I

5p: 5s

O 04—

0(9

I I I I i I

20 21 22 23 24 25

Photon energy (eV)

FIG. 10. The 5p:Ss branching ratio. The curves nearthe resonance region are represented by the parametersin Table II. The contribution from ISCI in the dottedcurve is 0.22, the solid curve 0.15, and the dashed curve0.06. The remaining contribution is from interchannelcoupling as discussed in the text.

tinguish between the largely energy-independent in-teractions (i.e., ISCI and final-ionic-state configura-tion interaction, FISCI) and the energy-dependentconfiguration mixings in the final state which in-clude the outgoing photoelectron. Such investiga-tions have been performed only for the rare gases.Correlation satellites from the photoionization ofCd have been observed previously. ' ' This earlierwork was restricted to the 4d '

5p P3/2 ]/2 satellites,which were the only ones detected at He I (2 1.21 eV)and He II (40.8 eV) resonance-lamp energies. Thetotal 5p intensity, relative to the Ss main line, wasfound to be 15% by Siizer et al. ' and 10% byHush et al. ' at 2 1 .2 1 eV. At 40.8 eV (Ref. 15) theSp ] /2 peak was obscured by an inelastic loss line,but the Sp3/2 to Ss ratio appeared to be the same asat 2 1 .2 1 eV. By comparisons with Zn and Hg, itwas concluded that most of the 5p satellite intensityarose from ISCI.' FISCI is not expected to contri-bute to the p satellite intensities of group II A andII B elements, for which the final ionic state is asingle electron outside a closed shell.

Hansen' calculated MCHF expansion coeffi-cients for Zn, Cd, and Hg which give 5p satellite in-

tensities that are too small by factors of 2.5 to 5.0.Siizer et al. pointed out that the MCHF expansioncoefficient ratios would have to be multiplied by thecross-section ratios for the different configurations,to yield relative intensities. This correction has nev-

er been made.Our measurements of the 5p:Ss ratio, shown in

Fig. 10, have a slightly downward sloping "base-line" value which is -0.22 at 21 eV. The 588 Aresonance and two resonances at 22.83 and 22.91 eV

perturb this smooth background. (This figure alsoillustrates the difficulty of obtaining a baselinewhen autoionization is present. )

Let us address the question of how large the ef-o

feet of the 588 A resonance will be on measure-ments made with a He I resonance lamp. Using thefits in Figs. 5 and 6 and Table II we calculate thatthe term in parentheses in Eq. ( 10) modifies thedirect photoemission intensity [oo(e) in Eq. 10] byfactors of 1.42 (Ss), 1.02(5p), 0.88 (4d&/2), and 0.83(4d3/2). This would cause the 5p:Ss ratio measuredwith He I resonance light to be 28 percent lowerthan the desired "off-resonance" value. The Sp:Ssratio of 0.15 of Suzer et al. is then in good agree-ment with the 0.22 value obtained in this work.

The Sp:Ss ratio shows a peaked resonance profile,with an enhancement factor of 2, about the 588 Aresonance, as discussed in the previous section. De-cay of the [4d (Ss5p P)] P3/26s 'Pt main com-ponent into the 4d Sp El continuum via autoioniza-tion leads only to an outgoing ed wave, by angularmomentum conservation. The nearly Lorentzianprofile of the 5p partial cross section signifies onlyweak interference between the resonant and non-resonant processes that produce the Sp satellite.This implies resonance enhancement by autoioniza-tion superimposed on a mostly ISCI-generatedbackground. The absorption spectrum shows thatthe Rydberg series converging on the 4d '

5p limitprobably derive their strength from interactionswith the 4d ' 5s 'So~(4d 5s 5p ) ' P~ resonance. '

Because this bound-state mixing (ESCI) should per-sist beyond the 5p threshold it is likely that part ofthe Sp satellite intensity originates from this in-teraction. To gauge the magnitude of this inter-channel coupling we have plotted three curves inFig. 10, each representing a different fraction ofISCI. The ISCI fraction is taken as being anenergy-independent contribution to the Sp:Ssbranching ratio. Interchannel coupling with thebound 4d 5s 5p ' P ] states at 12.8 eV is assumedto fall off as 1 /E . The data suggest that the ISCIcontribution to the branching ratio is around 0.15,which would correspond to a 4d Ss Sp ' P] admix-ture coefficient at 2 1 eV of less than 10 . Lower-energy measurements will be required to betterascertain the magnitude of the interchannel cou-pling contribution.

Two points were taken at 22.83 and 22.91 eV, tocoincide almost precisely with two of the strongestresonances seen by Mansfield at 22.83 and 22.92 eV.Mansfield tentatively assigned these features as

22. 83 eV[4d (5s5p P)] P3/26d

Page 13: Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

854 P. H. KOBRIN et al. 26

and

22.92 eV[4d (Ss5p P)] D, &z6d .

The Sp:Ss ratio is found to increase at theseresonant energies.

The branching ratio of the Sp spin-orbit split sa-tellite lines is shown in Fig. 11. The solid curve wasobtained by self-consistently fitting the Sp3/2 (a)and Sp&/2 (b) cross sections to Eq. (10) convolutedwith the monochromator bandpass, the total Spcross section to a symmetric Lorentzian equal toa+b, and the Sp branching ratio to a/b. The re-

sulting curve is given byT

3.24+0.33@+e

2 78—048 +The point at 20.81 eV is probably low due to asharp resonance at 20.83 eV. If the (unresolved) Sppartial cross section is a symmetric Lorentzian, thenthe Sp3/2 partial cross section has a larger high-energy tail and the Sp~/2 partial cross section has alarger low-energy tail. Previous measurements of pbranching ratios at the HeI energy' ' showed anonmonotonic decrease from Zn to Cd to Hg due to

0

the close proximity of the 588 A resonance in Cd.Our off-resonance value of 1.45+0.10 and the -2.0and 0.3 values obtained for Zn and Hg, respectively,clearly show the trend of increasing (p~/z) mixingwith the (ns) primary configuration as spin-orbitcoupling increases.

Three other satellite lines were seen for the firsttime in our spectra. They correspond to the 6s, Sd,

and 6p ionic states listed in Table I. By comparisonwith the higher binding-energy satellites found inthe group IIA elements, we would expect ISCI toproduce these satellites with no more than 2% ofthe intensity of the Ss main line. As can be seen inTable IV, the intensities detected in our experimentwere far greater than this.

The highest binding-energy (6p) satellite wasdetected only at the 22.83 and 22.92 eV resonances,while the 6s satellite was seen at two additionalwavelengths. At the 22.92 eV resonance the 6s sa-tellite had an intensity equal to 90% of the Ss mainline, as shown in Fig. 2. Since the 22.92 eV reso-nance width ( &1 A) is considerably less than ourmonochromator bandpass, the 6s satellite is prob-ably many times larger than the Ss main line at22.92 eV. The 5d satellite did not show enhance-ment due to autoionization at only a few selectedresonances; rather it was enhanced in every spec-trum that was recorded between 22 and 24 eV.Since the 5d satellite has a binding energy of 20.1

eV its absence below 22 eV photon energy may beonly a result of our lower sensitivity to low kineticenergy electrons. The same may be true of the 6ssatellite below 22 eV.

Production of the 6s and Sd satellites by the au-toionizing states between 22 and 24 eV can probablybe explained by ESCI and Auger decay. Theresonant states contain admixtures of several con-figurations having the form

4d SsSp6s 'P~

and

4d SsSpSd'Pj

O

0 2

~3/2 ~ I /2with various forms of internal couphng. ' Theseadmixtures can Auger decay to the Sd and 6s satel-lites.

CII0

CDKl

Photon energy (eV) 6s 5d 6p

TABLE IV. Satellite intensities relative to the Ssmain line ( =100)'.

t

zoI

2I

Photon energy (eV}

22

FIG. 11. The 5p branching ratio measurements near0

the 588 A resonance. The open square represents themeasurements of Suzer et al. , Ref. 14, and Hush et al. ,Ref. 15. The solid curve R(5p) is discussed in the textand includes monochromator broadening. The dashedcurve does not include broadening.

21.9122.4122.8322.9123.0023.4123.91

0(10)30(5)40(3)88(5)20(2)0(10)0(10)

27(4)19(4)7(2)

20(3)7(2)

31(3)12(2)

0(10)0(8)6(2)

19(3)0(8)0(7)0(6)

'Where intensity equals 0 the value in parenthesesrepresents an upper limit.

Page 14: Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

26 AUTOIONIZING RESONANCE PROFILES IN THE. . . 855

VI. CONCLUSIONS

The following conclusions were drawn from thisinvestigation of photoemission from cadmium va-

por in the h v= 19—27 eV range.(1) The 4d peaks show resonant behavior in both

P(e) and the branching ratio near 588 A. Devia-tions of the off-resonance branching ratio fromDirac-Fock calculations were observed, indicatingthe need for a more exact treatment of thisintermediate-Z atom.

(2) The Ss cross section is lower by about a factorof 2 than predictions based on RRPA theory. Itwas shown how most of this difference could be at-tributed to approximations made in the RRPA cal-culation.

(3) Photoelectron cross sections showed pro-nounced, and very different, resonance profiles atthe 588 A resonance for the 4d, Ss, and Sp lines.Thus photoemission resonances contain more infor-mation, and require a more detailed theory, than ab-

sorption resonances.(4) Parameters were derived from the cross-

section data for the 4d, Ss, and Sp lines at the 588 Aresonance, using a theoretical formalism given byStarace and by Davis and Feldkamp, together witha plausible set of assumptions.

(5) The resonance behavior of P(e) for the 4dpeaks could be fitted by an expression of the formgiven by Kabachnik and Sazhina, using parametersderived from the cross-section data and additionalamplitude parameters.

(6) The energy dependence of the Sp correlationsatellite was studied. Analysis showed that this sa-

tellite arises mostly from initial-state configurationinteraction (ISCI).

(7) The Sp peak intensity was greatly enhanced atthe 22.83 and 22.92 eV resonances.

(8) The Sp3/p and Sp&&2 satellites were analyzedseparately, and an earlier discrepancy in the sys-tematics of np satellites in group IIB elements wasresolved.

(9) Three new satellites —6s, Sd, and 6p—wereobserved for the first time, with high intensitiesprobably caused by autoionization.

In summary, this study has further demonstratedthe feasibility and value of variable-energy photo-emission measurements on metal vapors. By ob-serving several new phenomena in photoemissionfrom Cd, we have shown that correlation effectscan be elucidated in several ways in this type of ex-periment.

ACKNOWLEDGMENTS

This work was supported by the Director, Officeof Energy Research, Office of Basic EnergySciences, Chemical Sciences, Division of the U.S.Department of Energy under Contract No. W-7405-ENG-48. It was performed at the StanfordSynchrotron Radiation Laboratory, which is sup-ported by the National Science Foundation throughthe division of Material Sciences. One of us (U.B.)is indebted to the Deutsche Forschungsgemein-schaft (DFG) for financial support.

'Permanent address: Institut fur Strahlungs-und Kern-Physik, Fachbereich Physik, Technische UniversititBerlin, 1000 Berlin 12, West Germany.

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Page 15: Autoionizing resonance profiles in the photoelectron spectra of atomic cadmium

856 P. H. KOBRIN et al. 26

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The peak areas in Refs. 14 and 15 do not represent an-

gle integrated partial cross sections since the electronswere sampled 90' from the propagation axis of the un-

polarized light. This would most likely give a ratiolower than the desired angle integrated one.The Hg p branching ratio may also be perturbed by aresonance. See M. W. D. Mansfield, Astrophys. J.180, 1011 (1973).