Journal of Electron Spectroscopy and Related Phenomena, 13 (1978) 77-84 @ Elsevler Sclentlfic Pubhshmg Company, Amsterdam - Prmted m The Netherlands

BRANCHING RATIOS AND THE PARTIAL PHOTOIONIZATION CROSS-

SECTION FOR THE 3s ELECTRON OF ARGON

K H TAN and C E BRION

Department of Chemrstry, Unrvers@v of Br&sh Columbia, Vancouver V6T 1 W5 (Canada)

(First recewed 26 June 1977, m final form 8 August 1977)

ABSTRACT

Binding-energy spectra obtamed using the dipole (e, 2e) electron impact

comcldence method have been used to denve the 3s/3p cross-section ratios for the

photolomzatlon of argon up to 75 eV The 3s and 3p photolomzatlon branching ratios

have been obtained by making use of recently determined double photolomzatlon

yields The partial photolomzatlon cross-section (oscillator strength) for 3s lomzatlon,

obtained usmg the branching ratio and the known total photolomzatlon cross-sectlon,

shows the deep mnumum ca 10 eV above threshold which has been predicted by those theoretlcal calculations which mclude electron correlation effects Below 50 eV

the cross-sectlon 1s m excellent agreement with the SRPAE calculation The results

are m close agreement with recent measurements made using synchrotron radlatlon

but are consistently smaIler below the mlmmum and larger at the higher energies

INTRODUCX’ION

The partial photolomzatlon cross-sectlon of Ar(3s) 1s known to be very small

(< 1 Mb) In the region above the 3s lonlzatlon threshold (29 24 eV) the total photo-

lomzatlon (photoabsorptlon) cross-sectlon 1s also very small, passmg through a very

low “Cooper” minimum1 - 3 Consequently 3s and 3p photolomzatlon branching

ratros are difficult to measure m the energy region above 30 eV

Theoretlcal estimates of the total cross-sectlon4- 7 have achieved good

agreement with experiment when adequate account 1s taken of electron correlation

effects A variety of theoretlcal calculations have been carried out for the 3s partial

photolomzatlon cross-section Hartree-Fock calculations’ mdlcate a steady rise from

threshold and a levelhng off at ca 60 eV However, when rntershell electron correlation

effects with the 3p electrons are taken mto account the cross-section IS predIcted to

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decrease from threshold to an essentially zero mmlmum at ca 40 eV and thereafter

to mcrease agam, Ievelhng off at higher energies Several such calculations of the

Ar(3s) photolomzatlon cross-section have been made mcludmg those using the

RPAE’, SRPAE’ * and R-matrix’ methods While the general shape of these calcula-

trons IS slmllar the detailed behavlour differs

It 1s possible m prmclple to measure the separate 3s and 3p photolomzatron

cross-sections by means of photoelectron spectroscopy (PES) The rather hmlted

data provided by early PES experiments using both line sources1 ’ and synchrotron

radiation’ *? ’ 3 have confirmed the need for electron correlation effects to be included

If the correct form of the cross-sectlon 1s to be calculated but the results have not been defimtlve over a wide energy range Very recently Houlgate et al l4 have reported a

much more detalled PES study up to ca 90 eV using continuum radlatlon from the

Daresbury synchrotron In this experiment ’ 4 the 3s/3p photolomzatlon ratios were

measured by observing the photoelectrons m a direction along the electric vector of

the incident radiation (1 e at 8 = 90” to the mcldent beam) In such a configuration

the peak mtensltles are subject to angular dlstrlbutlon effects’ 5 Therefore Houlgate

et al l4 measured the angular dlstrlbutlon for 3p lomzatlon at each energy to obtain

the angular amsotropy parameter p3@ as a function of energy This measured value of

p3p was then used, together with an assumed vaIue of 2 for j&, to correct the observed

3s/3p ratio for angular dlstrlbutlon effects However the assumption /?3s = 2 IS very

questIonable m view of the strong mtershell correlation effects which cause the 3s electron to folIow the 3p behavlour to a considerable extent Allowance was also

made by Houlgate et al l4 for the percentage polarlzatlon and the transmlsslon

efficiency of the electron analyzer as a function of energy At higher energies correc-

tions for multiple romzatlon were made by using the data of Samson and Haddad 1 6

to give the photolomzatlon branchmg ratio Fmally the corrected 3s branching ratios

were converted mto absolute 3s cross-sections using the total photolomzatlon cross-

sectlon data of West and Marr3

From the angular-dependence of photoelectron eJection’ 5 It can readily be

deduced that at the so-called magic angle (0 = 54 7 “) the observed mtensltles are

directly proportional to the partial photolomzatlon cross-sectlons and no correction

for angular dlstrlbutlon effects IS necessary Thus a more direct determination of the

3s partial photolomzatlon cross-section could be made by magic-angle PES To date

no such measurement has been made with the exception of the three data points

reported by Samson and Gardner1 1

In this Iaboratory the dipole (e, 2e) electron Impact comcldence method has

been developed as a quantitative slmulatlon of photoelectron spectroscopy1 7 - 2 *

The virtual photon field associated with the fast lmpactmg electron provides a

continuously tuneable energy source (the energy loss m the forward channel 1s

analogous to the photon energy) Under condltlons (I e K* -+ 0) pertammg to the optical hmlt of the Bethe-Born approxlmatlon lg. ” dipole photolomzatlon cross- sections (oscillator strengths) may be obtained from the electron Impact measurements

79

Recent theoretical work1 * has mdlcated the existence of a correspondmg magrc angle

(54 7 “) for the dipole (e, 2e) slmulatlon of PES and partial photoromzatlon cross- sections have been reported for CH, (ref 22) and NH, (ref 23) In this paper we now report (e, 2e) measurements of the Ar 3s/3p dipole lomzatlon ratlo wrth the eJected electrons being observed at the magic angle

EXPERIMENTAL

The basic apparatus’ 3 and comcldence electromcs2’ have been described m earher pubhcatlons Briefly electrons are accelerated to 3 5 keV and allowed to interact with a gaseous target Forward, melastlcally scattered, electrons (sohd angle

ca 10e4 sterad) and electrons ejected at an average angle of 54 7’ (sohd angle ca

5 x lo- 3 sterad) with respect to the incident-beam direction are energy-analyzed by hemlspherlcal electrostatic analyzers and detected m comcldence The gas pressure 1s

maintained at a sufficiently low level such that losses arising from secondary scattermg are negligible This 1s particularly important for measurements near photolomzatlon thresholds where the ejected electron energy IS small It 1s also necessary to ensure that the transmlsslon efficiency 1s pressure-independent’ a The transmlsslon function

of the analyzer was determined using the comcldence method described earlier “1 ’ 3 Furthermore a background ramp of electrons near zero electron energy snmlar to that often observed m PES (see for example the work of Plummer et al 24) has been effectively suppressed by surtable collrslon chamber design as well as by freshly coating all surfaces with benzene soot This precaution 1s particularly necessary m the

present measurement since the 3s cross-section 1s exceedingly small and the accurate determmatlon of near-threshold mtensltles 1s crucial to a satrsfactory evaluation of the various theoretlcal models All measurements were carned out usmg a combined

comcldence FWHM energy resolution of 1 5 eV Gas samples were taken directly from commercial cylinders The binding-energy spectra did not mdlcate any measurable

impunties

RESULTS AND DISCUSSION

The 3s/3p mtenslty ratros were determmed using two different methods In the first method the bmdmg-energy spectrum was obtained at each energy loss (photon energy) by recording the comcldence count-rate as a function of the eJected electron energy Typical spectra are shown m Fig 1 at 33, 40 and 60 eV correspondmg to near-threshold, mmimum and higher energy regions of the 3s partial photolomzatlon cross-section It should be noted that the mtenslty scale m Fig 1 1s not the same for the

three spectra The raw spectra were then corrected for electron transmlsslon efficiency as a function of ejected electron energy usmg the correction curve we have reported m an earlier pubhcatlon2 ’ The 3s/3p mtenslty ratios were obtained from the corrected

peak areas The bmdmg-energy spectrum (Fig 1) at 33 eV 1s ca 4 eV above the 3s

80

IO 15 20 25 30 35 BINDING ENERGY (eV)

Figure 1 Binding-energy spectra for argon 3s and 3p electrons at 33, 40 and 60 eV (note vertrcal scales are different for each spectrum and the data are shown prior to correction for electron trans- mlsslon efficiency) The insert compares the Ar(3.s) and He(ls) peak shapes

lomzatlon threshold and it can be seen that there 1s a slgmficant contrlbutlon from

3s lomzatlon as 1s predlcted by all calculations which Include electron correlation

effects At 33 eV the 3p photolomzatlon cross-section 1s still quite appreciable as can

also be seen from the total photolomzatlon cross-sectlon2’ 3 The spectrum at 40 eV

shows a neghglble slgnal correspondmg to 3s m comparison to that correspondmg to

3p lomzatlon If it 1s remembered that m this energy region there 1s the very deep

Cooper mmlmum m the total cross-sectlon so that the 3p slgnal at 40 eV 1s Itself

exceedingly small then, evidently, the 3s cross-section must be quite mmlmal here At 60 eV the 3s/3p ratio has increased slgmficantly

The intensity ratios have also been determined from measurements of the

transmlsslon corrected count-rates at energies correspondmg to the maxlma of the

3p and 3s binding-energy peaks The peak energies were switched repetltlvely using a

voltage-level shifter synchronized with the multichannel analyzer sweep The relative

numbers of channels per scan were adJusted to make the countmg statlstlcs comparable

for both the 3p and the weaker 3s peak The 3s/3p ratio was obtamed directly (after

normahzmg the counting times and correcting for transmlsslon) smce the peak half-

widths for 3s and 3p were found to be the same wlthm experimental error at the

energy resolution employed (FWHM = 1 5 eV) A further check to show that the

doublet @‘3,2, 1/2, sphttmg = 0 178 eV) character of the (3~)~ 1 state did not cause

81

TABLE 1 .

BRANCHING RATIOS, AND PARTIAL CROSS-SECTIONS FOR THE PHOTOIONIZATION OF THE 3s ELECTRON OF ARGONa

Energy lOSS

leV)

32 8 0 031 0 030 ( 6) 33 8 0 023 0 022 ( 9) 35 8 0 023 0 022 ( 8) 37 8 0012 0 016 (10) 39 8 0000 OOOO( 4) 41 8 0 012 0011 (11) 448 0 061 0 057 (43) 46 8 0 103 0 093 (35) 49 8 0 124 0 102 (40) 51 8 0 129 0 106 (68) 54 8 0164 0 123 (28) 59 8 0 226 0 155 (38) 648 0 267 0 177 (35) 69 8 0 266 0 177 (37) 74 8 0 223 0 153 (68)

Measured mtenslty rat10 b

3sl3p

Branchrng ratloc

3s 3P

0 970 ( 6) 0 978 (10) 0 978 (10) 0 983 (13)

lOOO(4) 0 989 (11) 0 943 (44) 0 907 (46) 0 826 (59) 0 782 (65) 0 754 (40) 0 685 (38) 0 658 (42) 0 664 (48) 0 687 (68)

Total Argon 3s photolomzatron phutolonrzatmne cross-sectron (Mb)d cross-sectron o (Mb)

16 7 0 500 (100) 142 0 310 (127)

94 0 210 ( 75) 59 0 094 ( 59) 37 OOOO( 14) 22 0 024 ( 24) 1 25 0 070 ( 53) 0 97 0 091 ( 34) 0 92 0 094 ( 37) 1 01 OllO( 70) 1 19 0 146 ( 33) 1 37 0213 ( 52) 1 45 0 257 ( 51) 1 48 0 262 ( 55) 1 48 0 227 (101)

Values rn parentheses represent the uncertamtles m the derwed quantities This represents the 3s/3p mtenslty ratro corrected for analyzer transmwslon efficiency Branchmg ratlo (3s) = 3s/(3s + 3p + 2+) etc The data for multiple lomzatlon are taken from ref 30 Thrs correction has been made above 46 8 eV From data of West and Marr3 a(Mb) = 1 0975 x lOa(dfldE) (eV)-l

any slgmficant broadening of the 3p peak relative to that for 3s ionization IS shown by

the insert m Fig 1 From this it can be seen that the “doublet” Ar3p peak has the

same width, wlthm experimental error, as the Hels peak The 343~ mtenslty ratios

obtained by the two methods are m good agreement and the values are shown m Table

1 The photoromzatlon branching ratlo b, for a given lomc state z IS given by

(1)

where 6, = partial photolomzatlon cross-section, CT = total photolomzatlon cross-

section, df’/dE = partial oscdlator strength for photolomzatlon to state I, dfldE,,,, 1 =

total oscillator strength for photolomzatlon, and G (Mb) = 1 0975 x 10’ (dfdE)

(eV) - ’ At energies where total lomzatlon equals total absorption (1 e where the

loruzatlon efficiency IS umty) a, may be replaced by the total absorption cross-sectlon

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EJECTED ELECTRON ENERGY &(eV)

I I I I I 1___1 30 40

EGFRGY I? (eV) 70 80

Figure 2 Partial photolomzatlon cross-se&Ion (oscillator strength) for the 3s electron of argon, HF-Vs, RPAEg, SRPAElO, R-matnxv

(and slmrlarly for the oscillator strengths) In earher studies of molecules’ 1y 2 37 ’ ’ we

have equated (dfldE)t,t,L with E,(df/dE) since m these cases the contrlbutlon from

multiple loruzatlon has been shown to be negllglble26Y 27 However for argon, double

photolomzatlon must be taken into account smce It makes an appreciable contrlbu-

tlon’ 6$ ’ * - 3o to the total at the higher energies involved m the present experiment

(1 e above ca 50 eV) Multiple lomzatlon will only be observed as a broad background

m the (e, 2e) binding-energy spectrum The (2+/l+) mtenslty ratios for argon have

recently been the subject of three independent studies Samson and Haddad16 and

Schmidt et al 2g have employed methods using a many-line light source and synchro-

tron radiation respectively These results are m excellent agreement with those

obtamed by Wlght and van der Wle13’ using the (e, e + ion) experiment which

provides a quantitative slmulatlon of photolomzatlon mass spectrometry comple-

mentary to the present (e, 2e) experiment* Using the (2+/l +) ratlos3’, the corrected

3s and 3p branching ratios are obtained as shown m Table 1 Substltutmg the branch-

mg ratios into eqn (l), crl has been calculated for 3s lomzatlon using the total photo-

ionization cross-sectlons of argon reported by West and Marr3 The latter are in good

agreement with earlier measurements obtained optically2 and by electron-ion comcl-

dence”’ The 3s partial photolomzatlon cross-sections are shown m Table 1 The 3s

partial cross-section (oscillator strength) 1s shown rn Fig 2 together with the synchro-

* For a review of these slmulatlon experiments see ref 20 The complementary nature of the (e, 2e) and (e, e + ion) experiments IS well dlustrated by recent studies of the dipole-induced break- down of NHs (ref 23) and Hz0 (ref 31)

83

tron PES data of Houlgate et a1 I4 and the various theoretIca calculations The agreement with the PES data IS wlthm the respective error bars However, it IS

apparent that the present (e, 2e) results are consistently lower than the synchrotron

PES dataI below the mmimum whereas the (e, 2e) data pomts are consistently

higher above 60 eV The mlmmum IS estimated to he at ca 40 eV from the (e, 2e) data

whereas PES14 indicates a mmimum m the 41-43-eV region This raises the questlon

of the accuracy of the energy scales In the (e, 2e) experiment the energy scale was

calibrated dn-ectly m our instrument by tuning the energy Ioss (“photon energy”) m

the non-comcldent forward channel to the large excltatlon peak of argon at 11 8 eV

correspondmg to the excltatlon Ar(-3s23sp6) --, (-3~~3~~4s) which IS an unresolved doublet under our experimental condltlons The energy loss IS derived from a hlgh-

precision power supply (Fluke 412B) and it IS estimated that the energy scale IS

accurate to better than f 0 2 eV The difference between the (e, 2e) and PES data may

possibly be due, m part at least, to the fact that the PES determination IS less direct m

that It also mvolves the measurement and use of pJg, as well as the questionable

assumption that pas = 2, to remove the effects of the angular amsotropy The (e, 2e)

measurement IS, on the other hand, made directly at the magic angle The three data

points reported by Samson and Gardner1 1 usmg magic-angle PES are m close agreement with both sets of measurements The smgle data point of Samson and

Can-ns3’ IS also shown on Fig 2

The (e, 2e) data pomts fit the SRPAE curve lo very well from near threshold

and through the mnumum up to at least 50 eV At higher energies the experimental

data level off m near agreement with values predicted by the R-matrix’ and HF8

calculations The RPAE calculatlon9 gives perhaps the best compromise fit up to the hmlt of the calculation at ca 60 eV above which It appears to be levellmg off to a

cross-section close to the (e, 2e) measurements at the higher energies

In conclusion then the dipole (e, 2e) slmulatlon of photoelectron spectroscopy

gives results m close agreement with recent PES studies for the 3s photolomzatlon

cross-section of argon and confirms the existence of significant electron correlation

effects

ACKNOWLEDGEMENTS

Fmanclal support for this work was provided by the North Atlantic Treaty

Orgamzatlon and the Natlonal Research Council of Canada We thank A Hitchcock and M J van der Wlel for helpful comments

REFERENCES

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