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Multiple ionization of He and Ne by 10 keV electrons as a function of the energy loss
Physica 54 (1971) 41 l-424 6 North-Holland Publishing Co.
MULTIPLE
IONIZATION
OF He AND
AS A FUNCTION
OF THE
M. J. VAN DER WIEL F,O.M.-Institwt
Ne BY
10 keV ELECTRONS
ENERGY
LOSS
and G. WIEBES
VOOY Atoom- en Molecuulfysica, Amsterdam, Nederland Received 25 February 1971
Synopsis Oscillator-strength spectra are reported for transitions to the He’+. sf and Nei+ - 3+ continua. The spectra, covering a range of energy transfers from threshold up to 250 eV, were derived from the small-angle, inelastic scattering of 10 keV electrons in these gases, observed in coincidence with the ions. Our data show that the ratio of double and single ionization passes through a maximum before approaching the asymptotic value at high-energy transfers. This result is in disagreement with earlier photoionization experiments, but it supports recent theoretical work on double ionization in He.
1. Introduction. In order to study the effect of electron correlation in atoms, we have undertaken the investigation of multiple ionization of the noble gases by fast electrons. The first step in this program was the determination of the relative abundances of the different charge states of these gases (He, Ne and Arr), Kr and Xes)) as a function of electron impact energy. Next, we developed a methods) to measure the small-angle, inelastic scattering of a 10 keV electron in coincidence with the ions formed and to transform
the observed
intensities of scattering
into a spectrum
of
atomic oscillator strengths. Application of this method to ionization in both the M- and L-shell of Ar4) has revealed a number of new aspects of multipleelectron processes. In continuation of this program, we now present the data on He and the outer shell of Ne, i.e. the oscillator-strength distributions for Hei+? s+ and Ner+-3+ over the energy range from threshold up to 250 eV. The measurements were performed with a resolution of 5 eV fwhm. The main purpose of this work is to test whether in the ionization in an outershell the “shakeoff limit” [a constant ratio of double and single (photo)ionization] is reached so near threshold as it appears from the work of Carlsons). Our results for A+) are in disagreement with the general picture given in ref. 5. A clear maximum is reached in the ratio of double and single ionization as, a function of the energy transfer. Further, we presumed that the energy at which the 411
M. J. VAN DER WIEL AND G. WIEBES
412
curve levels off to an asymptotic value is influenced by the presence of a relatively close inner shell. Since He has only two 1s electrons and the K shell of Ne is considerably obtain more information
deeper than the Ar L shell, one may expect to
on the validity
of a shake-off
description
from an
investigation of these two gases. Furthermore, calculations are available69 7) of the oscillator-strength spectrum for formation of Hes+, with which we shall compare our data. Our previous valuesi) for a weighted integral of the oscillator-strength distribution, as obtained from the impact-energy dependence of the total cross section for multiple ionization, will serve to check the reliability of the present data. 2. Experimental. The apparatus and experimental procedure have been described elsewhereat4) in considerable detail. The essentials are: A 10 keV electron beam passes through a gaseous target of about 10-s torr density. The ions produced by the beam are extracted and charge-analysed. Electrons, scattered through a small angle ( RS5 x 10-3 rad) are retarded and selected in energy loss. The two particle detectors feed their signals into a delayed coincidence circuit. The true coincidences, after being separated from the simultaneously registered accidental ones, are stored in a data collectors), which drives the energy-loss scanning. When measuring He s+, the charge analyser also passes Hl fragments from background molecules. However, the total ion current of Hes+ exceeded that of Hz by a factor of 250. Since it is reasonable to assume that most of this Hz is formed at energy losses below the He s+ threshold, its contribution to the coincidence completely.
signal,
differential
in energy
loss,
can
be neglected
3. Results and discussion. 3.1. General. Since our results for multiple ionization will prove to differ markedly from those obtained by Carlsons) in photoionization, we emphasize one aspect of our derivation of (apparent) oscillator strengths in somewhat greater detail than before. The method, as described in ref. 3, is based on the Born relations) for electron scattering through
an angle 0 at an energy loss E (leaving out a few factors
not relevant 40, E) -
in the present
which are
discussion) :
(1/K2) df(K)/dE,
(1)
where K = K(8, E) is the magnitude of the momentum transfer and df(K)/dE the generalized oscillator strength. In the region of K < 1 a-u. it is convenient to expand df (K)/dE in terms of Kz: df(K)/dE
= df/dE + AK2 + BK4 + . . . .
(2)
Let us confine ourselves to the first two terms of this series and consider the magnitude of A with respect to df/dE. Silverman and Lassettreia) measured
MULTIPLE
-1I 0
IONIZATION
50
OF He AND Ne
413
I-2 100 energy loss(eV)
Fig. 1. a) Approximate ratio A/(df/dE) (see eq. 2) for He and H (solid curves, left vertical axis) ; b) Contribution of term AK2 (relative to df/dE) to the inelastic scatter& cross section at 0 = 5 x 10-3 rad (dashed curves, right vertical axis).
a part of the function df(K)/dE at a number of energies in the Her+ continuum. From an extrapolation of their results to K = 0, the optical limit (Samsonii)), we have obtained approximate values of A (df/dE)-1. It appears (see fig. 1, He, solid curve) that A is negative and of order unity at threshold. Further above threshold A (df/dE)-1 c h an g es sign and eventually approaches zero. A similar trend (a decrease from an appreciable value near threshold towards zero at high-energy transfers) is found for Hi”) (see fig. 1, H, solid curve). This is a general feature for all atoms, expressing the fact that at high energy transfers df(K)/dE is constant for all K up to a sharp “binary collision” peakis) at $Ks = E (in a.u.). In order to be justified in equating df(K)/dE to df/dE, as we did in ref. 3, without appreciable error due to the neglect of AK2 (and higher terms in eq. 2), we require K2 to be such that AKs(df/dE)-1 < 1 over the whole continuum. This condition is fulfilled in our experiment by taking a scattering angle of 5 x 10-s rad [see fig. 1, AKs(df/dE)-1, dashed curves]. The maximum error appears to amount to only a few percent. At energy losses is sufficiently small, data were taken above 150 eV, where A Ks(df/dE)-1 at an angle of 8 x 10-a rad. At smaller angles than this, a tiny fraction of the primary beam enters the energy analyser and is not suppressed completely (1 : 101”). Such primary electrons produce an unwanted signal (raising the number of accidental coincidences) on the electron detector, of a magnitude comparable to the true scattered signal at the very highest energy losses. In the case of double ionization one might suspect that, due to the (in zeroth order in the interelectronic interaction) forbidden character of any double electron transition, df/dE might be vanishingly small or at least
414
M. J. VAN DER WIEL AND G. WIEBES
He?’ E.lOO eV
scatt.angh(rad) Fig. 2. Angular dependence of intensity of scattering, leading to He”+ at E = 100 eV. Solid curve: (K2)-1 including correction for angular resolution. Dashed curve: (P-1. Dash-dotted curve: [(Kz)-1 + 11.
much smaller than AK3. For this reason we measured the angular dependence of scattering leading to He 2+ at an energy loss of 100 eV, an energy at which the scattering intensity is at its maximum and any higher terms in eq. (2) are expected to be largest. Fig. 2 shows that the experimental points do not deviate measurably from a behaviour according to eq. (1) with neglect of terms higher than dj/dE in eq. (2). The solid curve represents (K3)-1, including a correction3) for the angular resolution. The magnitude of this correction can be inferred from a comparison of the solid and the dashed curves, the latter giving (K3)-1 without correction. Also a curve representing a hypothetical case with A(df/dE)-1 equal to plus unity, i.e. [(K3)-1 + 11, has been drawn (fig. 2, dash-dotted line). It is evident that a term AK3 of such magnitude would be detectable in our experiment. From our data points at the two highest angles we can estimate an upper limit for A (df/dE)-r of roughly f0.3. This means the possible error due to the neglect of higher terms in eq. (2) at 5 x 10-3 rad amounts to f 1%. So in this respect the behaviour of df(K)/dE for the He3+ continuum is not drastically different from what was known already for the corresponding transitions in Ar3) or the 2s2p excitation of Herd). Fig. 2 also illustrates that the choice of scattering angle (5, respectively 8 x 10-3 rad) is a suitable one. On the one hand the correction for the angular resolution is small (although it is fairly well established, see e.g. ref. 3). On the other hand, higher terms of eq. (2), even if they are large, do not contribute significantly.
MULTIPLE
IONIZATION
OF
TABLE Values
of (df/dE)n+
He
AND
Ne
415
I
for He (n =
1,2) and Ne (n =
1, 2, 3)
Hel+
Hesf
Nel+
Nes+
Nes+
(in 10-3 eV-1)
(in 10-5 eV-1)
(in 10-s eV-1)
(in 10-3 eV-1)
(in 10-5 eV-1)
7.82
-
-
Energy loss E (eV) 30
47.5
40
28.0
50
17.3
60
13.2
-
7.73 6.88 6.10 5.25 4.45
0.72
11.3
3.70
2.10
3.95
13.8
3.05
2.44
3.02
13.6
2.55
2.60
2.33
12.9
2.20
2.62
-
1.84
9.9
1.80
0.15
70
8.75
80
6.60
90
5.05
100 110 120 130
1.28
1.57
140
1.52
8.3
1.55
2.59 2.51
150
1.26
6.9
1.32
2.38
2.2
0.60
160
1.03
5.8
1.13
2.15
170
0.88
5.0
0.99
1.90
3.3 4.1
180
0.75
4.1
0.86
1.70
4.6
190
0.66
3.5
0.74
1.55
5.0
200
0.57
3.0
0.65
1.37
5.4
210
0.49
2.6
0.58
1.26
5.6
220
0.43
2.2
0.50
1.15
5.7
230
0.38
1.9
0.44
1.06
5.7
240
0.33
1.6
0.39
0.97
5.8
250
0.29
1.4
0.34
0.90
5.9
TABLE Asymptotic
ratio
II
(df/dE)s+/(df/dE)l+ Independent
Atom
This work
electron
“Exact”
value
approximation He Ne Ar
-
7 x
1.5 to 2 x 2.5 x
10-l
10-l
lo-3
6)
4.5 x
10-s 5)
3.8 x
10-s 5)
1.66 x
10-s ‘3) -
Thus, a spectrum of scattering intensities measured at one of the angles mentioned, is converted into a df/dE spectrum by means of eq. (1)) including the correction for the angular resolution, but with neglect of higher terms in eq. (2) throughout the continuum. Our relative spectra are normalized, using the relation crphotoion.(Mb) = 109.75 df/dE (eV-r), on the F)hotoionization cross sections of Samsonrr) ; at 40 eV for He and at 35 eV for Ne. Accord-
M. J. VAN DER WIEL AND G. WIEBES
416
ing to fig. 1, AK2 (d//d-E-r for He equals about 8 x 10-a at 40 eV, which is smaller than the uncertainty of our measurements. The results have been plotted in figs. 3 and 4. In table I we listed the df/dE values at 10 eV energy loss intervals,
as obtained
from a smooth, averaged curve through the actual
data points. 3.2.
Helium
(fig. 3).
The present
Hei+ spectrum
agrees within
a few
percent with that of Samsonrr), from threshold up to 60 eV, except at threshold due to the effect of the energy resolution (5 eV fwhm for this study), At higher energy losses there is a wealth of calculations of 1ss - ( 1s&p) ionizationi5-is), with which to compare our data, but different wave-
. .
‘.
this work
,252P
10-L
-
(d’,” dE
o .
*
Bel1.K.
C$)n:Lukirskii.
BC.2
idem .AUen
10-C
10-L
10-L
10-s I 0
i
I 100
I 200
I 300 e-ergy
105s (aV)
Fig. 3. Oscillator-strength spectra for ionization of He. An averaged curve through our data points for He 1+ coincides with the spectrum of Bell and Kingston 17).
MULTIPLE
IONIZATION
OF He AND Ne
417
functions and formulations of the matrix elements still produce uncertainties of the order of 10%. We have chosen to plot one of the spectra of Bell and KingstonIT) (in dipole-length formulation), since it appears to agree quite well with the present data, in sofar as the large scatter above 200 eV permits to draw such a conclusion t. Due to the uncertainties of the theoretical values, the agreement with our results still leaves room for a contribution of excited Heif states, i.e. states of the ion with n 2 2, as included in our of such excited continua was measurement of (df/dE) I+. The contribution measuredra) to be about 8% and calculated2°p21) to be 7% at very high energy transfers. In the Hesf spectrum we observe the same features as we found to be characteristic for double ionization in Ar4) : a more or less linear rise, from a vanishing oscillator strength at threshold, to a broad, flat maximum at about 20 to 30 eV above threshold, followed by a monotonic decrease. The only data with which we can compare this spectrum, are the theoretical curves of Byron and Joachain6) (see fig. 3), which were recalculated with a different ground-state wavefunction by Brown 7). It appears that the curve calculated with the position matrix element is in good agreement with ours at energies up to and including the maximum, whereas the “momentum” curve, which has the correct asymptotic behaviour (E-g) seems to approach the same limit as our curve. Such a difference in the range of validity of two calculations, based on different matrix elements, is quite common. For instance in the case of single photoionization in Ne the situation is remarkably similarss). The uncertainties in He photoabsorption measurements, i.e. (df/dE)i+ + (df/dE)s+, for instance those obtained by Lukirskii et a1.23) from averaging their values with “best” values from literature or the one point by Allen24) (see fig. 3), are too large to detect a significant departure from the (df/dE)l+ spectrum of Bell and Kingstoni7). Therefore no independent determination of (df/dE)s+ can be made at present.
3.3. Neon (fig. 4). The Ne r+ data are in quite good agreement with those of Samsonrl) over the whole energy range (up to 60 eV), apart from a too strong decrease at threshold due to the effect of the energy resolution. Structure as reported in our previous paper-a) is not observed in the present, more accurate spectrum. A comparison of these data with the most recent “best wavefunction” calculation by Henry and Lipskyss) shows discrepancies of the same type as we discussed for Hes+. In this calculation no Nel+ excited states were taken into consideration. t The extremely bad statistics responsible for this scatter, is due to the fact that e.g. at 300 eV energy loss, only one or two out of 10s Her+ ions arriving on the ion detector produce a true coincidence. This corresponds to a scattering cross section of IO-s1 cms/eV sterad, observed with a solid angle of 2 x 10-5 sterad.
M. J. VAN
418
DEK
WIEL
-
AND
G. WIEBES
this work
10 ," t. - - i
df m ctd~I .this work
0
idem
.
idem
,Ederer. ,ALLen
T.
2P5 10
J
2
10’ 2P4
lo-
4
i
c
!o- 5
0
100
200
100
200
I
300 energy Loss tev1
Fig. 4. Oscillator-strength
spectra
for L-shell
ionization
of Ne.
For double ionization the spectrum exhibits the same trend as observed for Hesf. The very flat maximum can be considered as characteristic for double ionization. We can understand this by realizing how the total excess energy is divided over the two electrons. Near threshold, the probability for each of the electrons to have any energy in the range available will be fairly constant. Then (df/dE) 2+ tends to increase linearly with the length of the energy interval above threshold (see discussion in our paper on Ar*)).
MULTIPLE
IONIZATION
OF He AND Ne
419
Further above threshold this situation gradually changes into one, in which dominantly one electron carries away almost all the excess energy, leaving a near-zero energy for the second electrons). Therefore, the energy interval relevant for the evaluation of (df/dE)s+ is confined more and more to only a small part of the total range of possible excess energies. This effect is opposed to that of the increase of the energy interval. The two trends may balance each other over an extended range of energies, thus producing a flat maximum. Due to the vanishing value of the oscillator strength at threshold, no onsets can be detected of the higher Nes+ configurations, i.e. 2~12~5 at 85 eV and 95 eV, or 2~02~6 at 120 eV. A similar situation was encountered for double ionization in Xe by Cairns et al. 25) and in Ar4). As to the Nesf spectrum, only a limited part of it is measured in our energy range, as it appears to have only just reached its maximum at 250 eV. However, the data serve to conclude that triple ionization accounts for at most 2% of the total ionization in the L shell of Ne (at 250 eV energy loss). Therefore we may neglect the contribution of Ned+ in the comparison of photoabsorption data, i.e. Cn(df/dE)n+, with a summation of our spectra (the dashed line in fig. 4). A reasonable agreement exists between our spectrum and the values of Ederer and Tomboulian 26) and one value by Allen24). 3.4. Ratio of double and single ionization. We shall now discuss the ratios (df/dE)a+/(df/dE)i+, plotted in figs. 5 and 6, while also referring to our previous results on Ar4). We consider four aspects: i) The discrepancy of our ratios with the experimental values of Carlsons) has the same trend for all three gases studied. This supports our previous suggestion 4) that low-energy photons (below the threshold for double ionization) may have been present in the radiation used in the charge spectrometry experiment of ref. 5. Near the double-ionization threshold this should cause a strong depression of the ratios for He and Ar due to the steep increase of (df/dE) r+ for these gases towards lower energies. This effect should be less serious for Ne, since (df/dE)r+ for this gas does not vary so rapidly at low energies. This is what we observe in figs. 5 and 6t and fig. 5 of ref. 4. ii) In all gases studied the ratios have one feature in common: they pass through a maximum before approaching an asymptotic (high-energy transfer) value. Theoretical support for this is found in the work of Byron and Joachain6) and in that of Brown?). A maximum in the He ratio, though small and close to threshold, turns up already in a H.F. calculation (part of ref. 6). t If, in the study of multiple ionization in Xe by Cairns et al. 27, the calibration of the quantum conversion efficiency of the photon detector ivere performed with the present Nez+/Nel+ data, the Xes+ spectrum would have a shape more similar to our PfldE) 2+ curves, i.e. a more extended rise to a broad maximum.
M. J. VAN DER
420
WIEL
AND G. WIEBES
He
o
this work
‘1 [3
Carlson
high
energy
limit
Byron, J.
O‘-
’
200
I
---)
I
300
500
400 energy
loss (eW
Fig. 5. Ratio of oscillator strengths for double and single ionization of He; o - ref. 5, electron spectrometry; n - ref. 5, charge spectrometry.
o this work I] Carlson
energy
loss (eV)
Fig. 6. Ratio of oscillator strengths for double and single L-shell ionization of Ne; q - ref. 5, electron spectrometry; n - ref. 5, charge spectrometry.
MULTIPLE
IONIZATION
OF He AND Ne
421
Such a maximum was expected earlier by Carlson5) on qualitative grounds. If correlation in the ground state is included, the height of the maximum and the slowness of decrease towards the asymptotic limit are better represented in either of the matrix formulations (position or momentum form) of ref. 6. Still a marked discrepancy with our result remains, which is apparently due to final-state correlation. Quite generally the occurrence of a maximum in the double to single ionization ratio is to be expected. When going towards high energy transfer, two factors diminish the importance of the correlation effect: in the initial state, the average distance between the two electrons increases, because the part of the ground-state configuration space responsible for the initial absorption of energy by one of the atomic electrons, is confined more and more to a small region around the nucleusa774); in the final state, the interaction time is shortened with growing velocity of the first ejected electron. iii) Concerning the magnitudes of the high-energy limit, the only precisely calculable value is that of He s+ ( 1.66 x IO-sj, to which our data appear to converge reasonably well. In the case of Ne, the energy range of our measurements was extended up to 450 eV (see fig. 6), where an asymptotic value of 1.5 to 2 x 10-l seems to have been practically reached. For Ar we previously measuredd) an asymptotic ratio of 2.5 x 10-l, while the results of Cairns et al. 25) for Xe yield a value of the order 3 x 10-r. So it appears that double ionization of the He Is electrons has a significantly smaller probability than that of the outer electrons of Ne, Ar and Xe, even if we consider the probability per outer electron available for a “shake off”. Such a difference does not exist for the shake-off ratios as calculated with singleelectron product wavefunctions (see table II). Although the “singleelectron” ratios are all appreciably lower than both the “exact” and the experimental values, the departure is smallest for He. This can be understood by realizing that the shake-off approximation neglects the fact that ejection of a first electron with very high momentum takes place from a coordinate zero. Due to the radial correlation, the outer electron(s) have then moved TABLE III Values of Mzi Ion
This work
Earlier work 1)
Hel+ Hes+
(4.87 f (1.19 i
0.10) x 10-l 0.08) x 10-s
(4.90 * 0.10) x 10-l (0.99 f 0.09) x lo-st
Nel+ Nes+
1.65 f (4.1 f
0.08 0.2) x 10-Z
1.85 f (4.9 f
7 For electron impact energies 2 4 keV.
0.02 0.9) x 10-Z
M. J. VAN
422
outwards, However, function
DER
WIEL
AND
G. WIEBES
thereby increasing their overlap with the double continuum. this increase will be relatively small for He, since the 1s waveis the only one to reach a maximum
that this mutual
screening
is already
on the nucleus, which implies
partly represented
in the H.F. ground
state of He. The same peculiarity of the Is wavefunction, namely coordinates right up to zero are relevant, offers an explanation
that all for the
remarkably slow convergence of the He ratio towards the asymptotic value. For instance at 400 eV, i.e. (E-I.P.s+)/I.P.s+ m 4, the ratio for He is still twice the asymptotic one, whereas for similar conditions of E with respect to I.P.s+ for Ne and Ar, the ratio is considerably closer to the asymptotic value. iiii) We tentatively attribute the shoulder in the Ne curve (fig. 6) to the contribution of a higher Nes+ configuration. Most probably it is the 2~12~5 ionization, reaching its maximum with respect to (df/dE)l+ at an energy loss above that for the 2p4 maximum. Concerning this point we may refer to the photoelectron spectrum of Ne as measured by Carlson5), in which the double ionization continuum at 278 eV energy transfer shows a sizeable contribution of 2~12~5 ionization. 3.5. Consistency with compare the values of:
our
h’fz = r (df/dE)“+(R,/E) dE
previous
work.
(R is Rydberg
It is interesting
to
energy),
I.P.“+
as obtained in our earlier study 1) from the impact-energy dependence of the multiple-ionization cross sections, with the corresponding integrals over the df/dE distributions presented in this work. Especially since two different normalizations are involved: on photoionization cross sections in this work, and on total electron ionization cross sections in ref. 1. Table III lists the values from both studies. A few remarks must be made concerning this table : a) Near the threshold of Her+ and Nei+ the energy resolution (5 eV fwhm) strongly distorts our spectrum, a reason for which the data points at the lowest energies were not plotted in figs. 3 and 4. Since these regions contribute with a relatively large weight to M:, we have replaced our measured oscillator strengths for the first few eV above threshold by those of Samson lo). Energy losses above the range studied in this work do not contribute to any extent for both gases. b) Our measurements for the multiple ions do not extend to sufficiently high energies to measure Mii completely. However, for Hes+ and Nes+ reasonable extrapolations to higher energy losses can be made, which provide corrections of less than 10%. In the case of Nes+, such an extrapolation is not feasible; the part of the spectrum shown in fig. 4 covers only about one-third of the total Mii. This is to be expected, since the Nes+ spectrum appears to have only just reached its maximum at 250 eV.
MULTIPLE
IONIZATION
OF He AND Ne
423
c) From the spectra of figs. 3 and 4 we learn that energy transfers of many hundreds of eV still contribute significantly to the total multiple ionization. Therefore it is not surprising that at impact energies of only a few keV we observedi) slight departures from the Bethe-Born relation [eq. (1) of ref. I] for 021 and usi of Ne. This relation is generally assumed to be valid for impact energies at least ten times in excess of all relevant energy transfers. Therefore, in the evaluation of M& and M& we did not take into consideration the measurements below 4 keV impact energy. If we apply the same procedure for M&. of He, we obtain a value which is in better agreement with that of the present work. 4. Conchsion. In view of the discrepancies of our results with those of an earlier photon experiment on multiple ionization, we have given evidence for the reliability of the present df/dE distributions, both by a renewed evaluation of a possible breakdown of the approximations used and by a comparison with our previous data, obtained via an independent method. The ratio of oscillator strengths for double and single ionization was shown to pass through a maximum before approaching an asymptotic limit. This can be understood qualitatively and is also in accord with a theoretical study for He. We showed that the radial correlation of the He 1s electrons has some characteristics different from those of the outer electrons of the other noble gases. This is illustrated both by the magnitude of the asymptotic ratio (of double and single ionization) and by the slowness of convergence to this limit. Acknowledgements. The authors are grateful to Professor dr. J. Kistemaker for his continuous interest. They also express their thanks to Dr. F. J. de Heer for valuable discussions on the manuscript. This work is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (Foundation for Fundamental Research on Matter) and was made possible by financial support from the Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek (Netherlands Foundation for the Advancement of Pure Research).
REFERENCES 1) 2) 3) 4) 5) 6) 7)
Van der Wiel, M. J., El-Sherbini, Th. M. and Vriens, L., Physica 42 (1969) 411. El-Sherbini, Th. M., Van der Wiel, M. J. and De Heer, F. J., Physica 48’ (1970) 157. Van der Wiel, M. J.. Physica 49 (1970) 411. Van der Wiel, M. J. and Wiebes, G., Physica 53 (1971) 225. Carlson, T. A., Phys. Rev. 156 (1967) 142. Byron, F. W. and Joachain, C. J., Phys. Rev. 164 (1967) 1. Brown, R. L., Phys. Rev. A 1 (1970) 586.
424 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27)
MULTIPLE
IONIZATION
OF He AND Ne
Ikelaar, P., Van der Wiel, M. J. and Tebra, W., J. Phys. E 4 (1971) 102. Bethe, H., Ann. Physik 5 (1930) 325. Silverman, S. M. and Lassettre, E. N., J. them. Phys. 40 (1964) 1265. Samson, J. A. R., Adv. in Atomic and Molecular Physics, Vol. 2, Academic Press (New York, 1966) p. 177. Inokuti, M., Argonne Nat. Labor., Report 7220 (1966). Vriens, L., Case Studies in Atomic Collision Physics I, North-Holland Publ. Comp. (Amsterdam, 1969). Wiebes, G., Physica 48 (I 970) 407. Salpeter, E. E. and Zaidi, M. H., Phys. Rev. 125 (1962) 248. Stewart, A. L. and Webb, T. G., Proc. Phys. Sot. 82 (1963) 532. Bell, K. L. and Kingston, A. E., Proc. Phys. Sot. 90 (1967) 3 1. Bell, K. L. and Kingston, A. E., J. Phys. B, 3 (1970) 1433. Samson, J. A. R., Phys. Rev. Letters 22 (1969) 693. Brown, R. L., Phys. Rev. A 1 (1970) 341. Aberg, T., Phys. Rev. A 2 (1970) 1726. Henry, R. J. W. and Lipsky, L., Phys. Rev. 153 (1967) 5 1. Lukirskii, A. P., Brytov, I. A. and Zimkina, T. M., Optics and Spectrosc. (English Transl.) 17 (1964) 234. Allen, S. J. M. (1935), see ref. 11. Cairns, R. B., Harrison, H. and Schoen, R. I., Phys. Rev. 183 (1969) 52. Ederer, D. L. and Tomboulian, D. H., Phys. Rev. 133 (1964) A1525. Aberg, T., Ann. Acad. Sci. Fennicae, Series A, VI, Physica 308 (1969) 7.
MULTIPLE
IONIZATION
OF He AND
AS A FUNCTION
OF THE
M. J. VAN DER WIEL F,O.M.-Institwt
Ne BY
10 keV ELECTRONS
ENERGY
LOSS
and G. WIEBES
VOOY Atoom- en Molecuulfysica, Amsterdam, Nederland Received 25 February 1971
Synopsis Oscillator-strength spectra are reported for transitions to the He’+. sf and Nei+ - 3+ continua. The spectra, covering a range of energy transfers from threshold up to 250 eV, were derived from the small-angle, inelastic scattering of 10 keV electrons in these gases, observed in coincidence with the ions. Our data show that the ratio of double and single ionization passes through a maximum before approaching the asymptotic value at high-energy transfers. This result is in disagreement with earlier photoionization experiments, but it supports recent theoretical work on double ionization in He.
1. Introduction. In order to study the effect of electron correlation in atoms, we have undertaken the investigation of multiple ionization of the noble gases by fast electrons. The first step in this program was the determination of the relative abundances of the different charge states of these gases (He, Ne and Arr), Kr and Xes)) as a function of electron impact energy. Next, we developed a methods) to measure the small-angle, inelastic scattering of a 10 keV electron in coincidence with the ions formed and to transform
the observed
intensities of scattering
into a spectrum
of
atomic oscillator strengths. Application of this method to ionization in both the M- and L-shell of Ar4) has revealed a number of new aspects of multipleelectron processes. In continuation of this program, we now present the data on He and the outer shell of Ne, i.e. the oscillator-strength distributions for Hei+? s+ and Ner+-3+ over the energy range from threshold up to 250 eV. The measurements were performed with a resolution of 5 eV fwhm. The main purpose of this work is to test whether in the ionization in an outershell the “shakeoff limit” [a constant ratio of double and single (photo)ionization] is reached so near threshold as it appears from the work of Carlsons). Our results for A+) are in disagreement with the general picture given in ref. 5. A clear maximum is reached in the ratio of double and single ionization as, a function of the energy transfer. Further, we presumed that the energy at which the 411
M. J. VAN DER WIEL AND G. WIEBES
412
curve levels off to an asymptotic value is influenced by the presence of a relatively close inner shell. Since He has only two 1s electrons and the K shell of Ne is considerably obtain more information
deeper than the Ar L shell, one may expect to
on the validity
of a shake-off
description
from an
investigation of these two gases. Furthermore, calculations are available69 7) of the oscillator-strength spectrum for formation of Hes+, with which we shall compare our data. Our previous valuesi) for a weighted integral of the oscillator-strength distribution, as obtained from the impact-energy dependence of the total cross section for multiple ionization, will serve to check the reliability of the present data. 2. Experimental. The apparatus and experimental procedure have been described elsewhereat4) in considerable detail. The essentials are: A 10 keV electron beam passes through a gaseous target of about 10-s torr density. The ions produced by the beam are extracted and charge-analysed. Electrons, scattered through a small angle ( RS5 x 10-3 rad) are retarded and selected in energy loss. The two particle detectors feed their signals into a delayed coincidence circuit. The true coincidences, after being separated from the simultaneously registered accidental ones, are stored in a data collectors), which drives the energy-loss scanning. When measuring He s+, the charge analyser also passes Hl fragments from background molecules. However, the total ion current of Hes+ exceeded that of Hz by a factor of 250. Since it is reasonable to assume that most of this Hz is formed at energy losses below the He s+ threshold, its contribution to the coincidence completely.
signal,
differential
in energy
loss,
can
be neglected
3. Results and discussion. 3.1. General. Since our results for multiple ionization will prove to differ markedly from those obtained by Carlsons) in photoionization, we emphasize one aspect of our derivation of (apparent) oscillator strengths in somewhat greater detail than before. The method, as described in ref. 3, is based on the Born relations) for electron scattering through
an angle 0 at an energy loss E (leaving out a few factors
not relevant 40, E) -
in the present
which are
discussion) :
(1/K2) df(K)/dE,
(1)
where K = K(8, E) is the magnitude of the momentum transfer and df(K)/dE the generalized oscillator strength. In the region of K < 1 a-u. it is convenient to expand df (K)/dE in terms of Kz: df(K)/dE
= df/dE + AK2 + BK4 + . . . .
(2)
Let us confine ourselves to the first two terms of this series and consider the magnitude of A with respect to df/dE. Silverman and Lassettreia) measured
MULTIPLE
-1I 0
IONIZATION
50
OF He AND Ne
413
I-2 100 energy loss(eV)
Fig. 1. a) Approximate ratio A/(df/dE) (see eq. 2) for He and H (solid curves, left vertical axis) ; b) Contribution of term AK2 (relative to df/dE) to the inelastic scatter& cross section at 0 = 5 x 10-3 rad (dashed curves, right vertical axis).
a part of the function df(K)/dE at a number of energies in the Her+ continuum. From an extrapolation of their results to K = 0, the optical limit (Samsonii)), we have obtained approximate values of A (df/dE)-1. It appears (see fig. 1, He, solid curve) that A is negative and of order unity at threshold. Further above threshold A (df/dE)-1 c h an g es sign and eventually approaches zero. A similar trend (a decrease from an appreciable value near threshold towards zero at high-energy transfers) is found for Hi”) (see fig. 1, H, solid curve). This is a general feature for all atoms, expressing the fact that at high energy transfers df(K)/dE is constant for all K up to a sharp “binary collision” peakis) at $Ks = E (in a.u.). In order to be justified in equating df(K)/dE to df/dE, as we did in ref. 3, without appreciable error due to the neglect of AK2 (and higher terms in eq. 2), we require K2 to be such that AKs(df/dE)-1 < 1 over the whole continuum. This condition is fulfilled in our experiment by taking a scattering angle of 5 x 10-s rad [see fig. 1, AKs(df/dE)-1, dashed curves]. The maximum error appears to amount to only a few percent. At energy losses is sufficiently small, data were taken above 150 eV, where A Ks(df/dE)-1 at an angle of 8 x 10-a rad. At smaller angles than this, a tiny fraction of the primary beam enters the energy analyser and is not suppressed completely (1 : 101”). Such primary electrons produce an unwanted signal (raising the number of accidental coincidences) on the electron detector, of a magnitude comparable to the true scattered signal at the very highest energy losses. In the case of double ionization one might suspect that, due to the (in zeroth order in the interelectronic interaction) forbidden character of any double electron transition, df/dE might be vanishingly small or at least
414
M. J. VAN DER WIEL AND G. WIEBES
He?’ E.lOO eV
scatt.angh(rad) Fig. 2. Angular dependence of intensity of scattering, leading to He”+ at E = 100 eV. Solid curve: (K2)-1 including correction for angular resolution. Dashed curve: (P-1. Dash-dotted curve: [(Kz)-1 + 11.
much smaller than AK3. For this reason we measured the angular dependence of scattering leading to He 2+ at an energy loss of 100 eV, an energy at which the scattering intensity is at its maximum and any higher terms in eq. (2) are expected to be largest. Fig. 2 shows that the experimental points do not deviate measurably from a behaviour according to eq. (1) with neglect of terms higher than dj/dE in eq. (2). The solid curve represents (K3)-1, including a correction3) for the angular resolution. The magnitude of this correction can be inferred from a comparison of the solid and the dashed curves, the latter giving (K3)-1 without correction. Also a curve representing a hypothetical case with A(df/dE)-1 equal to plus unity, i.e. [(K3)-1 + 11, has been drawn (fig. 2, dash-dotted line). It is evident that a term AK3 of such magnitude would be detectable in our experiment. From our data points at the two highest angles we can estimate an upper limit for A (df/dE)-r of roughly f0.3. This means the possible error due to the neglect of higher terms in eq. (2) at 5 x 10-3 rad amounts to f 1%. So in this respect the behaviour of df(K)/dE for the He3+ continuum is not drastically different from what was known already for the corresponding transitions in Ar3) or the 2s2p excitation of Herd). Fig. 2 also illustrates that the choice of scattering angle (5, respectively 8 x 10-3 rad) is a suitable one. On the one hand the correction for the angular resolution is small (although it is fairly well established, see e.g. ref. 3). On the other hand, higher terms of eq. (2), even if they are large, do not contribute significantly.
MULTIPLE
IONIZATION
OF
TABLE Values
of (df/dE)n+
He
AND
Ne
415
I
for He (n =
1,2) and Ne (n =
1, 2, 3)
Hel+
Hesf
Nel+
Nes+
Nes+
(in 10-3 eV-1)
(in 10-5 eV-1)
(in 10-s eV-1)
(in 10-3 eV-1)
(in 10-5 eV-1)
7.82
-
-
Energy loss E (eV) 30
47.5
40
28.0
50
17.3
60
13.2
-
7.73 6.88 6.10 5.25 4.45
0.72
11.3
3.70
2.10
3.95
13.8
3.05
2.44
3.02
13.6
2.55
2.60
2.33
12.9
2.20
2.62
-
1.84
9.9
1.80
0.15
70
8.75
80
6.60
90
5.05
100 110 120 130
1.28
1.57
140
1.52
8.3
1.55
2.59 2.51
150
1.26
6.9
1.32
2.38
2.2
0.60
160
1.03
5.8
1.13
2.15
170
0.88
5.0
0.99
1.90
3.3 4.1
180
0.75
4.1
0.86
1.70
4.6
190
0.66
3.5
0.74
1.55
5.0
200
0.57
3.0
0.65
1.37
5.4
210
0.49
2.6
0.58
1.26
5.6
220
0.43
2.2
0.50
1.15
5.7
230
0.38
1.9
0.44
1.06
5.7
240
0.33
1.6
0.39
0.97
5.8
250
0.29
1.4
0.34
0.90
5.9
TABLE Asymptotic
ratio
II
(df/dE)s+/(df/dE)l+ Independent
Atom
This work
electron
“Exact”
value
approximation He Ne Ar
-
7 x
1.5 to 2 x 2.5 x
10-l
10-l
lo-3
6)
4.5 x
10-s 5)
3.8 x
10-s 5)
1.66 x
10-s ‘3) -
Thus, a spectrum of scattering intensities measured at one of the angles mentioned, is converted into a df/dE spectrum by means of eq. (1)) including the correction for the angular resolution, but with neglect of higher terms in eq. (2) throughout the continuum. Our relative spectra are normalized, using the relation crphotoion.(Mb) = 109.75 df/dE (eV-r), on the F)hotoionization cross sections of Samsonrr) ; at 40 eV for He and at 35 eV for Ne. Accord-
M. J. VAN DER WIEL AND G. WIEBES
416
ing to fig. 1, AK2 (d//d-E-r for He equals about 8 x 10-a at 40 eV, which is smaller than the uncertainty of our measurements. The results have been plotted in figs. 3 and 4. In table I we listed the df/dE values at 10 eV energy loss intervals,
as obtained
from a smooth, averaged curve through the actual
data points. 3.2.
Helium
(fig. 3).
The present
Hei+ spectrum
agrees within
a few
percent with that of Samsonrr), from threshold up to 60 eV, except at threshold due to the effect of the energy resolution (5 eV fwhm for this study), At higher energy losses there is a wealth of calculations of 1ss - ( 1s&p) ionizationi5-is), with which to compare our data, but different wave-
. .
‘.
this work
,252P
10-L
-
(d’,” dE
o .
*
Bel1.K.
C$)n:Lukirskii.
BC.2
idem .AUen
10-C
10-L
10-L
10-s I 0
i
I 100
I 200
I 300 e-ergy
105s (aV)
Fig. 3. Oscillator-strength spectra for ionization of He. An averaged curve through our data points for He 1+ coincides with the spectrum of Bell and Kingston 17).
MULTIPLE
IONIZATION
OF He AND Ne
417
functions and formulations of the matrix elements still produce uncertainties of the order of 10%. We have chosen to plot one of the spectra of Bell and KingstonIT) (in dipole-length formulation), since it appears to agree quite well with the present data, in sofar as the large scatter above 200 eV permits to draw such a conclusion t. Due to the uncertainties of the theoretical values, the agreement with our results still leaves room for a contribution of excited Heif states, i.e. states of the ion with n 2 2, as included in our of such excited continua was measurement of (df/dE) I+. The contribution measuredra) to be about 8% and calculated2°p21) to be 7% at very high energy transfers. In the Hesf spectrum we observe the same features as we found to be characteristic for double ionization in Ar4) : a more or less linear rise, from a vanishing oscillator strength at threshold, to a broad, flat maximum at about 20 to 30 eV above threshold, followed by a monotonic decrease. The only data with which we can compare this spectrum, are the theoretical curves of Byron and Joachain6) (see fig. 3), which were recalculated with a different ground-state wavefunction by Brown 7). It appears that the curve calculated with the position matrix element is in good agreement with ours at energies up to and including the maximum, whereas the “momentum” curve, which has the correct asymptotic behaviour (E-g) seems to approach the same limit as our curve. Such a difference in the range of validity of two calculations, based on different matrix elements, is quite common. For instance in the case of single photoionization in Ne the situation is remarkably similarss). The uncertainties in He photoabsorption measurements, i.e. (df/dE)i+ + (df/dE)s+, for instance those obtained by Lukirskii et a1.23) from averaging their values with “best” values from literature or the one point by Allen24) (see fig. 3), are too large to detect a significant departure from the (df/dE)l+ spectrum of Bell and Kingstoni7). Therefore no independent determination of (df/dE)s+ can be made at present.
3.3. Neon (fig. 4). The Ne r+ data are in quite good agreement with those of Samsonrl) over the whole energy range (up to 60 eV), apart from a too strong decrease at threshold due to the effect of the energy resolution. Structure as reported in our previous paper-a) is not observed in the present, more accurate spectrum. A comparison of these data with the most recent “best wavefunction” calculation by Henry and Lipskyss) shows discrepancies of the same type as we discussed for Hes+. In this calculation no Nel+ excited states were taken into consideration. t The extremely bad statistics responsible for this scatter, is due to the fact that e.g. at 300 eV energy loss, only one or two out of 10s Her+ ions arriving on the ion detector produce a true coincidence. This corresponds to a scattering cross section of IO-s1 cms/eV sterad, observed with a solid angle of 2 x 10-5 sterad.
M. J. VAN
418
DEK
WIEL
-
AND
G. WIEBES
this work
10 ," t. - - i
df m ctd~I .this work
0
idem
.
idem
,Ederer. ,ALLen
T.
2P5 10
J
2
10’ 2P4
lo-
4
i
c
!o- 5
0
100
200
100
200
I
300 energy Loss tev1
Fig. 4. Oscillator-strength
spectra
for L-shell
ionization
of Ne.
For double ionization the spectrum exhibits the same trend as observed for Hesf. The very flat maximum can be considered as characteristic for double ionization. We can understand this by realizing how the total excess energy is divided over the two electrons. Near threshold, the probability for each of the electrons to have any energy in the range available will be fairly constant. Then (df/dE) 2+ tends to increase linearly with the length of the energy interval above threshold (see discussion in our paper on Ar*)).
MULTIPLE
IONIZATION
OF He AND Ne
419
Further above threshold this situation gradually changes into one, in which dominantly one electron carries away almost all the excess energy, leaving a near-zero energy for the second electrons). Therefore, the energy interval relevant for the evaluation of (df/dE)s+ is confined more and more to only a small part of the total range of possible excess energies. This effect is opposed to that of the increase of the energy interval. The two trends may balance each other over an extended range of energies, thus producing a flat maximum. Due to the vanishing value of the oscillator strength at threshold, no onsets can be detected of the higher Nes+ configurations, i.e. 2~12~5 at 85 eV and 95 eV, or 2~02~6 at 120 eV. A similar situation was encountered for double ionization in Xe by Cairns et al. 25) and in Ar4). As to the Nesf spectrum, only a limited part of it is measured in our energy range, as it appears to have only just reached its maximum at 250 eV. However, the data serve to conclude that triple ionization accounts for at most 2% of the total ionization in the L shell of Ne (at 250 eV energy loss). Therefore we may neglect the contribution of Ned+ in the comparison of photoabsorption data, i.e. Cn(df/dE)n+, with a summation of our spectra (the dashed line in fig. 4). A reasonable agreement exists between our spectrum and the values of Ederer and Tomboulian 26) and one value by Allen24). 3.4. Ratio of double and single ionization. We shall now discuss the ratios (df/dE)a+/(df/dE)i+, plotted in figs. 5 and 6, while also referring to our previous results on Ar4). We consider four aspects: i) The discrepancy of our ratios with the experimental values of Carlsons) has the same trend for all three gases studied. This supports our previous suggestion 4) that low-energy photons (below the threshold for double ionization) may have been present in the radiation used in the charge spectrometry experiment of ref. 5. Near the double-ionization threshold this should cause a strong depression of the ratios for He and Ar due to the steep increase of (df/dE) r+ for these gases towards lower energies. This effect should be less serious for Ne, since (df/dE)r+ for this gas does not vary so rapidly at low energies. This is what we observe in figs. 5 and 6t and fig. 5 of ref. 4. ii) In all gases studied the ratios have one feature in common: they pass through a maximum before approaching an asymptotic (high-energy transfer) value. Theoretical support for this is found in the work of Byron and Joachain6) and in that of Brown?). A maximum in the He ratio, though small and close to threshold, turns up already in a H.F. calculation (part of ref. 6). t If, in the study of multiple ionization in Xe by Cairns et al. 27, the calibration of the quantum conversion efficiency of the photon detector ivere performed with the present Nez+/Nel+ data, the Xes+ spectrum would have a shape more similar to our PfldE) 2+ curves, i.e. a more extended rise to a broad maximum.
M. J. VAN DER
420
WIEL
AND G. WIEBES
He
o
this work
‘1 [3
Carlson
high
energy
limit
Byron, J.
O‘-
’
200
I
---)
I
300
500
400 energy
loss (eW
Fig. 5. Ratio of oscillator strengths for double and single ionization of He; o - ref. 5, electron spectrometry; n - ref. 5, charge spectrometry.
o this work I] Carlson
energy
loss (eV)
Fig. 6. Ratio of oscillator strengths for double and single L-shell ionization of Ne; q - ref. 5, electron spectrometry; n - ref. 5, charge spectrometry.
MULTIPLE
IONIZATION
OF He AND Ne
421
Such a maximum was expected earlier by Carlson5) on qualitative grounds. If correlation in the ground state is included, the height of the maximum and the slowness of decrease towards the asymptotic limit are better represented in either of the matrix formulations (position or momentum form) of ref. 6. Still a marked discrepancy with our result remains, which is apparently due to final-state correlation. Quite generally the occurrence of a maximum in the double to single ionization ratio is to be expected. When going towards high energy transfer, two factors diminish the importance of the correlation effect: in the initial state, the average distance between the two electrons increases, because the part of the ground-state configuration space responsible for the initial absorption of energy by one of the atomic electrons, is confined more and more to a small region around the nucleusa774); in the final state, the interaction time is shortened with growing velocity of the first ejected electron. iii) Concerning the magnitudes of the high-energy limit, the only precisely calculable value is that of He s+ ( 1.66 x IO-sj, to which our data appear to converge reasonably well. In the case of Ne, the energy range of our measurements was extended up to 450 eV (see fig. 6), where an asymptotic value of 1.5 to 2 x 10-l seems to have been practically reached. For Ar we previously measuredd) an asymptotic ratio of 2.5 x 10-l, while the results of Cairns et al. 25) for Xe yield a value of the order 3 x 10-r. So it appears that double ionization of the He Is electrons has a significantly smaller probability than that of the outer electrons of Ne, Ar and Xe, even if we consider the probability per outer electron available for a “shake off”. Such a difference does not exist for the shake-off ratios as calculated with singleelectron product wavefunctions (see table II). Although the “singleelectron” ratios are all appreciably lower than both the “exact” and the experimental values, the departure is smallest for He. This can be understood by realizing that the shake-off approximation neglects the fact that ejection of a first electron with very high momentum takes place from a coordinate zero. Due to the radial correlation, the outer electron(s) have then moved TABLE III Values of Mzi Ion
This work
Earlier work 1)
Hel+ Hes+
(4.87 f (1.19 i
0.10) x 10-l 0.08) x 10-s
(4.90 * 0.10) x 10-l (0.99 f 0.09) x lo-st
Nel+ Nes+
1.65 f (4.1 f
0.08 0.2) x 10-Z
1.85 f (4.9 f
7 For electron impact energies 2 4 keV.
0.02 0.9) x 10-Z
M. J. VAN
422
outwards, However, function
DER
WIEL
AND
G. WIEBES
thereby increasing their overlap with the double continuum. this increase will be relatively small for He, since the 1s waveis the only one to reach a maximum
that this mutual
screening
is already
on the nucleus, which implies
partly represented
in the H.F. ground
state of He. The same peculiarity of the Is wavefunction, namely coordinates right up to zero are relevant, offers an explanation
that all for the
remarkably slow convergence of the He ratio towards the asymptotic value. For instance at 400 eV, i.e. (E-I.P.s+)/I.P.s+ m 4, the ratio for He is still twice the asymptotic one, whereas for similar conditions of E with respect to I.P.s+ for Ne and Ar, the ratio is considerably closer to the asymptotic value. iiii) We tentatively attribute the shoulder in the Ne curve (fig. 6) to the contribution of a higher Nes+ configuration. Most probably it is the 2~12~5 ionization, reaching its maximum with respect to (df/dE)l+ at an energy loss above that for the 2p4 maximum. Concerning this point we may refer to the photoelectron spectrum of Ne as measured by Carlson5), in which the double ionization continuum at 278 eV energy transfer shows a sizeable contribution of 2~12~5 ionization. 3.5. Consistency with compare the values of:
our
h’fz = r (df/dE)“+(R,/E) dE
previous
work.
(R is Rydberg
It is interesting
to
energy),
I.P.“+
as obtained in our earlier study 1) from the impact-energy dependence of the multiple-ionization cross sections, with the corresponding integrals over the df/dE distributions presented in this work. Especially since two different normalizations are involved: on photoionization cross sections in this work, and on total electron ionization cross sections in ref. 1. Table III lists the values from both studies. A few remarks must be made concerning this table : a) Near the threshold of Her+ and Nei+ the energy resolution (5 eV fwhm) strongly distorts our spectrum, a reason for which the data points at the lowest energies were not plotted in figs. 3 and 4. Since these regions contribute with a relatively large weight to M:, we have replaced our measured oscillator strengths for the first few eV above threshold by those of Samson lo). Energy losses above the range studied in this work do not contribute to any extent for both gases. b) Our measurements for the multiple ions do not extend to sufficiently high energies to measure Mii completely. However, for Hes+ and Nes+ reasonable extrapolations to higher energy losses can be made, which provide corrections of less than 10%. In the case of Nes+, such an extrapolation is not feasible; the part of the spectrum shown in fig. 4 covers only about one-third of the total Mii. This is to be expected, since the Nes+ spectrum appears to have only just reached its maximum at 250 eV.
MULTIPLE
IONIZATION
OF He AND Ne
423
c) From the spectra of figs. 3 and 4 we learn that energy transfers of many hundreds of eV still contribute significantly to the total multiple ionization. Therefore it is not surprising that at impact energies of only a few keV we observedi) slight departures from the Bethe-Born relation [eq. (1) of ref. I] for 021 and usi of Ne. This relation is generally assumed to be valid for impact energies at least ten times in excess of all relevant energy transfers. Therefore, in the evaluation of M& and M& we did not take into consideration the measurements below 4 keV impact energy. If we apply the same procedure for M&. of He, we obtain a value which is in better agreement with that of the present work. 4. Conchsion. In view of the discrepancies of our results with those of an earlier photon experiment on multiple ionization, we have given evidence for the reliability of the present df/dE distributions, both by a renewed evaluation of a possible breakdown of the approximations used and by a comparison with our previous data, obtained via an independent method. The ratio of oscillator strengths for double and single ionization was shown to pass through a maximum before approaching an asymptotic limit. This can be understood qualitatively and is also in accord with a theoretical study for He. We showed that the radial correlation of the He 1s electrons has some characteristics different from those of the outer electrons of the other noble gases. This is illustrated both by the magnitude of the asymptotic ratio (of double and single ionization) and by the slowness of convergence to this limit. Acknowledgements. The authors are grateful to Professor dr. J. Kistemaker for his continuous interest. They also express their thanks to Dr. F. J. de Heer for valuable discussions on the manuscript. This work is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (Foundation for Fundamental Research on Matter) and was made possible by financial support from the Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek (Netherlands Foundation for the Advancement of Pure Research).
REFERENCES 1) 2) 3) 4) 5) 6) 7)
Van der Wiel, M. J., El-Sherbini, Th. M. and Vriens, L., Physica 42 (1969) 411. El-Sherbini, Th. M., Van der Wiel, M. J. and De Heer, F. J., Physica 48’ (1970) 157. Van der Wiel, M. J.. Physica 49 (1970) 411. Van der Wiel, M. J. and Wiebes, G., Physica 53 (1971) 225. Carlson, T. A., Phys. Rev. 156 (1967) 142. Byron, F. W. and Joachain, C. J., Phys. Rev. 164 (1967) 1. Brown, R. L., Phys. Rev. A 1 (1970) 586.
424 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27)
MULTIPLE
IONIZATION
OF He AND Ne
Ikelaar, P., Van der Wiel, M. J. and Tebra, W., J. Phys. E 4 (1971) 102. Bethe, H., Ann. Physik 5 (1930) 325. Silverman, S. M. and Lassettre, E. N., J. them. Phys. 40 (1964) 1265. Samson, J. A. R., Adv. in Atomic and Molecular Physics, Vol. 2, Academic Press (New York, 1966) p. 177. Inokuti, M., Argonne Nat. Labor., Report 7220 (1966). Vriens, L., Case Studies in Atomic Collision Physics I, North-Holland Publ. Comp. (Amsterdam, 1969). Wiebes, G., Physica 48 (I 970) 407. Salpeter, E. E. and Zaidi, M. H., Phys. Rev. 125 (1962) 248. Stewart, A. L. and Webb, T. G., Proc. Phys. Sot. 82 (1963) 532. Bell, K. L. and Kingston, A. E., Proc. Phys. Sot. 90 (1967) 3 1. Bell, K. L. and Kingston, A. E., J. Phys. B, 3 (1970) 1433. Samson, J. A. R., Phys. Rev. Letters 22 (1969) 693. Brown, R. L., Phys. Rev. A 1 (1970) 341. Aberg, T., Phys. Rev. A 2 (1970) 1726. Henry, R. J. W. and Lipsky, L., Phys. Rev. 153 (1967) 5 1. Lukirskii, A. P., Brytov, I. A. and Zimkina, T. M., Optics and Spectrosc. (English Transl.) 17 (1964) 234. Allen, S. J. M. (1935), see ref. 11. Cairns, R. B., Harrison, H. and Schoen, R. I., Phys. Rev. 183 (1969) 52. Ederer, D. L. and Tomboulian, D. H., Phys. Rev. 133 (1964) A1525. Aberg, T., Ann. Acad. Sci. Fennicae, Series A, VI, Physica 308 (1969) 7.