- Email: [email protected]
Multiple ionization of He, Ne and Ar by 2–16 keV electrons
Physica 42 (1969) 41 l-420
0 North-Holland Publishing Co., Amsterdam
MULTIPLE
IONIZATION BY
M. J. VAN DER FOM-Instituut
OF He, Ne AND
2-
16 keV ELECTRONS
WIEL,
TH. M. EL-SHERBINI
Ar
AND L. VRIENS
VOOY Atoom- en Molecuulfysica, Amsterdam, Nederland Received 30 September 1968
Synopsis Relative abundances of multiply charged ions formed by electron impact (2-16 keV) on some noble gases were measured using a charge analyzer with 100°/Otransmission. Large discrepancies exist between our values and those obtained in low-transmission mass spectrometers. Cross sections were determined by normalization on the absolute gross ionization cross sections of Schram et al. The measured proportionality constants of the E,i’ In &r-term in the cross section are compared with those obtained from an analysis of photoionization data. The agreement with our values is good if besides oneelectron ejection from an inner shell also the multiple electron ejection from the outer shell is taken into account.
1. Irttrodaction. In order to obtain more detailed information on multiple ionization in electron-atom collisions, we set up an experiment to measure energy losses of 2-16 keV electrons passing through gases in coincidence with the corresponding multiply charged ions formed. As a first step in this program it appeared worthwhile to remeasure the relative cross sections for the formation of the different charge states because of the large discrepancies found in literature (see refs. 1 and 2). In most cases these differences can be ascribed to the use of low transmission - and therefore probably charge discriminating - mass spectrometers. 2. Exfierimental.
A. Apparatus.
The apparatus (see fig. 1) contains an electron gun with oxide cathode (A), and a collision region (B), where the electron beam is crossed by a neutral beam emerging from a multi-channel gas jet. Ions are extracted by a homogeneous extraction field (- 100 V/cm) produced by electrodes (H), with slits much larger than the ion beam dimensions. So the ion optical object of the charge analyzer (I) is formed by the intersection (B) of the electron beam (0.5 mm diameter) with the neutral beam (1 x 8 mm). The charge resolving power of the analyzer magnet is 1 : 8. The background pressure is 5 x 10-s torr. When target gas is introduced, the pressure rises to about 1 x 10-s torr. In the collision region (B) we then 411
412
M. J. VAN DER
WIEL,
TH. M. EL-SHERBINI
AND L. VRIENS
Fig. 1. Schematic diagram of the apparatus. A : electron gun with Einzel lens; B: neutral beam from multi-channel gas jet crossing the electron beam; C: plate for measuring the total ion production; H : homogeneous extraction field; I : 30” charge analyzer; K : post-acceleration; L: Bendix M-306 magnetic multiplier. D through G are not discussed in this paper.
have
a few times
1O-5 torr,
as determined
from known
ionization
cross
sections 3). As there is no axial magnetic field, the electron beam will be deflected in the extraction region. It is brought back to the axis of the apparatus for analysis in the velocity selector (F), which will be discussed in another paper, by applying electric cross fields before and after the ion extraction plates. These fields also serve to keep secondary electrons away from the collision region. In addition to a rough compensation of the earth magnetic field with coils around the apparatus, we also reduced the stray field of the analyzer magnet at the electron bean axis to less than 10-s gauss by enclosing the magnet in a layer of iron and one of “CO-NETIC”. B. Initial checks. Behind a slit in the upper extraction field plate, facing the entrance to the extraction system, a highly insulated electrode (C) has been placed for a dual purpose. First: to measure (after reversal of the extraction field) the total ion current produced, and compare it with the sum of the DC-measured currents
MULTIPLE
IONKZATION
OF
He,
Ne
AND Ar
413
at the end of the charge analyzer. When measuring on electrode C, we keep it at such a voltage with respect to the upper extraction field plate that saturation in the collected current is ensured. In this way a transmission of (100 & 3)% is found for extraction voltages ranging from 50 V/cm to 600 V/cm. Second: to determine the energy dependence of the total ion production, which in our energy range is very sensitive to the presence of secondary electrons. After normalization at 10 keV, this check on Ar showed a 3% reproduction of Schram’s gross ionization datas), which we believe to be free from secondary-electron effects. Suppression of these effects in our apparatus is comparatively easy due to the absence of an axial magnetic field. C. Detect ion. Ion pulse counting was performed with a Bendix M-306 multiplier, together with a 50 Q input solid state current amplifier (voltage gain of 1600 at 4 ns risetime). This combination enabled us to count ions with a partly flat discriminator response at a background of about 1 pulse per 5 minutes. Furthermore, changes in post-acceleration voltage between 4 keV and 12 keV had no effect on the count rate. So we assume a counting efficiency of 1, which was confirmed to an accuracy of 10% by a DCmeasurement. The ratios of the Ar+, Arz+ and Ars+ count rates were checked against a Faraday-cage measurement and found to agree within 3%. 3. Results. We determined the ratios of the ion abundances for thegases He, Ne and Ar at a number of energies between 2 and 16 keV and normalized TABLE I Partial
ionization
cross sections
of He, Ne and Ar
1)
He+
1)
Ed
He2+
He+
He2+
Ne+
Ne2+
Nes+
Ned+
Ar+
A++
Ars+
A++
in keV
in 10-18
in lo-20
in 10-1s
in lo-20
in
in
in
in
in
in
in
in
in
in
IO-17
10-19
IO-20
IO-21
10-17
10-13
10-13
10-13
IO-20
IO-21
cm2
cm2
cm2
cm2
cm2
cm2
cm2
cm2
cm2
cm2
cm2
cm2
cm2
11) 11)
Ars+
Are+
cm2
2
6.20
3.43
7.30
4.21
1.63
9.75
8.03
5.89
3.85
3.39
1.04
2.58
4.69
3
4.43
2.34
5.21
2.86
1.20
7.17
6.24
5.91
2.81
2.41
0.745
1.77
2.99
5.88
4
3.53
1.78
4.08
2.14
0.970
4.85
3.99
4.73
2.20
1.90
0.590
1.45
2.21
4.38
6
2.53
1.21
2.90
1.44
0.714
3.50
2.90
3.42
1.64
1.35
0.408
0.916
1.51
3.02
8
1.98
0.944
2.28
1.12
0.702
1.11
2.47
1.88 1.61
0.892 0.753
2.73 2.05 1.93
0.332
0.758 0.642
2.32 1.86 1.74
1.05
1.66 1.42
2.59 2.22 1.90
1.28
10 12
0.568 0.477 0.413
1.07 0.945
14
1.27
0.557
1.42
0.643
0.367
1.63
1.45
1.62
0.811
0.883 0.742 0.648
0.276 0.238 0.214
0.581 0.516 0.456
0.910 0.796 0.715
2.07 1.63 1.53
16
1.12
0.498
1.26
0.583
I) He+ normalized II)
He+ normalized
on Schram on Vriens’).
et al.
3).
8.59
414
M. J. VAN
DER
WIEL,
TH.
M. EL-SHERBINI
AND
L. VRIENS
them on the absolute gross ionization cross sections of Schram et al. 3) (see table I). The He-results have also been normalized on a set of cross sections evaluated from sum rules6) by Vriens7). According to this calculation Schram’s cross section for He+ at 1 keV is (19 &- 2)x too low. The discrepancy with Schram’s partial cross sections19 z), which were measured in an apparatus different from that of ref. 3, is large. Our values for the multiple ions are higher by about a factor 1.5 for 2+ ions up to a factor 4 for 6+ ions, the 1 + cross section being consequently lower: 1y0 for He to 9% for Ar. In our energy range only a few data from other authors495) are available; a comparison at 2 keV is made in table II. TABLE II Comparison of relative abundances of multiply charged ions at an impact energy of 2 keV Gas
author
He
Gaudin and H. 4) Schram et al. 1.3) this work
5.5 x 10-3 4.2 x 10-3 5.8 x 10-3
Ne
Gaudin and H. 4, Ziesel 5, Schram et al. 1~2) this work
4.4 4.4 3.4 6.0
Ar
Gaudin and H. 4) Schram et al. 1.2) this work
3+/1+
2+/1+
4+/1+
2.7 x 10-3 2.7 x 10-3 1.9 x 10-3 4.9 x 10-3
1.6 1.8 1.0 3.6
5.7 x 10-3
1.1 x 10-3
5.3 x
10-Z
1.2 x 10-Z
8.8 x 10-3
2.7 x 10-3
2.4 x 10-3 2.3 x 10-3 6.7 x 10-3
x x x x
10-3 10-3 10-3 10-3
x x x x
5+/1+
10-4 10-4 10-4 10-4 2.9 x 1O-4 3.0 x 10-4 1.2 x 10-3
4. Analysis of electron impact data. Our results can be compared with photo-ionization data using the well-known Bethe (first Born) relation:
oniEe1 = Eel -.Mii ln 7 4xaiR
+
CT&
where cni is the cross section for n+ ionization, Eel is the impact energy corrected for relativistic effects, i.e. Eel = $m~~v~~, where me and Z)erare the electron rest mass and velocity respectively (see also ref. 8), R is the Rydberg energy and Mii and C,r are constants; Mii is given by Mii =
df(n+) R ____ -dE, dE E s ?L+
(2)
continuum
df (n+)
being the differential dE sition to the n+ continuum
dipole oscillator
strength
at an energy transfer
for an ionizing trandf (n+) is equal to E. As dE
MULTIPLE
IONIZATION
OF He, Ne AND Ar
415
. I
q
Ne+ Ne'+(x10) Ne3+(x100)
x 0
I
1
0
n
n
---AA
n
n
;;
0
(
I
!
1
2
3
B
6
I
8 -
10
12
lb
16
Eel in keV
Fig. 2. Plot of o,~E,~/4xa~R v.In Eel for the partial ionization cross sections of He and Ne. He2+ values from normalization on Vriens 7),
mc -a$+> (E), where g$,T? (E) is the n+ photo-ionization xezh
cross section, we
can compare with photo-ionization results. As is demonstrated in fig. 2 for He and Ne, and in fig. 3 for Ar, the measured cross sections can be described by eq. (1). For the Nezf, Neaf and Ne*+ ions, we find a constant slope in the crE,l vs. In E,l plots at energies above 4 keV; for A++ and Ars+ there is a break in the curves at about 8 keV. These points will be accounted for in section 6. The constants Mfi and C,i, as obtained from a least squares analysis of our data, are listed in table III (columns 5 and 8). For comparison the table includes the values of Schram et al. 192) (columns 6 and 9). The fact that the constant C,i is not always positive is caused by the arbitrariness in the choice of a unit for E,l in the In term (in our case R).
3.6
Ne4f
t
Values
:
4 x
in parentheses
(<5
(
(1.6
(2.7
4.5
(1.6
x
x
x
x
x
x
1.3 x
x
5 x
(column
-j
(II)
0.02 0.9)
x
0.5)
1.0)
8 keV: + 2.4)
(5.5
10-4
above
< 1 x
8 keV: +
10-4
(1.9
x
x
0.14 0.07)
-& 2.3)
*
* *
1.8)
above
<5
(8.8
(8.5
3.72 (2.22
(5.2 *
(5.2 & 1.3) x
(4.9 *
1.85 f
x x
0.5)
by substraction
He+ normalized
10-i
lO-3
10-3
this work
(4.4 + 0.9)
0.49
5)
10-4(1)
10-4)
10-3
1O-3
10-s
10-i 1.0
8.1
x
x
x
x
lo-”
1O-2
10-l
1O-4
10-3
10-3
5 and 2.
3.76 2.31
3.6
of columns
x
1.0 x
8.8
1.82
< 0
on Vriens 7)
x
x
x
x
x
10-4
10-3
10-s
IO-4(n)
et al.
Schram
0.489
6)
impact
for He, h:e and Ar
from electron
and C,i
10-4 (7.7 i
3)
3) were obtained
et al. 3)
10-S)
x
x
%-
j
10-3)
10-4)
j
j
10-3)
10-s
2.0
3.8
10-3
x
5 x
5.1
10-4)
of
sum
2) c
10-e
10-4
shell
outer
4)
experiments
ej. from
electron
multiple
4.2
3)
on Schram
10-4
4.6 x 10-5; + K-shell :
1 x 10-3
+ K-shell
10-3
(I) He+ normalized
Ars+
7.2 x
4.8 x 10-4
Ars+
10-e
Ar4f
x
5.8
Ar3f
10-i
10-4
10-3
10-3
1.5 x
x
x
x
Ar3+
3.80
2.5
Ne3f
Ar+
shell
sec. proc.
9.0
1.74
0.49
shell
outer
from inn.
ejection
in
ioniz.
iFez+
Ne+
He3+
He+
ion
2) one elect.
1) single
from photoionization
Mfi
M$
TABLE III
theory
x
2.5823)
1.7122)
5.3
lo-4(10)
0.488521)
7)
this
10-3
6 x
-1.1
-1.95
10-3
- 0.77
-9.9
0 x
10-3
1 x
6.5
2.0
-2.0
10-3
5 x
x
x
x
x
x
x
10-3
10-i
10-i
10-4
10-3
10-i
et al.
Schram
-2.07
0.18
9)
impact
-2.60 3 x 10-i
10-i
lo-2(11)
1.3 x
-2.34
1.5 x
1.0 x
0.72(11) 10-“(I)
work
0.18(I)
8)
electron
Cni
MULTIPLE
IONIZATION
417
OF He, Ne AND Ar
_-15
10 '-
x
Ar .?+ (x10)
D
A?+
1x20)
A A#+
(x50)
o
A?+
(x500)
V
A?
(x5000)
0 --0
5 1; 2
1
1
3
4
a I
6
-----+
Fig. 3. Plot of o,,iE,J4xa$?
VS.
7v 10
12
14
E., in keV
In Eel for the partial ionization cross sections of Ar.
5. Analysis of photo-ionizatiolz data. Contributions to M~i, the integrated dipole oscillator strength (see eq. (2)), d 0 not arise from one-electron transitions only but also from multiple electron jumps if we take into account the correlation between the atomic electronsg*la). Because inner and outer shells interact only weakly, as is demonstrated by the relative slowness of the Auger process, one may roughly distinguish between two different channels leading to an n+ continuum: a. single electron ejection from an inner shell followed by a variety of secondary events like Auger processes, electron shake-off and direct collisions of the ejected inner shell electron with another atomic electron; no clear distinction between these secondary processes can be made. b. multiple electron ejection from the outer shell, which process is entirely due to correlation effects. A refinement of this classification should include excitation of inner shell electrons and correlation in these, and between different, shells. As presumably these phenomena contribute only littlell) to Mzi, we limit our discussion to the aforementioned processes a and b.
418
M. J. VAN
DER
WIEL,
TH.
M. EL-SHERBINI
AND
L. VRIENS
Process a. In order to obtain the contribution of a certain inner shell electron ejection to M~i, we have to know two things: first, the integrated dipole oscillator strength for such an electron ejection and second, the probability of subsequent formation of a lz+ ion. For Ne no K-shell photo-ionization data are available. Therefore we took MF (K-shell) = 1.2 x 10-2, an average of what can be found from sum rulesrs) (1.38 x 10V2) and by analyzing in a crE,i VS.In Eel plot the measurements of K-shell electron ejection of Glupe and Mehlhornia) (1.24 x 10-2) and the calculation of Arthurs and Moiseiwitschr4) (1.03 x 10-2). For Ar we took MF (Lr-shell) = 4.6 x 10-a and MiJ (Lrr, rrr-shell) = 1.6 x 10-1, on the basis of an extrapolation (see fig. 4) and integration of the photoabsorption measurements of Lukirskii et al. 15). Sum rules were used to obtain MF (K-shell) = 4.2 x 10e3. dfW+) Carlson and Krause 11~16*17) measured how 2 -.___ is distributed among dE n the various charges as a function of E. Their results and the above Mf (inner shell) values provided us with the results listed in table III, column 2.
df(n+) Process
Nesf, Nea+ and A+,
df(l+) dE-
for Hezf, dE i using photons with energy below the threshold of the
b. Carlsonis)
1.5x10‘
determined
the ratio ~
L, m_edge
e
1.0
0.5
0 _
Fig. 4. Plot of (1 /E) (df/dE) ments by Lukirskii
against
600
E for Ar, taken from photo-absorption
ef al. 15). The broken estimate
Energy transfer
lines show how we extrapolated
the contributions
of the two inner shells.
EW)
measurethe curves
to
MULTIPLE IONIZATION OF He, first
can
combined
for He, Ne and Ar by Lukirskii
rr dE by Samsonis)
dfU+)
and of ___ dE
Ar
419
df(?a+)
et aZ.15), of 2 n -=
for Ne
for He, Ne and Ar by Com”es and Elzersa), to
df(n+)
give absolute values of dE.
Ne
In overlapping
energy regions an average
was taken. Integration over the various continua yields the contribution of outer shell processes to Mii. The results are presented in table III, columns 1 (n = 1) and 3. 6. Comparison of electron impact ad photo-ionization data. Table III, column 4, shows the sum of the two contributions of processes a and b (see section 5) t0 M~i. When taking into account the poor accuracy of the integrated oscillator strengths (lO_20x), we find a good agreement with the M$ measured in this work. In those cases where no data were available to calculate the contribution of the outer shell correlation effect, its magnitude was found by subtracting the inner shell part from the measured Mii (column 3, values in parentheses). Comparison of a summation in column 4 with the slope in a uEel vs. In Eel plot (column 5) is only justified in an energy region where eq. (1) holds also for inner shells. For Neaf, Nes+ and Ne4+ (I.P. K-shell = 867 eV) this apparently (see fig. 2) is the case for energies above 4 keV. For Ars+ and Ar6+ our measurements have been expressed in two numbers for Mi,: one at energies below 6 keV, where formation of these ions largely occurs via Lr- and LII,II~-electron ejection; a second at energies above 8 keV, where the K-shell (I.P. = 3.2 keV) contribution, though possibly not reaching its asymptotic behaviour, becomes dominant (see fig. 3). For a number of ion species theoretical data on photoionization cross sections exist. Table III, column 7 gives the integrated values of Bell and Kingstonsi) for He+, of Byron and Joachainio) for Hes+ and of Cooperss) for Nef and Ar+ (taking only the p-electrons into account). 7. Conclusion. Cross sections for multiple ionization were measured with an apparatus, in which special attention was paid to avoid any of the effects which often disturb these measurements: 1) secondary electrons in the collision region ; 2) charge discrimination in the ion source ; 3) low and unknown transmission in the extraction and focusing system; 4) unknown detection efficiency, which necessitates frequent calibration of the multiplier. From an analysis of photo-ionization data on a number of ions it has proved possible to evaluate separately the two contributions to Mzi, that from single electron ejection from an inner shell and that from multiple processes in the outer shell. Good agreement is found with the electron
420
MULTIPLE
measurements
presented
IONlZATlON
OF
He,
Ne AND
Ar
here. In those cases, where the contribution
of the
correlation effect to n/r~ihad to be obtained from a subtraction (see section 6), we always found positive values which decrease with increasing number of ejected electrons. This realistic behaviour further supports our analysis and illustrates the importance of correlation effects. Acknowledgments. The authors are indebted to Dr. A. J. H. Boerboom and Mr. E. de Haas for their help in designing the apparatus, and to Mr. A. N. van der Steege for his assistance in the experimental work. They also express their gratitude to the Electronics Department of the Institute and especially to Mr. H. Buis for developing the preamplifier. Professor J. Kistemaker and Dr. F. J. de Heer have greatly stimulated this work by their constant interest. The authors are further indebted to Professor U. Fano and Dr. M. Inokuti for valuable comments. This work is part of the research program of the Stichting voor Fundamentaal 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 Organization for the Advancement of Pure Research).
REFERENCES 1) Schram,
B. L., Boerboom,
2) 3)
Schram, Schram,
B. L., Physica 32 (1966) 197. B. L., de Heer, F. J., van der Wiel,
4.
(1965) 94. Gaudin, A. and Hagemann,
R., J. Chim.
5)
Ziesel,
62 (1965)
6) 7)
Inokuti, M., Kim, Y. K. and Platzman, Vriens, L., unpublished.
J. P., J. Chim.
8)
Bethe,
9.
Van der Wiel,
H., Ann.
A. J. H. and Kistemaker,
phys.
Physik
5 (1930)
M. J., de Heer,
M. J. and Kistemaker,
phys.
64 (1967)
32 (1966)
185.
J., Physica
31
1209.
328.
325;
R. L., Phys. Fano,
Rev.
U., Phys.
F. J. and Wiebes,
F. W. and Joachain,
J., Physica
164 (1967)
Rev.
G., Phys.
10)
Byron, Carlson,
12)
Schram,
13)
Glupe,
14) 15)
Arthurs, A. M. and Moiseiwitsch, B. L., Proc. Roy. Sot. A247 (1958) 550. Lukirskii, A. P., Brytov, I. A. and Zimkina, T. M., Optics and Spectrosc.
16)
(U.S.A.) Carlson,
17 (1964) 234. T. A. and Krause,
M. O., Phys.
Rev.
137 (1965)
A 1665.
17)
Carlson,
T. A. and Krause,
M. O., Phys.
Rev.
151 (1966)
41.
18) 19)
Carlson, Samson,
T. A., Phys. Rev. 156 (1965) 142. J. A. R., J. Opt. Sot. Am. 55 (1965)
20)
Comes,
21)
Bell,
22)
Cooper,
B. L., Thesis,
F. J. and Elzer,
164 (1967) 140 (1965)
W.,
of Amsterdam,
Phys.
Letters
A., Z. Naturforsch.
K. L. and Kingston, Phys.
Rev. Rev.
University
G. and Mehlhorn,
J. W.,
C. J., Phys.
1198.
24 A (1967) 423.
11)
T. A. and Krause,
M. O., Phys.
95 (1954)
Letters
55.
Rev.
-4. E., Proc. 128 (1962)
phys. 681.
1. A 1057.
p. 89 (1966).
25 A (1967)
274.
935. 19 A (1964) Sot.
721.
90 (1967)
31.
0 North-Holland Publishing Co., Amsterdam
MULTIPLE
IONIZATION BY
M. J. VAN DER FOM-Instituut
OF He, Ne AND
2-
16 keV ELECTRONS
WIEL,
TH. M. EL-SHERBINI
Ar
AND L. VRIENS
VOOY Atoom- en Molecuulfysica, Amsterdam, Nederland Received 30 September 1968
Synopsis Relative abundances of multiply charged ions formed by electron impact (2-16 keV) on some noble gases were measured using a charge analyzer with 100°/Otransmission. Large discrepancies exist between our values and those obtained in low-transmission mass spectrometers. Cross sections were determined by normalization on the absolute gross ionization cross sections of Schram et al. The measured proportionality constants of the E,i’ In &r-term in the cross section are compared with those obtained from an analysis of photoionization data. The agreement with our values is good if besides oneelectron ejection from an inner shell also the multiple electron ejection from the outer shell is taken into account.
1. Irttrodaction. In order to obtain more detailed information on multiple ionization in electron-atom collisions, we set up an experiment to measure energy losses of 2-16 keV electrons passing through gases in coincidence with the corresponding multiply charged ions formed. As a first step in this program it appeared worthwhile to remeasure the relative cross sections for the formation of the different charge states because of the large discrepancies found in literature (see refs. 1 and 2). In most cases these differences can be ascribed to the use of low transmission - and therefore probably charge discriminating - mass spectrometers. 2. Exfierimental.
A. Apparatus.
The apparatus (see fig. 1) contains an electron gun with oxide cathode (A), and a collision region (B), where the electron beam is crossed by a neutral beam emerging from a multi-channel gas jet. Ions are extracted by a homogeneous extraction field (- 100 V/cm) produced by electrodes (H), with slits much larger than the ion beam dimensions. So the ion optical object of the charge analyzer (I) is formed by the intersection (B) of the electron beam (0.5 mm diameter) with the neutral beam (1 x 8 mm). The charge resolving power of the analyzer magnet is 1 : 8. The background pressure is 5 x 10-s torr. When target gas is introduced, the pressure rises to about 1 x 10-s torr. In the collision region (B) we then 411
412
M. J. VAN DER
WIEL,
TH. M. EL-SHERBINI
AND L. VRIENS
Fig. 1. Schematic diagram of the apparatus. A : electron gun with Einzel lens; B: neutral beam from multi-channel gas jet crossing the electron beam; C: plate for measuring the total ion production; H : homogeneous extraction field; I : 30” charge analyzer; K : post-acceleration; L: Bendix M-306 magnetic multiplier. D through G are not discussed in this paper.
have
a few times
1O-5 torr,
as determined
from known
ionization
cross
sections 3). As there is no axial magnetic field, the electron beam will be deflected in the extraction region. It is brought back to the axis of the apparatus for analysis in the velocity selector (F), which will be discussed in another paper, by applying electric cross fields before and after the ion extraction plates. These fields also serve to keep secondary electrons away from the collision region. In addition to a rough compensation of the earth magnetic field with coils around the apparatus, we also reduced the stray field of the analyzer magnet at the electron bean axis to less than 10-s gauss by enclosing the magnet in a layer of iron and one of “CO-NETIC”. B. Initial checks. Behind a slit in the upper extraction field plate, facing the entrance to the extraction system, a highly insulated electrode (C) has been placed for a dual purpose. First: to measure (after reversal of the extraction field) the total ion current produced, and compare it with the sum of the DC-measured currents
MULTIPLE
IONKZATION
OF
He,
Ne
AND Ar
413
at the end of the charge analyzer. When measuring on electrode C, we keep it at such a voltage with respect to the upper extraction field plate that saturation in the collected current is ensured. In this way a transmission of (100 & 3)% is found for extraction voltages ranging from 50 V/cm to 600 V/cm. Second: to determine the energy dependence of the total ion production, which in our energy range is very sensitive to the presence of secondary electrons. After normalization at 10 keV, this check on Ar showed a 3% reproduction of Schram’s gross ionization datas), which we believe to be free from secondary-electron effects. Suppression of these effects in our apparatus is comparatively easy due to the absence of an axial magnetic field. C. Detect ion. Ion pulse counting was performed with a Bendix M-306 multiplier, together with a 50 Q input solid state current amplifier (voltage gain of 1600 at 4 ns risetime). This combination enabled us to count ions with a partly flat discriminator response at a background of about 1 pulse per 5 minutes. Furthermore, changes in post-acceleration voltage between 4 keV and 12 keV had no effect on the count rate. So we assume a counting efficiency of 1, which was confirmed to an accuracy of 10% by a DCmeasurement. The ratios of the Ar+, Arz+ and Ars+ count rates were checked against a Faraday-cage measurement and found to agree within 3%. 3. Results. We determined the ratios of the ion abundances for thegases He, Ne and Ar at a number of energies between 2 and 16 keV and normalized TABLE I Partial
ionization
cross sections
of He, Ne and Ar
1)
He+
1)
Ed
He2+
He+
He2+
Ne+
Ne2+
Nes+
Ned+
Ar+
A++
Ars+
A++
in keV
in 10-18
in lo-20
in 10-1s
in lo-20
in
in
in
in
in
in
in
in
in
in
IO-17
10-19
IO-20
IO-21
10-17
10-13
10-13
10-13
IO-20
IO-21
cm2
cm2
cm2
cm2
cm2
cm2
cm2
cm2
cm2
cm2
cm2
cm2
cm2
11) 11)
Ars+
Are+
cm2
2
6.20
3.43
7.30
4.21
1.63
9.75
8.03
5.89
3.85
3.39
1.04
2.58
4.69
3
4.43
2.34
5.21
2.86
1.20
7.17
6.24
5.91
2.81
2.41
0.745
1.77
2.99
5.88
4
3.53
1.78
4.08
2.14
0.970
4.85
3.99
4.73
2.20
1.90
0.590
1.45
2.21
4.38
6
2.53
1.21
2.90
1.44
0.714
3.50
2.90
3.42
1.64
1.35
0.408
0.916
1.51
3.02
8
1.98
0.944
2.28
1.12
0.702
1.11
2.47
1.88 1.61
0.892 0.753
2.73 2.05 1.93
0.332
0.758 0.642
2.32 1.86 1.74
1.05
1.66 1.42
2.59 2.22 1.90
1.28
10 12
0.568 0.477 0.413
1.07 0.945
14
1.27
0.557
1.42
0.643
0.367
1.63
1.45
1.62
0.811
0.883 0.742 0.648
0.276 0.238 0.214
0.581 0.516 0.456
0.910 0.796 0.715
2.07 1.63 1.53
16
1.12
0.498
1.26
0.583
I) He+ normalized II)
He+ normalized
on Schram on Vriens’).
et al.
3).
8.59
414
M. J. VAN
DER
WIEL,
TH.
M. EL-SHERBINI
AND
L. VRIENS
them on the absolute gross ionization cross sections of Schram et al. 3) (see table I). The He-results have also been normalized on a set of cross sections evaluated from sum rules6) by Vriens7). According to this calculation Schram’s cross section for He+ at 1 keV is (19 &- 2)x too low. The discrepancy with Schram’s partial cross sections19 z), which were measured in an apparatus different from that of ref. 3, is large. Our values for the multiple ions are higher by about a factor 1.5 for 2+ ions up to a factor 4 for 6+ ions, the 1 + cross section being consequently lower: 1y0 for He to 9% for Ar. In our energy range only a few data from other authors495) are available; a comparison at 2 keV is made in table II. TABLE II Comparison of relative abundances of multiply charged ions at an impact energy of 2 keV Gas
author
He
Gaudin and H. 4) Schram et al. 1.3) this work
5.5 x 10-3 4.2 x 10-3 5.8 x 10-3
Ne
Gaudin and H. 4, Ziesel 5, Schram et al. 1~2) this work
4.4 4.4 3.4 6.0
Ar
Gaudin and H. 4) Schram et al. 1.2) this work
3+/1+
2+/1+
4+/1+
2.7 x 10-3 2.7 x 10-3 1.9 x 10-3 4.9 x 10-3
1.6 1.8 1.0 3.6
5.7 x 10-3
1.1 x 10-3
5.3 x
10-Z
1.2 x 10-Z
8.8 x 10-3
2.7 x 10-3
2.4 x 10-3 2.3 x 10-3 6.7 x 10-3
x x x x
10-3 10-3 10-3 10-3
x x x x
5+/1+
10-4 10-4 10-4 10-4 2.9 x 1O-4 3.0 x 10-4 1.2 x 10-3
4. Analysis of electron impact data. Our results can be compared with photo-ionization data using the well-known Bethe (first Born) relation:
oniEe1 = Eel -.Mii ln 7 4xaiR
+
CT&
where cni is the cross section for n+ ionization, Eel is the impact energy corrected for relativistic effects, i.e. Eel = $m~~v~~, where me and Z)erare the electron rest mass and velocity respectively (see also ref. 8), R is the Rydberg energy and Mii and C,r are constants; Mii is given by Mii =
df(n+) R ____ -dE, dE E s ?L+
(2)
continuum
df (n+)
being the differential dE sition to the n+ continuum
dipole oscillator
strength
at an energy transfer
for an ionizing trandf (n+) is equal to E. As dE
MULTIPLE
IONIZATION
OF He, Ne AND Ar
415
. I
q
Ne+ Ne'+(x10) Ne3+(x100)
x 0
I
1
0
n
n
---AA
n
n
;;
0
(
I
!
1
2
3
B
6
I
8 -
10
12
lb
16
Eel in keV
Fig. 2. Plot of o,~E,~/4xa~R v.In Eel for the partial ionization cross sections of He and Ne. He2+ values from normalization on Vriens 7),
mc -a$+> (E), where g$,T? (E) is the n+ photo-ionization xezh
cross section, we
can compare with photo-ionization results. As is demonstrated in fig. 2 for He and Ne, and in fig. 3 for Ar, the measured cross sections can be described by eq. (1). For the Nezf, Neaf and Ne*+ ions, we find a constant slope in the crE,l vs. In E,l plots at energies above 4 keV; for A++ and Ars+ there is a break in the curves at about 8 keV. These points will be accounted for in section 6. The constants Mfi and C,i, as obtained from a least squares analysis of our data, are listed in table III (columns 5 and 8). For comparison the table includes the values of Schram et al. 192) (columns 6 and 9). The fact that the constant C,i is not always positive is caused by the arbitrariness in the choice of a unit for E,l in the In term (in our case R).
3.6
Ne4f
t
Values
:
4 x
in parentheses
(<5
(
(1.6
(2.7
4.5
(1.6
x
x
x
x
x
x
1.3 x
x
5 x
(column
-j
(II)
0.02 0.9)
x
0.5)
1.0)
8 keV: + 2.4)
(5.5
10-4
above
< 1 x
8 keV: +
10-4
(1.9
x
x
0.14 0.07)
-& 2.3)
*
* *
1.8)
above
<5
(8.8
(8.5
3.72 (2.22
(5.2 *
(5.2 & 1.3) x
(4.9 *
1.85 f
x x
0.5)
by substraction
He+ normalized
10-i
lO-3
10-3
this work
(4.4 + 0.9)
0.49
5)
10-4(1)
10-4)
10-3
1O-3
10-s
10-i 1.0
8.1
x
x
x
x
lo-”
1O-2
10-l
1O-4
10-3
10-3
5 and 2.
3.76 2.31
3.6
of columns
x
1.0 x
8.8
1.82
< 0
on Vriens 7)
x
x
x
x
x
10-4
10-3
10-s
IO-4(n)
et al.
Schram
0.489
6)
impact
for He, h:e and Ar
from electron
and C,i
10-4 (7.7 i
3)
3) were obtained
et al. 3)
10-S)
x
x
%-
j
10-3)
10-4)
j
j
10-3)
10-s
2.0
3.8
10-3
x
5 x
5.1
10-4)
of
sum
2) c
10-e
10-4
shell
outer
4)
experiments
ej. from
electron
multiple
4.2
3)
on Schram
10-4
4.6 x 10-5; + K-shell :
1 x 10-3
+ K-shell
10-3
(I) He+ normalized
Ars+
7.2 x
4.8 x 10-4
Ars+
10-e
Ar4f
x
5.8
Ar3f
10-i
10-4
10-3
10-3
1.5 x
x
x
x
Ar3+
3.80
2.5
Ne3f
Ar+
shell
sec. proc.
9.0
1.74
0.49
shell
outer
from inn.
ejection
in
ioniz.
iFez+
Ne+
He3+
He+
ion
2) one elect.
1) single
from photoionization
Mfi
M$
TABLE III
theory
x
2.5823)
1.7122)
5.3
lo-4(10)
0.488521)
7)
this
10-3
6 x
-1.1
-1.95
10-3
- 0.77
-9.9
0 x
10-3
1 x
6.5
2.0
-2.0
10-3
5 x
x
x
x
x
x
x
10-3
10-i
10-i
10-4
10-3
10-i
et al.
Schram
-2.07
0.18
9)
impact
-2.60 3 x 10-i
10-i
lo-2(11)
1.3 x
-2.34
1.5 x
1.0 x
0.72(11) 10-“(I)
work
0.18(I)
8)
electron
Cni
MULTIPLE
IONIZATION
417
OF He, Ne AND Ar
_-15
10 '-
x
Ar .?+ (x10)
D
A?+
1x20)
A A#+
(x50)
o
A?+
(x500)
V
A?
(x5000)
0 --0
5 1; 2
1
1
3
4
a I
6
-----+
Fig. 3. Plot of o,,iE,J4xa$?
VS.
7v 10
12
14
E., in keV
In Eel for the partial ionization cross sections of Ar.
5. Analysis of photo-ionizatiolz data. Contributions to M~i, the integrated dipole oscillator strength (see eq. (2)), d 0 not arise from one-electron transitions only but also from multiple electron jumps if we take into account the correlation between the atomic electronsg*la). Because inner and outer shells interact only weakly, as is demonstrated by the relative slowness of the Auger process, one may roughly distinguish between two different channels leading to an n+ continuum: a. single electron ejection from an inner shell followed by a variety of secondary events like Auger processes, electron shake-off and direct collisions of the ejected inner shell electron with another atomic electron; no clear distinction between these secondary processes can be made. b. multiple electron ejection from the outer shell, which process is entirely due to correlation effects. A refinement of this classification should include excitation of inner shell electrons and correlation in these, and between different, shells. As presumably these phenomena contribute only littlell) to Mzi, we limit our discussion to the aforementioned processes a and b.
418
M. J. VAN
DER
WIEL,
TH.
M. EL-SHERBINI
AND
L. VRIENS
Process a. In order to obtain the contribution of a certain inner shell electron ejection to M~i, we have to know two things: first, the integrated dipole oscillator strength for such an electron ejection and second, the probability of subsequent formation of a lz+ ion. For Ne no K-shell photo-ionization data are available. Therefore we took MF (K-shell) = 1.2 x 10-2, an average of what can be found from sum rulesrs) (1.38 x 10V2) and by analyzing in a crE,i VS.In Eel plot the measurements of K-shell electron ejection of Glupe and Mehlhornia) (1.24 x 10-2) and the calculation of Arthurs and Moiseiwitschr4) (1.03 x 10-2). For Ar we took MF (Lr-shell) = 4.6 x 10-a and MiJ (Lrr, rrr-shell) = 1.6 x 10-1, on the basis of an extrapolation (see fig. 4) and integration of the photoabsorption measurements of Lukirskii et al. 15). Sum rules were used to obtain MF (K-shell) = 4.2 x 10e3. dfW+) Carlson and Krause 11~16*17) measured how 2 -.___ is distributed among dE n the various charges as a function of E. Their results and the above Mf (inner shell) values provided us with the results listed in table III, column 2.
df(n+) Process
Nesf, Nea+ and A+,
df(l+) dE-
for Hezf, dE i using photons with energy below the threshold of the
b. Carlsonis)
1.5x10‘
determined
the ratio ~
L, m_edge
e
1.0
0.5
0 _
Fig. 4. Plot of (1 /E) (df/dE) ments by Lukirskii
against
600
E for Ar, taken from photo-absorption
ef al. 15). The broken estimate
Energy transfer
lines show how we extrapolated
the contributions
of the two inner shells.
EW)
measurethe curves
to
MULTIPLE IONIZATION OF He, first
can
combined
for He, Ne and Ar by Lukirskii
rr dE by Samsonis)
dfU+)
and of ___ dE
Ar
419
df(?a+)
et aZ.15), of 2 n -=
for Ne
for He, Ne and Ar by Com”es and Elzersa), to
df(n+)
give absolute values of dE.
Ne
In overlapping
energy regions an average
was taken. Integration over the various continua yields the contribution of outer shell processes to Mii. The results are presented in table III, columns 1 (n = 1) and 3. 6. Comparison of electron impact ad photo-ionization data. Table III, column 4, shows the sum of the two contributions of processes a and b (see section 5) t0 M~i. When taking into account the poor accuracy of the integrated oscillator strengths (lO_20x), we find a good agreement with the M$ measured in this work. In those cases where no data were available to calculate the contribution of the outer shell correlation effect, its magnitude was found by subtracting the inner shell part from the measured Mii (column 3, values in parentheses). Comparison of a summation in column 4 with the slope in a uEel vs. In Eel plot (column 5) is only justified in an energy region where eq. (1) holds also for inner shells. For Neaf, Nes+ and Ne4+ (I.P. K-shell = 867 eV) this apparently (see fig. 2) is the case for energies above 4 keV. For Ars+ and Ar6+ our measurements have been expressed in two numbers for Mi,: one at energies below 6 keV, where formation of these ions largely occurs via Lr- and LII,II~-electron ejection; a second at energies above 8 keV, where the K-shell (I.P. = 3.2 keV) contribution, though possibly not reaching its asymptotic behaviour, becomes dominant (see fig. 3). For a number of ion species theoretical data on photoionization cross sections exist. Table III, column 7 gives the integrated values of Bell and Kingstonsi) for He+, of Byron and Joachainio) for Hes+ and of Cooperss) for Nef and Ar+ (taking only the p-electrons into account). 7. Conclusion. Cross sections for multiple ionization were measured with an apparatus, in which special attention was paid to avoid any of the effects which often disturb these measurements: 1) secondary electrons in the collision region ; 2) charge discrimination in the ion source ; 3) low and unknown transmission in the extraction and focusing system; 4) unknown detection efficiency, which necessitates frequent calibration of the multiplier. From an analysis of photo-ionization data on a number of ions it has proved possible to evaluate separately the two contributions to Mzi, that from single electron ejection from an inner shell and that from multiple processes in the outer shell. Good agreement is found with the electron
420
MULTIPLE
measurements
presented
IONlZATlON
OF
He,
Ne AND
Ar
here. In those cases, where the contribution
of the
correlation effect to n/r~ihad to be obtained from a subtraction (see section 6), we always found positive values which decrease with increasing number of ejected electrons. This realistic behaviour further supports our analysis and illustrates the importance of correlation effects. Acknowledgments. The authors are indebted to Dr. A. J. H. Boerboom and Mr. E. de Haas for their help in designing the apparatus, and to Mr. A. N. van der Steege for his assistance in the experimental work. They also express their gratitude to the Electronics Department of the Institute and especially to Mr. H. Buis for developing the preamplifier. Professor J. Kistemaker and Dr. F. J. de Heer have greatly stimulated this work by their constant interest. The authors are further indebted to Professor U. Fano and Dr. M. Inokuti for valuable comments. This work is part of the research program of the Stichting voor Fundamentaal 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 Organization for the Advancement of Pure Research).
REFERENCES 1) Schram,
B. L., Boerboom,
2) 3)
Schram, Schram,
B. L., Physica 32 (1966) 197. B. L., de Heer, F. J., van der Wiel,
4.
(1965) 94. Gaudin, A. and Hagemann,
R., J. Chim.
5)
Ziesel,
62 (1965)
6) 7)
Inokuti, M., Kim, Y. K. and Platzman, Vriens, L., unpublished.
J. P., J. Chim.
8)
Bethe,
9.
Van der Wiel,
H., Ann.
A. J. H. and Kistemaker,
phys.
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M. J., de Heer,
M. J. and Kistemaker,
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R. L., Phys. Fano,
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U., Phys.
F. J. and Wiebes,
F. W. and Joachain,
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164 (1967)
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G., Phys.
10)
Byron, Carlson,
12)
Schram,
13)
Glupe,
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Arthurs, A. M. and Moiseiwitsch, B. L., Proc. Roy. Sot. A247 (1958) 550. Lukirskii, A. P., Brytov, I. A. and Zimkina, T. M., Optics and Spectrosc.
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(U.S.A.) Carlson,
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M. O., Phys.
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Carlson,
T. A. and Krause,
M. O., Phys.
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151 (1966)
41.
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Carlson, Samson,
T. A., Phys. Rev. 156 (1965) 142. J. A. R., J. Opt. Sot. Am. 55 (1965)
20)
Comes,
21)
Bell,
22)
Cooper,
B. L., Thesis,
F. J. and Elzer,
164 (1967) 140 (1965)
W.,
of Amsterdam,
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K. L. and Kingston, Phys.
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J. W.,
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T. A. and Krause,
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