ABSOLUTE ELECTRON IMPACT IONIZATION
CROSS SECTIONS OF N, O AND Ne
G. Glupe, W. Mehlhorn
To cite this version:
G. Glupe, W. Mehlhorn. ABSOLUTE ELECTRON IMPACT IONIZATION CROSS SECTIONS OF N, O AND Ne. Journal de Physique Colloques, 1971, 32 (C4), pp.C4-40-C4-43.
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Submitted on 1 Jan 1971
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JOURNAL DE PHYSIQUE
Colloque C4, supplkment au no 10, Tome 32, Octobre 1971, page C4-40
ABSOLUTE ELECTRON IMPACT IONIZATION CROSS _SECTIONS
OF N, 0 AND Ne (*)
G. GLUPE and W. MEHLHORN
Institute of Nuclear Physics, University of Miinster, Germany
Rbsumb. - Les sections efficaces d'ionisation par impact klectronique ont ktk mesurkes en valeur
relative et absolue au moyen des transitions Auger pour la couche K de M, 0 et Ne et des knergies
electroniques comprises entre E = 1,5 EK et E = 10,5 KeV (dans le cas de M et Ne) et 13 KeV
(dans le cas de 0). Une cible gazeuse est utilide dans tous les cas. Les rksultats expkrimentaux sont
cornparks aux valeurs thkoriques calculkes par Burhap, Rudge et Schwarz (thkorie quantique) et par
Gryzminski (thkorie classique).
Abstract. - By means of Auger transitions the relative and absolute electron impact ionization
cross sections of the K shell of N, 0 and Ne have been measured for electron energies from
E = 1.5 EKup to E = 10.5 keV (in the case of N and Ne) and 13 keV (in the case of 0). In all cases
gaseous targets have been used. The experimental results are compared with theoretical values
calculated by Burhop and Rudge and Schwartz (quantum theory) and by Gryzinski (classical
theory).
1. Introduction. - During the last years there
was a growing interest, experimentally [l] as well as
theoreticcally 121, in electron impact ionization cross
sections. Most experiments determined ionization
cross sections of the outermost shells, whereas there
is little experimental knowledge of inner shell cross
sections. Figure 1 presents in graphical form elements
FIG. 1. -Elements
and reduced energy regions of K shell
ionization cross section measurements.
and energy regions (in units of binding energy E,)
which have been investigated so far [3a-k]. The experimental cross sections for elements of medium and
large Z agree satisfactorily with theoretical values
calculated by Arthurs and Moiseiwitsch 141 with
relativistic theory. Nonrelativistic values calculated
by Burhop [5] are considerably smaller than experimental values even for elements of medium 2, e. g.
(*) This work has been financially supported by the Deutsche
Forschungsgemeinschaft.
Ni [3d], Cu [3e], Sn [3k]. Very recently Hink and
Ziegler [3b] found also for A1 the nonrelativistic
values by Burhop to be smaller than the experimental
values by about 30-60 %. The same discrepancy has
been shown earlier by Glupe and Mehlhorn [3a]
for C, N, 0 and Ne. In order to test the validity of the
present nonrelativistic theory of impact ionization by
electrons we repeated the measurements of K shell
cross sections of N, 0 and Ne with smaller experimental errors and for the larger energy region from
E = 1 . 5 E K u p t o10.5 keV(forNandNe)and 13 keV
(for 0 ) .
2. Method and Experiment. - In all cases, except
for C, N, 0 and Ne, inner shell ionization cross
sections have been determined by the emission of K
X-radiation. In the present investigation we measured
K shell cross sections by means of the emission of K
shell Auger electrons. This method, introduced
earlier [3a], has advantages over the former method
in all cases, where the ionization energy of the inner
electrons is small, less than 1 keV, because in these
cases no accurate fluorescence yields are available.
E. g., the flourescence yield of neon is known to be
U, = 0.025 $. 0.015 161, here the error is 60 %.From
this the probability of an Auger process is
aK = 1 - W, = 0.975
+ 0.015,
here the error is only 1.5 %. This demonstrates clearly
the higher accuracy of the new method for low 2.
In order to avoid energy losses of the low energy
Auger electrons we used gaseous targets (NZ,0 2 , CO,
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971408
ABSOLUTE ELECTRON IMPACT IONIZATION CROSS SECTIONS
Ne) with pressures of about 1 X 10-3 torr. The apparatus used in this investigation has been discribed
earlier [7]. The Auger electrons were analyzed by
means of an electrostatic cylindrical mirror analyzer
with an energy resolution of 1 % and were measured
by a Faraday cage followed by a vibrating reed electrometer. The output voltage of the electrometer was
recorded by an XY-recorder, the X-axis being given
by the spectrometer voltage, which has been varied
continuously.
The target gas pressure has been measured by a
MCLeod gauge. In order to reduce systematical errors
in pressure readings by the mercury diffusion stream
from the gauge to the spectrometer [8], we cooled the
walls of the MC Leod by solid COz just above the
mercury reservoir. Thus the error of the pressure
measurements is believed to be less than 3 %.
3. Results and Discussion. - a) RELATIVECROSS
SECTION.- Figure 2 presents as example the recorder
FIG.2.
- K-Auger spectra of NZ and neon excited by 3,2 keV
electrons.
plots of the K Auger spectra of NZand Ne. In measuring relative cross sections all parameters were held
constant except the intensity and energy of the primary electron beam. Evaluating relative cross sections
we used the peak heights of the dominant Auger line
of the spectrum. The only correction applied to the
relative cross sections is due the intensity loss of primary electrons on the way from the target volume to
the Faraday cage and was always less than 3 %.
The main error of relative cross sections is given
by the uncertainty of the background below the Auger
spectrum, the total error of relative cross sections is
certainly less than 2 %.
Figure 3 presents the experimental relative cross
sections of N, 0 and Ne (also relative cross sections
of C are included). For E/EK > 3 all experimental
values fall to within 1 % on a general curve given by
the center of the shaded band of figure 3. For energies
E/EK < 3 the error increases to about 2 % due to the
C4-41
mEwiM
-----.
---.
Ihdge, Schwartz
GryzinsVi
FIG.3. - Relative experimentaI and theoretical ionization
cross sections as a function of reduced primary electron energy.
uncertainties of the background. The width of the
shaded band corresponds to an error of 2 %. For
comparison we calculated theoretical ionization cross
sections using Burhop's formula [5] (quantum theory
with Born approximation) and Gryzinski's [g] formula
derived by classical theory. Rudge and Schwratz [l01
calculated ionization cross sections of the 1 S-electron
of H, He' and a fictitious hydrogenic ion with nuclear
charge 2 = 128 using quantum theory and Born
exchange approximation. Their tabulated values of
reduced cross sections QR(E/EK)can be transformed to
absolute values by
Because the change in Q, going from Z = 1 to Z = 2
is larger than the change going from Z = 2 to Z = 128
we used for all elements investigated (Z = 7, 8, 10)
the reduced cross sections Q, calculated for Z = 128.
The error given by this procedure is probably in the
order of or less than 1 % [3b]. All theoretical curves
were fitted to the experimental curve at E/EK = 19.
From figure 3 it can readily be seen that for large
E/& the energy dependence of the values given by
Rudge and Schwartz [l01agrees with that of the experimental values, whereas the values given by Burhop [5]
and Gryzinski [9] decrease faster than the experimental values. The maximum of experimental cross section is at EIE;, = 4, this agrees with Gryzinski's
values but neither with Burhop's values nor with
the values by Rudge and Schwartz (Q,,, at E/EK = 3).
h) ABSOLUTE
CROSS SECTION. - Absolute cross sections Q have been evaluated by means of the following
equation
Here I,,,,, is given by the total area of the Auger
spectrum corrected for the dispersion of the spectro-
C4-42
G. GLUPE AND W. MEHLHORN
meter and the loss of intensity due to the scattering of
Auger electrons on the way through the spectrometer,
I,, is the intensity of primary electron beam at the
site of the target volume,
n(p, T) is the number of target particles per cm3,
n, gives the number of atoms under investigation
in one target particle,
A is given by the area of the spectrometer window
function, which is related to the transmission of the
spectrometer and w, is the fluorescence yield of
the K shell.
The quantity A has been determined experimentally
by measuring the intensity of elastically scattered
electrons, IelaStic,by He atoms at various energies
under the same conditions of the spectrometer as in
the case of Auger electrons. The peak area IelaStic
of
the elastic scattered electrons is given by
From eq. (3) the quantity A has been evaluated FIG.5. - Absolute experimental and theoretical ionization
cross sections of oxygen.
using the theoretical values of differential elastic
cross sections dQelaSticcalculated by Khare and
Moisewitsch [l l ] for He. The theoretical values agree
to within 2 % with experimental values, measured sections given by Burhop [5], Rudge and Schwartz [IO],
very recently by Bromberg [12], in the angular range and Gryzinski [9] are plotted. In all three cases the
of our spectrometer. The total error of absolute cross Burhop values are smaller than the experimental
sections are estimated to be 5 %, given mainly by values by more than 30 %. The Gryzinski values agree
the uncertainties of gas pressure (3 X), the shape of well with experimental values for E/E, < 10, whereas
the background (2 %) and the differential elastic the values by Rudge and Schwartz are slightly better
for E/EK > 10. These results are in concordance with
cross sections of He (2 X).
those found recently for the K shell cross sections of
Figures 4, 5 and 6 present the absolute ionization
A1 by Hink and Ziegler [3b]. Also there the Burhop
cross sections of N, 0 and Ne as functions of reduced
values were too small whereas the values by Gryenergy E/E,. For comparison also theoretical cross
zinski and Rudge and Schwartz agreed much better
with the experimental values.
/
I
I
I
l
I
I
11
FIG.4. - Absolute experimental and theoretical ionization
cross sections of nitrogen.
,---..
- ------
=
Experiment
Burhop
- Gryzinski
Rudge,Schwartz
FIG. 6. - Absolute experimental and theoretical ionization
cross sections of neon.
ABSOLUTE ELECTRON IMPACT IONIZATION CROSS SECTIONS
References
[3h] HANSEN
(H,) and FLAMMERSFELD
(A.), Nucl. Phys.,
[l] KIEFFER
(L. J.) and DUNN(G. H.), Rev. Mod. Phys.,
1966,79,135 (Ag, Sn, W, Au, Pb).
1966, 38, 1. LOTZ(W.), IPP 1/47, Institut fiir
Plasmaphysik, Garching b. Miinchen, 1966.
[3i] RESTER
(D. H.) and DANCE
(W. E.), Phys. Rev., 1966,
152, 1 (Ag, Sn, Au).
[2] RUDGE(M. R. H.), Rev. Mod. Phys., 1968, 40, 564.
[3a] GLVPE(G.) and MEHLHORN
(W.), Phys. Letters, 1967,
[3k] MOTZ(J. W.) and PLACIOUS
(R. C.), Phys. Rev., 1964,
25A, 274 (C, N, 0,Ne).
136A, 662 (Sn, Au).
[3b] HINK(W.) and ZIEGLER
(A.), Z. Phys., 1969, 226,
(A. M.) and MOISEIWITSCH
(B. L.), Proc.
[4] ARTHURS
222 (AI).
Roy. Soc. (London), 1958, A 247,550.
[3c] FISCHER
(B.) and HOFFMANN
(K.-W.), Z. Phy~.,1967,.
(E. H. S.), Proc. Cambridge Phil. Soc., 1940,
[S] BURHOP
204, 122 (AI, Mn, Cu, Se, Ag, Sn).
36,43.
[3d] SMICK(A. E.) and KIRKPATRICK
(P-), Phys. Rev.,
1945, 67, 153 (Ni). POCKMAN
(L. T.), WEBSTER [6] FINK(R. W.), JOPSON(R. C.), MARK(Hans) and
SWIFT(C. D.), Rev. of Mod. Phys., 1966,38, 513.
(D. L.), KIRKPATRICK
(P.) and HARWORTH
(K.),
MEHLHORN
(W.), Z. Phys., 1965,187,21.
[7]
Phys. Rev., 1947, 71, 330 (Ni).
[g] SCHRAM
(B. L.), DE HEER(F. J.), VANDER WIEL(M. J.)
[3e] GREEN
(G. W.), Proc. 3rd Int. Symp. X-ray Microc.,
and KISTEMAKER
(J.), Physica, 1965, 31, 94.
Standford 1962 (Academic Press New York);
[g] GRYZINSKI
(M.), Phys. Rev., 1965, 138, A 336.
Thesis Cambridge 1962 (Ni, Cu, Ag).
(S. B.), Proc.
[3f ] HANSEN
(H.), WEIGMANN
(H.) and FLAMMERSFELD
[l01 RUDGE(M. R. H.) and SCHWARTZ
Phys. Soc., London, 1966, 88,563.
(A.), Nucl. Phys., 1964, 58, 241 (Zr, Sn, W, Pb).
(B.HL.), Proc. Phys.
[3g] WEBSTER
(D. L.), HANSEN
(W. W.) and DUVENECK[l l] KHARE(S. P.) and M O I S E ~ S C
Soc., 1965, 85, 821.
(F. B.), Phys. Rev., 1933, 43, 839 (Ag). CLARK
[l21 BROMBERG
(J. P.), J. Chem. Phys., 1969, 50, 3906.
(J. C.), Phys. Rev., 1935, 48, 30 (Ag).
DISCUSSION
VAN DER WIEL,M. J. - Did YOU include in your
evaluation of the Auger Spectrum area the contribution of Auger satellite lines ?
The intensity of these lines amounts to about 10-20 %
of the normal lines, in the gases you mentioned.
Therefore a deviation between your experimental
value and the calculated ones is to be expected,
since the calculations only take into account pure
1 S-ionisation and no two-electron processes, in
which the 1 S-hole is accompanied by one in the outer
shell.
CARLSON:
T. A. - Experimentally, it has been
determined at Oak Ridge that the sum of satellite
lines in the Auger spectrum of neon amounts to about
20 % of the normal Auger lines indicating a similar
degree of doubt t o single ionization.
Answer : Yes, we included also Auger satellite lines.
In theoretical calculations of ionization cross
sections one considers the ionization process only
as a two-particle process, i. e. one neglects in theory
all electrons of the atoms except the one, which is
ionized. If shake-off theory and sudden approximation
is valid to explain the ratio of double to single ionization, then treating the ionization process as twoparticle process includes all shake-off transitions
which are induced by the primary ionization in the
inner shell. That is, experimentally the total Auger
intensity, including satellite lines, correspond to theoretical values based on the two-particle process.