Ionization cross sections for electrons (100–600 eV) in noble and diatomic gases

Schram, Monstafa, Schutten, De Heer, 1966

B. L.

Physica 32 734-740

H. R. J. F. J.

IONIZATION CROSS SECTIONS FOR ELECTRONS (100-600 eV) IN NOBLE AND DIATOMIC GASES by B. L. SCHRAM, H. R. MOUSTAFA, and F. J. DE HEER FOM-Laboratorium

voor Massascheiding,

J. SCHUTTEN

Amsterdam,

Nederland.

synopsis Gross ionization cross sections have been measured for electrons with energy of 100-600 eV for all the noble gases and H s, Ne and Oz. From this experiment and our previously made measurements with electrons of higher energy it is found that the experimental values satisfy the Bethe-Born relation above 700 to 800 eV. For helium a comparison is made with theoretical values.

Irttrodzlction. In this paper we report our results on the gross ionization cross sections for electrons with energy varying from 100 to 600 eV, incident on noble and diatomic gases. The data were obtained by means of the condenser technique; a beam of electrons, guided by a magnetic field, is shot between two condenser plates and the ions produced between these plates are collected on one of them by applying a small transverse electric field. The present experiment is an extension of our previous study on the ionization cross sections for electrons with energy from 0.6-20 keV1). That investigation showed that the high energy data were in good agreement with the Bethe-Born relation, which predicts the cross section to be proportional to (l/Eel) In Eel. As it is well known that at low electron energies this theory overestimates the cross sections, an extension of this type of measurements to lower energies is interesting in order to see to what energies the experimental data do follow the theory. Some absolute cross section measurements have been made in this energy rangea) 3) 4), but in view of the mutual differences it is worthwhile for obtaining the correct shape of the cross section curves to have the cross sections, at these intermediate electron energies, determined with the same apparatus as was used in our high energy experiments. Exfierimental. The same apparatus was used as in the work with the on the high energy electrons 1). With the same potential distribution -

734 -

IONIZATION

electrode

system,

CROSS

SECTIONS

the electron

FOR

ELECTRONS

accelerating

100 eV when the highest magnetic

735

IN GASES

voltage

could

be lowered

to

fields (400 gauss) were used.

The accelerating voltage of the electrons is equal to the (negative) voltage of the electron source plus half the voltage across the condenser plates, provided that the electron beam passes in the plane exactly in the middle of the condenser plates. A simple check to see whether this condition is fulfilled can be made by varying the voltage over the condenser plates and readjusting the voltage on the electron gun so that -V,,,,, + $Voond. = = constant. If the beam does not pass exactly through the middle of the electrode system, the accelerating electron voltage will vary too. In doing so (at about 180 eV) no change in the ratio of I+/I- was observed, indicating that there is no serious deviation in the position of the electron beam. Some random tests showed that the absolute cross sections above 600 eV agreed within 3% to our previous values. Therefore no absolute pressure measurements were made but only relative cross sections were determined which were normalized to our high energy data. As the cross sections are proportional to (1+/r._) . (1 /fi), we can obtain these relative data by measuring at constant pressure (1+/I-) as a function of electron energy, for which a special automatic technique was developed by one of us (J.S.), which is described in the appendix. Results. The values for the gross ionization cross sections are listed in table I. The measurements were made for all the noble gases and the TABLE

r

Gross

imization

Gas

\I \,I

He

100

0.326

120

0.325

140

cross

-

-I

sections

I

for electrons

I

in units

of

lo-lscm*.

Ne

Ar

Kr

Xe

HZ

N2

0.639

2.78

4.42

6.21

0.804

2.46

0.653

2.68

4.14

6.15

0.750

2.43

0.32 1

0.678

2.56

3.93

5.89

0.707

2.36

160

0.311

0.686

2.43

3.69

5.57

0.664

180

0.300 0.291

0.678 0.671

2.32

300 400

0.245

0.607 0.541

1.87

2.74

5.34 5.14 4.23

0.627

2.26

3.50 3.38

2.28 2.19

0.595 0.472

2.10 1.72

1.60

2.38

3.67

0.392

1.48

500

0.182

3.17

0.334 0.293

1.27

0.159

1.37 1.20

2.02

600

0.478 0.430

Eel

200

0.209

-

I

1.84

I

2.84

I

1.15

diatomic gases Hz, Nz and 02. The accuracy is of the same order as in our previous work. A comparison of the present data with those of Tat e and Smit hz) 3) shows our values to be lower by 10 to 3Oo/o. This discrepancy can be reduced to some extent when a correction is applied to the measurements of Tate

736

B. L. SCHRAM,

and Smith previously

on their

H. R. MOUSTAFA,

pressure

made assumption

J. SCHUTTEN

determinations that

their

AND F. J. DE HEER

with a McLeod

cross sections

might

gauge.

Our

be enlarged

by contributions of secondary electrons, is presumably not fully correct, because also at low electron energies our values are smaller. When we compare

our results with those of Rapp4)

and of Asundi

and

Kurep as), we find also their values to be higher than ours. In general the data of Rapp are higher by 8 to 20% while those of Asundi and Kurepa, who measured from threshold up to 100 eV, show a trend to be higher by about 20 to 35%. The reason for the mutual differences is not clear, as in most cases the accuracy claimed is in the order of 5%. Most probably it must be explained by unknown inaccuracies in the pressure measurements. Discussion.

To see how far the experimental data satisfy the theoretical relations, we have made graphs of ogE;l against In ELt, in which both the present data and our previously obtained high energy data are plotted. At the high electron energies it is necessary to make corrections because of relativistic effects. In our energy range (up to 20 keV) this can be accounted for, by replacing Eel by ELl. Here ELl is defined by: ELl = $mavs (ma = = rest mass of the electron) and is related to Eel by:

Fig. 1. Plot of oaE&/4nao2R versus In E;l for helium and hydrogen.

Fig. 1 shows such graphs of aaE;l against In ELl for the atomic gas He and the molecular gas Hz. Obviously below about 800 eV the experimental *)

This

expression

was

misprinted

in ref.

1.

IONIZATION CROSS SECTIONS FOR ELECTRONS IN GASES

737

values fall below the extrapolated high energy data. The same graphs were made for the other gases and in nearly all cases the gross ionization cross sections start to deviate from the straight line below 700 or 800 eV. Theonly exception seemed to be with the heavier noble gases Kr and Xe, which showed a very small difference between the experimental data at low electron energy and the extrapolated high energy values. This behaviour can be understood when one realizes that there is a great contribution from multiple ionizations in the gross ionization cross sections for these gases. From fig. 2 one can see the difference in krypton between the gross and the

Fig. 2. Plot of o~E~~/4na$Rversus In EL1 for krypton; q : gross ionization cross section, x : partial cross section for single ionization.

100

imo

600 Ed in lV

Fig. 3. Graph of calculated cross sections expressed in units of our experimental cross sections ; B-B : Bethe-Born relation, B: Born approximation, P: modified Born approximation by Peach, V: semi-empirical relation of Vriens.

738 partial

B. L. SCHRAM,

H. R. MOUSTAFA,

cross section

measured

for single

J. SCHUTTEN

ionization.

by us over the energy range 0.5-15

This

AND

partial

keV6).

F. J. DE

HEER

cross section

was

Below 500 eV we used

the data of Tate and Smi t h7) and calculated from their ratios and our gross ionization cross sections, the partial cross sections in the region lOO500 eV. These partial cross sections show indeed the expected behaviour. At lower electron energies, where the cross sections do not fit the BetheBorn relation, more refined theoretical treatments are needed. We shall restrict ourselves here to helium as for this compound the most accurate calculations have been made. So we have plotted in fig. 3 values of calculated cross sections expressed in units of our experimental cross sections at the same electron energy. Included in this graph are the results of calculations by the Born approximation*), by a modified Born approximation of Peat h*), by the Bethe-Born relation (using relation (4) from ref. 9) and by a semi-empirical relation of Vr iens 10). The latter two are both normalized on our high energy data. At energies of 700 eV the theoretical data agree to within 6% with the experimental values, but at decreasing electron energies both sets of data rapidly diverge, the deviation being greater, the lower the energy, and e.g. at 100 eV the results of the Bethe-Born relation are too high by 60%, the Born approximation by 50% and Peach’s values by 35%. From the graph one gets the impression that the values calculated by the Bethe-Born relation are lower than those calculated by the Born method (for electron energies above 125 eV) but this is only due to the normalization of the Bethe-Born values to our high energy data which are about 6% lower than the Born values. The semi-empirical relation by Vriens gives, however, good agreement over the full energy range investigated here and seems to be a very useful relation in (difference from +4 to -5%) view of its relative Acknowledgements. Dr. J. Kistemaker

simplicity. The authors like to express their thanks to Prof. for his stimulating interest in this work.

This work is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie and was made possible by financial support from the Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek.

APPENDIX

As the ionization cross section is proportional to (1+/I_) . (1 ifi), we can obtain a relative cross section graph by measuring (1+/r_) at constant pressure as a function of the electron energy. With the use of a modified self-compensating pen-recorder, automatically plotted graphs were obtained. The principle of this method is indicated in fig. 4. An amplifier amplifies the difference between I+ RI and I- aRz (CY is the fraction of R:! determined

IONIZATION CROSS SECTIONS FOR ELECTRONS IN GASES

739

Fig. 4. Scheme of the electronic circuit.

by the setting of the potentiometer) and drives a servomotor; the direction of rotation is determined by the polarity of the difference voltage. In the equilibrium position the following relation holds:

I+ RI = I- aR2 SO

R2

I+

I-=aRl’

In this way the pen-recorder registrates the ratio of (1+/I_), as a is equal to the pen travel and RI, Rs are constant. The accuracy obtained depends on the value of I+ and I-, the amplification, the linearity of Rs, the sensitivity of the servomotor and on the friction of the moving parts. The amplification is limited by conditions of stability; as loop gain is proportional to I_, stability is also dependent on this current. The properties of our apparatus are indicated in fig. 5, from which we see that an accuracy of better than 0.5% is obtained for values of I+ corresponding with the voltage I+ R1 between 10 and 500 mV. If a second potentiometer is mechanically coupled with Rs, Rs being connected

4 l2 0 -2 A / 10

1D

so

200

IO0 1000

-&iinmV

Fig. 5. Output of the ratiometer as a function of the input voltage. Input 1 of the ratiometer was directly connected to a voltage E, = I+R,, variable from 10 to 500 mV; input 2 was connected to a constant ratio of this voltage by a resistor divider. Deviation of the recorded ratio from the true ratio is less than 0.5% in the range 1O- 500mV.

740

IONIZATION

CROSS

SECTIONS

FOR

ELECTRONS

to a battery of constant voltage E, a voltage be applied to the Y axis of an X-Y-recorder. proportional

to the electron

By varying

the electron

IN GASES

proportional To the X

to (1+/I_) can axis a voltage

energy is applied. energy,

a relative

ionization

cross section versu:

energy graph can be obtained in a few minutes. Normalizing our high energy data gives then the absolute cross sections. Of course in some cases the corrections

mentioned

at 0.6 kV to

in our previous article 1)

should be taken into account. However, the scattering of fast electrons against the ion collecting electrode is negligiable at low electron energies and the collection of slow electrons at the electron collector can be minimized by working at low pressures. Received

9-9-65

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P. T., Phys.

F. J., Van

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J. T. and Smith,

Rapp,

D., Englander-Golden, D., and Englander-Golden,

Asundi,

6)

Schram,

7) Tate,

R. K. and Kurepa, B. L., Phpsica

J. T. and Smith,

Peach,

9) Schram, 10) Vriens,

der

Wiel,

&I. J, and Kistemaker,

J., Physica

1293.

P. T., Phys. Rev. 39 (1932) 270.

Rapp, 5)

8)

B. L., De Heer, 94.

P. and Briglia, M. V., J. Electron.

38 (1966)

D. D., J. them.

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Phys.

Contr.

197.

P. T., Phys.

Rev. 48 (1934) 773.

G., Proc. Phys. SIX. 83 (1965) 709. B. L. and Vriens, L., Physica

L., Physica

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1431.

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Phys. 41 (1965) 4081;

(1965)

15 (1963) 41.

1464.

31