Absolute cross sections for excitation of helium by electrons (20–2000 eV) and the polarization of the emitted radiation

Physica 53 (197 1) 45-59 0 North-Holland Publishing Co.

ABSOLUTE

CROSS SECTIONS

BY ELECTRONS

FOR EXCITATION

OF HELIUM

(20-2000 eV) AND THE POLARIZATION

OF THE EMITTED

RADIATION

A. F. J. VAN RAAN, J. P. DE JONGH, J. VAN ECK and H. G. M. HEIDEMAN Fysisch Laboratorium van de Rijksuniversiteit Utrecht, Nederland Received 8 December 1970

synopsis Absolute cross sections for excitation by electrons from the ground state of helium to 4rS, 5rS, 6rS, 3rP, 4iD. 5lD, 6rD, 43s and 33P states of helium have been determined by observing the resulting light emission. The energy region covered extends from 20 to 2000 eV. Two devices were used, one for electron energies from threshold up to 100 eV and another for higher impact energies. All line-intensity measurements were corrected for the polarization of the radiation, the polarizing effect of the monochromator and space-charge effects. In the evaluation of the excitation cross sections cascading effects were taken into account. The energy dependence of the lrS3rP cross section is in very good agreement with theoretical calculations above about 200 eV. The experimental values for the n.rSt and 3iP levels are in the asymptotic high-energy region about 10% larger than the theoretical ones according to the Born approximation. The energy dependences of the nrS and 3iP cross sections are in good agreement with the results of Moustafa Moussa et al. Our nrD cross sections are, although 14 to 35% larger than the theoretical values, closer to the Born values than previous experimental results. In a plot of cross section times electron energy against the logarithm of the electron energy the nrD curves exhibit a maximum. This effect becomes less pronounced for higher principal quantum numbers. The energy dependences of the 4% and 3sP cross sections do not agree with the Ez3 law as predicted by Ochkur. For energies larger than 100 eV we find a decrease proportional to E; 2*o for the 43s level and to Ez2s4 for the 33P level. The polarization results for the 3rP-2% light emission show very good agreement with the Born theory. The energy dependence of the polarization degree of the radiation of nrD-2rP transitions is over a large energy range (15&l 000 eV) in agreement with theoretical calculations; however, the magnitude of the polarization degree differs with theory which is also the case in previous experiments of other investigators.

t When speaking of the “cross section of a state”, we mean the cross section for excitation from the ground state to that state. This is for the sake of brevety. 45

VAN

46

RAAN,

DE JONGH,

VAN

ECK

AND

HEIDEMAN

1. Introduction. Although a considerable amount of work has been done on the experimental determination of excitation cross sections of helium, there is still a need for additional experiments. Recentlys) niS and ?ziP excitation cross sections have been measured, which in the asymptotic region differ by at most 10% with the calculations of Kim and Inokutir). However, cause

for niD and triplet

of the large

mutual

levels new experimental

discrepancies

between

data are needed be-

the results

of different

investigators. Recent theoretical cross-section values for higher impact energies are available by the work of Kim and Inokutil), of Bell, Kennedy and Kingston”) and of Oldhama) for singlet excitation and of Ochkur and Brattsevd) for singlet and triplet excitation. Only a few investigators published absolute experimental cross sections. Measurements up to about 500 CV have been reported by St. John et al.“), Jobe and St. JohnG), Zapesochnyi?) and measurements up to 2000 eV have been performed by Moustafa Moussa et al. 8), by De Heer et al. 9) and by McConkey andW oolsey 1”). Literature reviews on the excitation of helium by electrons have been given by St. John et al. 5), by Moiseiwitsch and Smithii) and by Kiefferi”). When determining absolute cross sections by optical measurements one has to pay much attention to a number of important points. First an accurate determination of the quantum efficiency of the optical equipment is necessary. Secondly the negative space charge due to the beam electrons causes a shift of the energy scale, which is dependent on the beam current and on the accelerating voltage. This shift Av is given by is) AI’ = -O.O3(ln

R/Ra) v-+1,

where 211 is the diameter of the measuring cage, 2x0 is the beam diameter, I’ the acceleration voltage and I the current in PA. When beam currents of 1 mA are used the energy shift is about 10 V at 50 V acceleration voltage in our setup. Though at energies above the ionization potential the voltage shift is lowered considerably due to positive ion formation, it is advisable not to use beam currents larger than 20 PA below 100 eVi4). Another important point is the influence of secondary electrons, which can cause considerable trouble especially in the case of triplet excitations). It is very well possible that secondary electrons are for a great deal responsible for the very large mutual differences between the results of St. John et a1.5), Weaver and Hughesis) (both up to 500 eV) and of Kay and Showalterr6) (up to 200 eV). Measurements at higher impact energies (Moustafa Moussa et al. 8)) are necessary for a reliable comparison with theory, but there the effect of secondary electrons is even stronger. Apart from the correction for cascading and for the polarization of the radiation it is necessary to take the polarizing effect of the monochromator into account. This can be done by measuring this polarizing effect as a

EXCITATION

function

of the wavelength

Polarization Moustafa

results

have

OF HELIUM

or by removing been published

BY ELECTRONS

47

this effect by special provisions. by McFarland

Moussa et al. s) and HeidemaniJ).

and Soltysik17),

Our polarization

measurements

have previously been published in the work of Moustafa Moussas) also included in a review given by Scharmann and Schartner is). We determined 6rS, 4iD,

the absolute

51D, 61D, 3iP,

cross sections

43s and 33P states

for excitation of helium

and are

of the 4iS, 5iS, by measuring

the

intensities of the appropriate spectral lines. The measurements have been performed with two different devices; one (device I) specially suitable for low impact energies (from threshold up to 100 eV) and another (device II) suitable for higher energies (from 40 eV up to 2000 eV). The latter device has been calibrated absolutely and the relative measurements of the first device were normalized to the absolute values at 100 eV obtained with device II. We measured the light intensities by observing the electron beam both under 90” (device I and II) and 55” (device II). All the measurements have been corrected for cascading, polarization of the radiation and the polarizing effect of the monochromator. With device II we determined for each spectral line the pressure region where the line intensity is proportional with pressure and performed our measurements in that region, except for the 3iP-21s transition (see section 3.2). The polarization degree of the 3iP-2iS, 4iD-2lP and 5iD-2iP lines as a function of energy has been determined with device II. 2. Apparatus. A detailed description of device I is given in ref. 19. This apparatus is specially suitable for threshold measurements and for the study of resonance structures in the excitation functions. The helium gas is contained in a closed excitation tube at a fixed pressure of 10-s torr. The electrons are emitted by an oxide-coated cathode and accelerated by electrodes into a field-free excitation chamber. The light emitted by a small cross section of the electron beam is focussed on the entrance slit of a Bausch and Lomb monochromator. Electron-beam currents of about 20 ~.LAwere used. Only relative measurements were done with device I. Device II is discussed in ref. 20 and is suitable for higher energies. Much care has been taken to keep secondary electrons away from the field-free region of the excitation chamber. This was achieved by a good collimation of the beam which was checked by measuring the currents on the front and back plates of the measuring cage. These currents were always less than a few tenths of a percent of the total beam current of 100 to 150 PA. The target gas pressure in the excitation chamber could be varied with a needle valve. Below 100 eV a weak axial magnetic field (maximum 10-s Wb/m2) was used to achieve a better collimation of the electron beam. Light produced along the electron beam was analyzed by a Leiss monochromator, equipped with a Bausch and Lomb grating and detected with a photo-

VAN

48

RAAN,

DE JONGH,

VAN

ECK

AND

HEIDEMAN

multiplier. The quantum yield of the monochromator and photomultiplier was determined with the aid of a calibrated tungsten filament lamp (see section 3.1). The measurements with device II have been repeated and extended with a somewhat cally the same results.

modified

excitation

tube which produced

practi-

3. Evaluation of the excitation CYOSSsections; polarization of the emitted radiation. 3.1. The excitation cross section. The cross section ai for excitation from the ground state to level i by electrons can be written as follows : ai

c

__

ai

TiAij

_

C

ski.

k>i

Here ail is the cross section for the production of photons resulting from the transition of level i to level j, pi is the lifetime of level i, Aij is the transition probability from i to j. The second term on the right-hand side represents the cascading to level i from higher levels k. The cross section aij is given by

where S(&J) is the signal which is proportional to the intensity of the spectral line emitted into a solid angle cc)as measured (in A) by the spectrometer (monochromator plus photomultiplier), N is the number of helium atoms per ms in the excitation chamber, I/e is the number of beam electrons per second in a plane perpendicular to the beam direction, L(&) is the length of that part of the beam viewed from the monochromator, K(&) is the quantum yield of the spectrometer, P(0) is the correction factor for the polarization of the radiation and 6 is the angle of observation of the emitted light with respect to the electron beam. In our experiment both 0 = 90” and 0 = 55” were used (see section 3.3). The quantum yield of the monochromator and photomultiplier of device II has been determined with the aid of a tungsten filament lamp of accurately known intensity. To make the determination of the quantum yield as accurate as possible the length of the lamp filament and the distance of the filament to the entrance slit were chosen equal to the effective length of the electron beam and to the distance of the beam to the entrance slit, respectively. So the geometrical situation was the same during the calibration and the cross section measurements, also with respect to the slit widths. In the calibration procedure we have carefully corrected for straylight intensities. The effect of background light intensities due to for instance nitrogen bands can be important especially when measuring the 4aS-23P (47 1.3 nm)

EXCITATION and 3sP-2%

(388.9 nm) transitions.

ing the background intensity.

OF HELIUM

intensity

We performed

BY ELECTRONS

We corrected

and subtracting

this correction

49

for this effect by measur-

this intensity

for all intensity

from the line

measurements.

3.2. Pressure dependence of the line intensities. The intensities of the spectral lines were linear with pressure up to 10-s torr for 1s lines and up to 5 x lo-4 torr for the rD lines and for the triplet lines 4%2sP and 3sP-2%. The intensity of the 3iP-21s line (501.6 nm) is strongly pressure dependent because of the absorption and reemission of resonance radiation. A proportional relationship is found for pressures below 5 x 10-s torr. At such low pressures the light intensities are very weak, especially at electron energies above 100 eV. Therefore we measured for the 3rP-21s line at several energies the ratio of the radiation intensities at 3 x IO-4 torr and the values extrapolated from the region where the intensities are proportional with pressure (see fig. 1). In this way a correction factor of 0.72 at 3 x 10-a torr is found which is independent of the energy. The intensities of the other spectral lines are also measured at 3 x IO-4 torr. 3.3. Polarization of the emitted radiation. The radiation emitted by atoms excited by a unidirectional beam is in general polarized as a result of a nonuniform population of the magnetic sub-levels. The monochromator has a polarizing effect on the radiation (factor Bzl)). The polarization degree L! and factor B have been determined for the lines 3rP-2rS, 4rD-2rP and 5rD-21P (see table I). A comparison of different polarization measurements is given in the work of Moustafa Moussa et al. 8) and of Scharmann and Schartnerrs) where our results (Van Eck and De Jongh) are included. The rS lines are not polarized. We checked this for the 4rS-2rP transition. With 17 and B known, the polarization correction factor P(0) 21) for the emission cross section [see formula (2)] can be determined. We measured radiation intensities at 90” and 55” with respect to the beam. The cross

intensity/p

2

3’P _ 2’s (501.6 nm)

(arb. units) -It

,*--_

p(torr) 0

I 0

1

2

I 3

I 4 x10-.

Fig, 1. Ratio of intensity and pressure vs. helium pressure for the 501.6 nm (31P-2%) line.

VAN

50

KAAN,

DE

JONGH,

VAN

TAELE Polarization effect

&I

degree

I7 for three

B of the apparatus 501.6 nm 31P-2%

(eV)

ECK

AND

HELDEMAN

I helium

lines ancl polarizing

for these wavelengths 492.2 nm

438.8 nm

41D-211’

5l1)-211’

40

0.308

0.505

0.530

60

0.298

0.430

0.460 0.405

80

0.215

0.375

100

0.212

0.320

0.355

150

0.115

0.200

0.260

200

0.056

0.112

0.180

250

- 0.005

0.052

0.120

300

0.010

0.008

0.075 0.000

400

- 0.075

-- 0.050

600

-mO.lll

PO.118

800

~-0.162

PO.152

-0.125

1000

-0.170

0.172

-0.145

0.110

0.365

0.195

B

0.080

sections evaluated with the appropriate correction factors for these two angles were in good agreement and the results have been averaged. For the 33P-2% transition we used the polarization results of McFarland and Soltysik i7). 4. Results. 4.1. Excitation cross sections. In the tables 11 and III the excitation cross sections as a function of the electron impact energy are given for different He I levels (table II from threshold up to 100 eV and table III from 100 eV up to 2000 eV). The values are subject to a total random error of about 7%. The differences between the values obtained with device I and those obtained with device II are small (at most 50/) for singlets. For triplets the differences are larger, at most 2010 (see curve shapes, table IV). In table IV we compare the shapes of the curves obtained in our experiment with those obtained by De Heer and Vroomg). In table 1’ the peak values of the absolute cross sections obtained in our experiment and by other investigators are given. 4.2. Comparison between experiment and theory. At sufficiently high impact energies the experimental results for singlet excitation may be compared with the Bethe-Born approximation. For an optically allowed transition (IiS-nip) the excitation cross section is (apart from negligible terms) given by 4xaiR2fn ‘n =

EnEel

4c, ln ~ R

E,I,

(3)

EXCITATION

OF HELIUM

BY

ELECTRONS

51

TABLE II Experimental

absolute

cross

sections

in

lo-24 ms from devices

41s $;

5%

41D

I

II

I

II

Peak

18.5

18.5

8.47

8.21

25

11.4

4.69

30

16.2

7.44

11.3

35

18.3

8.37

13.1

40

17.6

45

16.5

50

15.8

55

15.2

60

14.6

65

14.0

70

13.6

75

13.0

80

12.5

85

12.1

90

11.8

95

11.5

100

11.3

7.5

8.21

I

7.34

7.70 6.93

6.62

6.37

3.0

6.11

5.86

5.91 12.2

5.66

5.56

11.7

5.30

5.30

11.3

5.10

5.10

II

I

II

7.82

7.78

300.2

300.2

I

II

31.6

28.0

63.7

69.8

15.4

53.0

53.1

9.53

38.3

35.6

5.84

26.7

24.4

3.95

19.3

17.1

2.96

14.2

12.6

2.30

10.6

89.5

30.6

7.67

168.1

14.0

7.82

199.3

14.0

7.82

223.6

13.5

7.56

243.2

7.32

7.27

260.0

12.5

7.01

272.3

12.0

6.71

281.6

11.3

6.40

287.6

10.8

6.10

6.15

5.84

291.8

9.81

5.54

296.0 298.4

9.36

5.33

299.6

9.00

9.00

5.08

5.08

300.2

33P II

131.2

13.1

25.4 145.3

19.9 15.3

202.6

11.8 9.25 7.43

238.7

6.07 5.00

262.5

4.24 279.8

3.64 3.06

292.7

2.50

absolute

cross sections

in lo-24 ms from with device

Eel (ev)

41s

5%

6%

100

11.3

41D

300.2

1.88

1.88

8.15

5.10

2.92

150

9.58

4.25

2.40

200

8.12

3.64

2.05

4.41

2.50

300

5.96

2.78

1.57

2.79

400

4.61

2.16

1.22

2.01

1.63 1.20

500

3.91

600 700

3.35 2.87

1.57

0.866

1.25 1.07

0.763

1.26

0.658

0.972

800

2.53

900 1000

2.37 2.05

1500

1.37

2000

9.00

5.08

2.03

0.779

31P

43s

33P 8.15

300.2 278.2

1.88

1.45

253.0

0.461

1.44

0.960

204.4

0.201

0.512

0.722

167.8

0.113

0.251

0.536

143.8

0.0725

0.158

125.5 112.6

0.0491 0.0361

0.105 0.0725

0.559

0.475 0.402 0.357

102.1 93.1

0.0281 0.0217

0.0540 0.0449

0.450

0.319 0.304

87.1

0.0176

0.877 0.567

61D

3.33

1.52

1.01

100 eV up to 2000 eV measured

II

51D

9.28

2.16

TABLE III Experimental

with

I

7.06 14.3

measured

43s

I

4.54

10.4

5.20

31P

5.94

10.8

5.46

100 eV

31.6

13.1

6.38

up to

40.5

13.8

6.99 4.1

14.3

8.67

7.80 5.7

51D II

14.0

threshold

I and II

0.487

65.7

0.364

54.0

0.0394 0.0262

8.15

787s

732s

6773

6343

6103

60

70

80

90

100

1113

738”

1000

1500

b) Normalized

denote

5524

7134

1003

1233

1643

2303

the negative

124s

1533

1913

2633

power

1193

1383

1823

2573

3303

432s

5053

61S3

II

6lSb)

254“

3404

545“

6794

874”

1403

1953

3083

6293

7553

912”

3214

6201

7281

9554

1473

2073

2983

5973

723s

8803

1

I

100”

667”

780’

158s 1043

2103

3163

6293

II

100’

9943

9723

938”

8663

7453

5603

1

I

1803

2193

2903

3403

5593 418”

6813

8433

9273

100”

9753

9323

874”

7953

675s

4843

1

II

were performed

be multiplied.

6lD “)

should

5794

7194

9804

1543

2103

3223

427s

6293

7913

the number

6493

708s

7793

8573

9353

1

II

9353

51D

624”

100”

175”

403”

718j

164”

671”

819”

1053

1413

2083

3403

5503

1

II

107-1

1361

2144

667-1

1023

2193

5673

1

III

at lower energies).

5954

7864

1153

158”

2353

3743

6313

1

I

of De Heer and \-rooms) _ 31f’ 4%

at peak values) a).

measurements

(normalized

recent

9813

III:

functions

100”

1

1II

of 10 by which

6413

6993

769s

8533

9293

9943

I 100”

1

II

9813

I

411)

I resp. II;

of the excitation

with device

at the mean value of 1%= 4 and 5 at 100 eT’ (no measurements

“) The superscripts

2000

1813

1373

600

800

249s

400

3393

4433

2963

3223

3773

4383

200

6213

646s

677s

7143

776s

8453

938s

1

II

300

6023

627s

669s

723s

7833

867s

9703

1

I

51s

obtained

Curve shapes

518s

5783

6483

7613

9253

I

III

results

150

6103

634s

659s

7013

762s

8453

8543

50

I

9453

1

9513

Peak

II

40

I

(%;

41s

I, II:

TABLE IV

1283

1663

223s

3033

4193

60t3

8323

1

I

375”

5646

7746

150s

3605

7345

2064

1173

1333

1813

2453

3503

5t03

7613

1

II

33P

9635

1484

228”

9354

1633

3313

7433

I

III

EXCITATION

OF HELIUM

BY ELECTRONS

53

TABLE V Peak cross sections in lo-24 m2

Device I Device II De Heer and Vroom9) St. John et al. 5) Zapesochnyi7)

4%

51s

31P

41D

51D

43s

33P

18.5 18.5 16.4 23.5 24.5

8.47 8.21 8.05 9 12.3

300.2 300.2 284 320 530

14.0 14.3 13.1 15.5 28

7.82 7.78

31.6 28.0 31.0 27 37

63.7 69.8 100 76 105

8 13

where (TVis the excitation cross section, ao is the radius of the first Bohr orbit of hydrogen, R is the Rydberg energy, Eel is the electron energy, E, is the excitation energy, Cn is a constant l) and fn is the optical oscillator strength. Eq. (3) indicates that a straight line is obtained when aE,l is plotted against In Eel (Bethe plot). At electron energies above 150 eV our 31P data lie on this straight line (see fig. 2). The intersection of this line with the abcissa determines Cn which is related to the energy dependence of the cross section. The slope of the line gives the optical oscillator strength fn. From our experimental 3lP results we derived c31p = 0.160; within the experimental error this number is equal to the value of c31p as calculated by Kim and Inokutil). We determined from our absolute cross sections for the 31P level the corresponding oscillator strength and found fpp = 0.0803. The theoretical value of Schiff and Pekeris22) amounts to 0.0734: hence a difference of about 10%. For an optically forbidden singlet transition the excitation cross section for high impact energies is given by G = C/&L

(4)

CfE,j

m2eV)

(lo-”

/ /

loo-

t

50 -’

Eel 0

, 10

(eV)

/

50

I

100

I

I

500 1000

Fig. 2. Bethe plot (csE,~ vs. In Eel) for 1lS31P

I

5000

excitation of helium by electrons.

VAN

54

KAAN,

DE

JONGH,

VAN

ECK

AND

HElDEMAX

where C is a constant. In fig. 3 plots of 4rS, 51s and 61s are given. We notice that our uEel data just,begin to approach a constant value at about 2 keV. This was also measured by Moustafa Moussa et al. 8). When comparing

the

experimental

lzrS curves

with

the

theoretical

curves

of Bell

et al. 2) we notice that in all cases our values are about lO”/b higher at 1000 eV. When our experimental setup is calibrated by means of the theoretical value of the optical 1r.S3rP oscillator strength [see formula (3)], the values presented by the open circles in fig. 3 are obtained. These values are in a very good agreement with the theoretical calculations at high energies. For energies below 400 eV the experimental cross sections become smaller than the theoretical ones, in contrast with the nrD cross sections (see fig. 4) where the experimental values always remain larger than the

2.0.

1.5.

1.0

t

dEe,(10-2’

m’ev)

0.5

-m=

Eel(eV)

s-&J&

6’0 Eel (eV

0

i 10

50

100

500

1000

10

5000

50

plot

(aE,r

500

vs. In E,r)

for excitation levels.

of helium

to the 4rS, 51s and 61s

a Our experimental results; o our experimental results reduced to absolute by means of the theoretical optical oscillator strength f( lrS-31P) (see text) ; retical Fig. 4. Bethe plot n Our experimental by means

1000

Lqig. 4.

Pig. 3. Fig. 3. Bethe

100

calculations

-

values theo-

of Bell et al. 2).

(o&r vs. In I&) for excitation results; o our experimental

of the 4lD, 511) and 6rD levels. results reduced to absolute values

of the theoretical optical oscillator strength ,f( 11%3rP) retical calculations 292s) (see section 4.2).

(see text)

; -

theo-

1

EXCITATION

theoretical between

OF HELIUM

BY ELECTRONS

values. This effect can be caused by the difference direct and exchange

excitation

55

of interference

for nlS and nlD levelsss).

In fig. 4 it is shown that the nrD levels reach constant aE,i values at lower electron impact energies than the niS levels. The lziD curves exhibit a maximum before they reach a constant nounced for higher principal quantum

aE,i. This effect becomes less pronumbers. Scharmann and Schart-

ner23724) found an opposite effect for excitation of helium by fast protons: their uEei vs. In E,i plots of nlD exhibit maxima which become more pronounced for higher principal quantum numbers. A similiar effect, although less pronounced, is found for nrS excitation by protons. In our results on nrS excitation by electrons no maxima appear. TABLE VI Ratios of cross sections 41s/51s

51S/6lS

41D/51D

51D/61D

Experimental This work

2.11

1.80

1.64

1.57

Moustafa Moussa et al. 8)

1.87

1.84

1.74

1.99

St. John et a1.5)

2.45

2.04

1.95

1.92

De Heer and Vroomg)

2.04

1.79

1.74

1.72

Theoretical n-3 Law

1.95

1.73

1.95

1.73

Bell et al. 2) Oldham 3)

2.05 2.05

1.78 1.78

1.80

1.66

The theoretical curves for &D excitation are found by using the theoretical data for 31D excitation of Kim and Inokutiss) and the ratios a(utlD)/o(3iD) according to Bell et aZ.2) (see table VI). In the asymptotic limit for high impact energies the ratios of our experimental cross sections and the theoretical values amount to 1.14 (1.04), 1.27 (1.16) and 1.35 (1.23) for the 4iD, 5lD and 6iD levels, respectively. The ratios between parentheses are obtained when the values, presented by the open circles in fig. 4, are used. For triplet excitation a comparison between theory, given by Ochkur, and experiment is made in figs. 5 (4%) and 6 (33P). Ochkur predicts a Ei3 dependence. Our results for triplet cross sections do not obey this Ea3 relation. We have measured a Eg2*’ dependence up to 1 keV for the 4% excitation and a Ei2,” dependence u p to 800 eV for the 33P excitation. At impact energies above 800 eV our experimental cross sections for 3aP excitation tend to decrease at a slower rate. It is questionable whether this effect is due to the influence of secondary electrons only. It seems plausible

VAN

56

KAAN,

DE

JONGH,

VAN

ECK

AND

HEIDEMAN

10-22-

Fig. 5. Cross sections A

Our

(device

experimental I);

results

o McConkey

et al. 5); -

for excitation

(broken

line)

of helium

(device

II);

to the 4% level. D our

experimental

results

and WoolseylO); x Moustafa Moussa et u2.s); v St. John theoretical calculations of Ochkur and Brattsev 4).

that processes other than direct excitation play an important role. However, the discrepancy between theory and our experimental results is not as large as in previous experiments of Moustafa Moussa et al. 8) and St. John et aZ.5). Kay and Showalteri6) found a E$“.” relation for energies up to 200 eV (relative measurements) ; above 200 eV their excitation curve tends to fall off at a slower rate. McConkey and Woolseyl”) measured triplet excitation up to 300 eV; above 150 eV there is a reasonable agreement with our values. The excitation cross sections in the range from threshold up to 100 eV measured with the special device I (table II) may be compared with results of close-coupling calculations applied to helium levels (Chung and Lin26)). However, at present no accurate theoretical data are available for the whole

EXCITATION

OF HELIUM

BY ELECTRONS

57

X

10-26 10

/ 20

I 50

I 100

I 1000

I

Fig. 6. Cross sections for excitation of helium to the 3sP level. Our experimental results (broken line) (device II) ; q our experimental results (device I) ; o McConkey and Woolsey 10); x Moustafa Moussa et al.*); ‘y St. John et al. 5); - theoretical calculations of Ochkur and Brattsev 4). A

low-energy range so that no meaningful comparison between experimental and theoretical low-energy cross sections can be made. According to previous experiments and theory (Ochkur and Petrunkins7)) cross sections for excitation of levels belonging to the same term series i.e. with the same azimuthal quantum number 1 and multiplicity, should show the same energy dependences and should be proportional to n-3 for sufficiently high principal quantum number n. In table VI we compare the average ratios of our cross sections with the values derived from the n-s law, with the theoretical calculations of Bell, Kennedy and Kingstonz) and of Oldhams) and with the experimental values of Moustafa Moussa et cd.*), of St. John et al. 5) and of Vroom and De Heerrs? s2). Our values are an average of the ratios between 200 and 1500 eV. The mutual differences are at most 10%.

VAN

58

RAAN,

DE

JONGH,

VaS

ECK

_kND HEIDEMAN

3d ~Ee,(10-2’

rn2eV)

.

4’s

. II

Ee,(eV)

IO Fig. 7. A comparison A Our experimental et al. *) ;

500

of cross sections

by different by means

100

50

results;

of the theoretical

for excitation

investigators optical

oscillator

57St. John et al. 5) ; l McConkey retical

of helium to the 4lS level measured

and as predicted

o our experimental

5000

1000

results

strength

by theory. reduced

to absolute

values

f( 1 IS-31P)

; x Moustafa Moussa and \Voolsey 1”) ; n Zapesochnyi7) ; ~ theo-

calculations

of Bell e2 nl. “).

In fig. 7 we compare our cross sections for 41s excitation with results obtained by other investigators and with theory. Our polarization results (Van Eck and De Jongh) are discussed in detail in the work of Moustafa Moussa et al. 8). A4s far as the 3lP-2rS polarization is concerned, there is a good agreement between our experimental values and the Born theory over a large energy interval. The energy dependence of the polarization degree of the radiation of niD-2rP transitions is over a large energy range ( 150- 1000 eV) in agreement with theoretical calculations. However, the magnitude of this polarization degree differs with theory which is also the case in previous experiments

of other investigators.

Acknowledgements. The authors wish to thank Professor J. A. Smit and Dr. F. J. de Heer for their valuable comments. We are indebted to J. van der Weg and M. I,. H. Huijnen for their assistance in taking the experimental data. This work was performed as part of the research programs of Euratom and the “Stichting voor Fundamenteel Onderzoek der Materie” (F.O.M., financially supported by the “Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek” (Z.W.O.) and Euratom) and the State University of Utrecht.

EXCITATION

OF HELIUM

BY ELECTRONS

59

REFERENCES 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28)

Kim, Y. K. and Inokuti, M., Phys. Rev. 175 (1968) 176. Bell, K. L., Kennedy, D. J. and Kingston, A. E., Proc. Phys. Sot. B 1 (1969) 26. Oldham, W. J. B., Phys. Rev. 174 (1968) 145; 181 (1969) 463. Ochkur, V. I. and Brattsev, V. F., Optics and Spectroscopy (USSR, English Transl.) 19 (1965) 274. St. John, R. M., Miller, F. L. and Lin, C. C., Phys. Rev. 134 (1964) A888. Jobe, J. D. and St. John, R. M., Phys. Rev. 164 (1967) 117. Zapesochnyi, I. P., Soviet Astronomy - A J 10 (1967) 766. Moustafa Moussa, H. R., de Heer, F. J. and Schutten, J., Physica 40 (1969) 517. De Heer, F. J., Vroom, D. A., de Jongh, J. P., van Eck, J. and Heideman, H. G. M., Proc. VIth Int. Conf. Electr. At. Coll. (1969), Cambridge, Mass., p. 350. McConkey, J. W. and Woolsey, J. M., Proc. VIth Int. Conf. Electr. At. Coll. (1969) Cambridge, Mass., p. 355. Moiseiwitsch, B. L. and Smith, S. J., Rev. mod. Phys. 40 (1968) 238. Kieffer, L. J,, Atomic Data 1 (1969) 120. Smit, C., thesis University of Utrecht (196 1). Heideman, H. G. M., thesis University of Utrecht (1968). Weaver, L. D. and Hughes, R. H., J. them. Phys. 47 (1967) 346. Kay, R. B. and Showalter, J. G., Proc. VIth Int. Conf. Electr. At. Coll. (1969) Cambridge, Mass., p. 361. McFarland, R. H. and Soltysik, E. A., Phys. Rev. 127 (1962) 2091. Scharmann, A. and Schartner, K. H., Z. Phys. 219 (1969) 55. Heideman, H. G. M., Smit, C. and Smit, J. A., Physica 45 (1969) 305. Van Eck, J. and de Jongh, J. P., Physica 47 (1970) 141. Van den Bos, J., Winter, G. and de Heer, F. J., Physica 40 (1969) 357. Schiff, B. and Pekeris, C. L., Phys. Rev. 134 (1964) A640. Scharmann, A. and Schartner, K. H., Proc. VIth Int. Conf. Electr. At. Coll. (1969), Cambridge, Mass., p. 822. Scharmann, A. and Schartner, K. H., Z. Phys. 228 (1969) 254. Kim, Y. K. and Inokuti, M., Phys. Rev. 184 (1969) 38. Chung, S. and Lin, C. C., Proc. VIth Int. Conf. Electr. At. Coll. (1969) Cambridge, Mass., p. 363. Ochkur, V. I. and Petrunkin, A. M., Optics and Spectroscopy (USSR, English Transl.) 14 (1963) 245. Vriens, L., Phys. Rev. 160 (1967) 100.