Z. Physik 248, 254-263 (1971) 9 by Springer-Verlag 1971

Absolute Excitation Cross Sections for the 41S-, 4 ID- and 3 P-Levels of Helium Excited by Fast Protons D. HASSELKAMP, R. HIPPLER, i . SCHARMANN, a n d K. H. SCHARTNER I. Physikalisches Institut der Universiffit GieBen Received September 17, 1971 We have measured absolute cross sections for proton excitation of the 3 xp_, 4 1S- and 4 1D-levels of He in the energy range from 200 keV to 1 MeV. Calibration with a tungsten lamp mounted in the collision chamber and normalization on the high energy first Born approximation 3 ~P values for protons and electrons were used to obtain absolute data. At 1 MeV the experimental results agree within 10% with the first Born approximation values.

I. Introduction In the high energy range the first B o r n a p p r o x i m a t i o n for the cross sections referring to the process H + + H e - + H + + H e * ( n 1S, n 1p, n aD) predicts theoretical values which are expected to be a g o o d a p p r o x i m a t i o n to the e x p e r i m e n t a l values. I n the energy range b e l o w 1 M e V a b s o l u t e cross sections for the a b o v e m e n t i o n e d processes have been m e a s u r e d by Denis, D u f a y and G a i l l a r d ~, by R o b i n s o n a n d G i l b o d y 2 a n d b y T h o m a s a n d Bent 3. Below 100 keV the m o s t recent values have been p u b l i s h e d by van den Bos, W i n t e r a n d de Heer 4, new results will be p u b l i s h e d by Blair a n d G i l b o d y 5. T h e e x p e r i m e n t a l d a t a disagree m o r e t h a n the q u o t e d errors allow. T h e d e m a n d for m o r e e x p e r i m e n t a l d a t a is the r e a s o n for o u r o w n investigations. W e have limited the experiments to the 3 Xp_, 4 ~Sa n d 41D-levels. The wavelenghts of the c o r r e s p o n d i n g observed transitions differ only b y 126/k. Systematic errors resulting f r o m optical calib r a t i o n are by t h a t w a y minimized. 1 2 3 4 5

Denis, A., Dufay, M., Gaillard, M. : Compt. Rend. B 264, 440 (1967). Robinson, J. M., Gilbody, H. B. : Proc. Phys. Soc. (London) 92, 589 (1967). Thomas, E. W., Bent, G. D.: Phys. Rev. 164, 143 (1967). Bos, J. van den, Winter, G. J., Heer, F. J. de: Physica 40, 357 (1968). Blair, W. F. G., Gilbody, H. B. : Abstracts of papers of the VIIth ICPEAC, p. 837. Amsterdam: North-Holland 1971.

lb cm

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B

[l

E

Monochr ornat or

Collision Chamber

l,v, J

. . . . . . . . . . . . . . . . . . . . . . .

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Differential Pumping Chamber

~

~ M2

5"

D 3

2.

256

D. Hasselkamp, R. Hippler, A. Scharmann, and K. H. Schartner:

For comparison with the first Born approximation we used the results of Kim and Inokuti 6, Bell, Kennedy and Kingston 7 and of Oldham, Jr. 8.

II. Apparatus A 1.3 M e V - v a n de Graaff accelerator has been used to produce the fast protons. Fig. 1 shows the target chamber which is different from the one used in former experiments 9. It consists of a dynamically pumped collision chamber and a differential pumping chamber. A parallel beam is formed by two diaphragma, 1.5 m m in diameter and 50 m m separated from each other. Secondary electrons have been suppressed by suitable biased shieldings. The observation region is focused on the entrance slit of a Leiss m o n o c h r o m a t o r equipped with a plane Bausch and L o m b grating (1800 lines/ram). The exit slit is focused on the cathode of a E M I 6256 S multiplier cooled by Peltier elements. A quarter wave plate is used to minimize the influence of instrumental polarization. The multiplier pulses are counted over a period depending on the pulse rate. A tungsten strip lamp can be switched into the proton beam position. The temperature of the observed part of the strip has been carefully measured by an accurate pyrometer. An electron gun of the type used in television tubes is placed inside the differential pumping chamber. It can be switched in front of the entrance openings of the collision chamber replacing the ion beam by an electron beam. In this case a second Faraday cage is used, which can be shifted into the electron beam. The ion currents varied between 10 and 30 gA. The measurements have been performed at extremly low pressures, the highest value being 6 9 10 -5 Torr. At the low pressures at least 15 minutes are necessary to get a reasonable signal to noise ratio. The corresponding charge of the proton beam is collected by a capacitor via a Faraday cage. The helium pressure is regulated by a m o t o r driven needle valve. It is measured by an ionization gauge which is calibrated against a reliable standard gauge at the laboratories of Leybold-Heraeus. The accuracy of the pressure measurements is estimated to be _ 10%. The residual vacuum in the collision chamber amounts to 4- 10 - 7 Tort.

IlI. Results We have used three methods to obtain absolute values for the excitation cross sections a 31p, a4 Is and a 4 ID6 Kim, Y. K,, Inokuti, M.: Phys. Rev. 175, 176 (1968). 7 Bell, K. L., Kennedy, D. J., Kingston, A. E. : J. Phys. B (Proc. Phys. Soc.) 1, 1037 (1968). 80ldham, J. B., Jr.: Phys. Rev. 174, 145 (1968). 9 Scharmann, A., Schartner, K. H. : Z. Physik 219, 55 (1969).

Absolute Excitation Cross Sections Table 1. EH§

200

300

257

Cross sections in units o f 10 -20 cm z

400

500

600

700

800

900

1000keV

~311o 295 248 215 a41s 18,9 12,5 9,5 ff41D 6,8 3,8 3,2

189 7,5 2,4

178 6 2,1

156 5,1 1,7

146 4,6 1,5

138 4,1 1,4

130 3,6 1,1

1. We carried out a usual absolute calibration using a tungsten strip of dimensions comparable with the diameter of the ion beam. The calibration has been repeated 15 times within 6 weeks. A detailed description of the calibration procedure has been given for example by van den Bos, Winter and de Heer 4 and by Thomas and Bent 3. As mentioned before the tungsten strip can be switched into the beam position. By using the tungsten strip in this manner the determination of the observed beam length and of the solid angle is not necessary, which is a great simplification. The geometrical dimensions still to be determined are the width of the tungsten strip and of the monochromator slit. Both can be measured accurately. 2200 ~ have been chosen as the true temperature of the tungsten lamp. A disadvantage of simulating the ion beam by the tungsten strip is the large difference between the calibration pulse rate and the signal pulse rate. This difference amounts to orders of magnitude. Three neutral density filters have been used in series to weaken the intensity of the tungsten lamp by a factor of 0.87 9 107. This value has been determined with the filters fixed in the position also used during the determination of the quantum efficiency of the optical system. The accuracy of this number is _+10~, the overall accuracy of the quantum efficiency + 15 ~ . The accuracy of the cross section values obtained by this method is estimated to be ___25 7oo. Fig. 2 and 3 show the results of the tungsten calibration for the 31p_ and the 41S-level. Table 1 gives the values corresponding to Fig. 2 and 3. 2. We used the first Born approximation 3~P cross section for electrons to normalize the data for the same level excited by protons, that is we compared the signal resulting from the impact of 360 keV protons with the signal from the impact of 400 eV electrons. This way of normalization is justified by the good agreement of the relative theoretical and experimental electron impact excitation functions above 300 eV. Our own measurements confirm this agreement (Fig. 4). Furthermore the absolute values for the electron excitation cross section a 3 le obtained by Moustafa, de Heer and Schutten 1~ and by van Raan, 10 Moustafa Moussa, H. R., Heel F. J. de, Schutten, J. : Physica 40, 517 (1969).

258

D. Hasselkamp, R. Hippler, A. Scharmann, and K. H. Schartner: 10-20 cm2 MeV

I H+ + H e -

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250 v a n den Bo s x Thomas o Denis 9 present results - - - Bert

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Fig. 2. Excitation cross section a 3 ~p x energy as a function of proton energy. 9 9 present results, 9 9 9 Denis, Dufay and Gaillard 1, x x x Thomas and Bent 3, zx A van den Bos, Winter and de Heer 4, - - Bell, Kennedy and Kingston 7

9 zx

de Jongh, van Eck and Heidemann 11 agree at the interesting energies above 300 eV with the first Born approximation within 10 %. By that way we obtained results for the proton excitation cross section ~ ,e which are in good agreement with the results obtained by method 1. The accuracy of method 2 is estimated to be 4- 10 %. 3. In order to derive absolute values for ar is and a4 ~0, we determined the ratios a 3 , e / a 4 is and a 3 , p / a r ~D as a function of proton energy. We used the 31P-level for normalization. This is reasonable because the data obtained from the first Born approximation and from Coupled State a2 calculations for o-3 ,p agree very well at 1 MeV. Fig. 5 shows the results obtained by this method. The ratios a3 i p / a 4 is and a a ~e/a4 ~o are plotted against energy. The values should be accurate to +10%. The single points give former results for c%~p/a4~s; these 11 Raan, A. F. J. van, Jongh, J. P. de, Eck, J. van, Heideman, H. G. M. : Physica 53, 45 (1971).

12 Bos, J. van den: Phys. Rev. 181, 191 (1969).

Absolute Excitation Cross Sections

259

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Z. Physik, Bd, 248

260

D. Hasselkamp, R. Hippler, A. Scharmann, and K. H. Schartner:

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Theory 7 . I._.~P O3

Experiment

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measurements have been carried out at probably too high pressures. Experiment and first Born approximation approach each other at 1 MeV for tr3 le/Crr The respective values for tralp/tr, l D differ even at 1 MeV. Assuming the first Born approximation 3 ~P calculations to be valid

Absolute Excitation Cross Sections

261

150 H"-.-~He

300keV

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at 1 MeV the 41S calculations are also in closest agreement with experiment. The 41D-cross sections are 1 0 ~ larger than the first Born approximation values of Bell, Kennedy and Kingston 7 at 1 MeV, as shown in Fig. 6. The respective numerical values are also given in Table 1. It should be pointed out that our measurements have been carried out at very low pressures to avoid imprisonment of resonance radiation and collisions of the second kind. Fig. 7 shows an intensity against pressure plot. The signals have been linear with beam current. The polarization of the radiation and cascade contributions have been taken into account. The polarization has been measured carefully as has been reported recently 13. Cascade contributions have been calculated from theoretical cross sections 7. They vary from 5 ~ to 2 ~o depending upon level and energy. IV. Discussion The values of the tungsten calibration are in excellent agreement with the values obtained by normalization on the electron impact first Born approximation calculations (Table 2). : Within the range of the uncertainty of the tungsten calibration (_+25~) and also of the normalization on the theoretical electron cross sections (_+10Y/oo) our experimental and the first Born approximation values are in agreement for the 31P-level. We carried out a least squares 13 Hasselkamp, D., Hippler, R., Scharmann, A., Schartner, K.H.: Abstracts of papers of the VIIth ICPEAC, p. 835. Amsterdam: North-Holland 1971. 18"

262

D. Hasselkamp, R. Hippler, A. Scharmann, and K. H. Schartner: Table 2.

Comparisonof methods1 and 2

Tungsten c a l .

a s 1p

228 9 10-2o c m

Table 3.

2

Normalization on electron excitation

Theory6,7

232"10-20 cm2 El_i+= 360 keV

241 9 10-20 cm2

Comparisonwith Born-Betheapproximation

lncn fn

Experiment

Theory 6

--2.15 0.086

--1.833 0.073

linear fit through our data points. We compare the results of this procedure with the values cn and fn referring to the Bethe asymptonic term 6

4ha2~ a . - T/R ( E 7

ln(4c,

T/R))

where ao is the Bohr radius, R is the Rydberg energy, T is the energy of an electron having the same velocity as the regarded proton, E~ is the excitation energy of the level n, c~ is a constant and f~ is the optical oscillator strength (Table 3). We find a difference between the experimental and theoretical values of 20 ~ for In G and of 15 ~o forfn, which is satisfactory when taking into account an error of _+10% for tr3,e. We compare our results with the experimental values of van den Bos, Winter and de Heer 4 and of Thomas and Bent a. Looking at the shape of the excitation functions there is good agreement between the measurements of Thomas and Bent 3 and our results as has been mentioned earlier 14. The measurements of van den Bos, Winter and de Heer 4 fit quite well to our measurements. The absolute values of Thomas and Bent a for the 41S - and 41D-cross sections are in both cases about the same factor smaller than our results. It is therefore surprising, that their values for the 31P-level are in agreement with our values. We explain this agreement with a systematic error in the calibration of Thomas and Bent 3 which is cancelled for the 31P-level by too high pressures resulting in too large cross sections (in spite of their extrapolation to low pressures). Because of the good agreement between calibration method 1 and 2 for the 3 ~P level we believe our values for a4 ts to be accurate within to +_10~. That means experiment and first Born approximation are in 14 Seharmann, A., Sehartner, K. H.: Z. Physik 228, 254 (1969).

Absolute Excitation Cross Sections

263

reasonable agreement above proton energies of about 500 keV. The measurements of van den Bos, Winter and de Heer 4 and our measurements prove that the first Born approximation gives too small values for a 4 is between 50 and 500 keV. As mentioned above we receive the absolute values for a41 o by combining the ratio measurement with method 1 or 2. We quote the accuracy of the values for the 4 ~D-level to be __+25 ~ . Within these limits our results and the values of Bell, Kennedy and Kingston 7 are in agreement at the high energies. The different shapes of the theoretical and the experimental excitation functions and the numerical results of van den Bos, Winter and de Heer 4 demonstrate that the first Born approximation values of Bell, Kennedy and Kingston 7 give too small values in the experimentally investigated energy region. We are indebted to Dr. de Heer for helpful discussions and to Mr. Trylat for his assistance in constructing the target chamber and in taking the experimental data. Prof. Dr. A. Scharmann Dr. K.-H. Schartner Dipl.-Phys. D. Hasselkamp cand. phys. R. Hippler I. Physikalisches Institut der Justus Liebig-Universit/it D-6300 Giegen, Leihgesternerweg 104 Germany