Volume 53, number 2 CHEMICAL PHYSICS LETTERS 15 January 1978

COMPTON PROFILE OF CI-14 GAS

T. PAAKKARI and M. MERISALO Department of Physics, University of Helsinki, 00170 Helsinki I7. Finland

Received 2 September 1977

New experimental results for the Compton profde of methane are presented. The data obtained by using 59.54 keV Trays from a 241Am source are compared with theoretical calculations and with experimental results obtained from elec- tron scattering. The comparison shows that substantial discrepancies still exist and the validity of the binary encounter ap- proximation in electron spectroscopy is questioned.

1. Introduction

The Compton profile of methane has been measured by Eisenberger et al. [l] using X-rays and more re- cently, by Klapthor et al. [Z] using electron scatter- ing. Theoretical calculations for this Compton profile

have been made by Epstein 131, Smith et al. [4], Whangbo et al. [S] , and Ahlenius et al. [6] _ These theoretical calculations are reported to agree very well with the results obtained by electron scattering out to q = 5 au 121. But Eisenberger’s [1] X-ray results were measured only out to q = 2 au and it is clearly seen that already around this q-value his experiment and the theory do not agree.

Because of the fundamental nature of any so-called accurate knowledge of the electron properties of sim- ple systems, it seemed motivated to undertake a fur- ther, independent measurement of the Compton profile of CH4. Comparison with the result obtained from high energy electron impact spectroscopy is also obtained in this work. In the present context, special attention is paid to values of the Compton profile obtained at high momenta.

2. Experimental

59.54 keV r-rays from a 900 mCi *4IAm source were scattered by CH4 gas in a pressure cell, which was

made of stainless steel. The cell walls were covered in- side by lead to reduce the wall-gas scattering, and the

portholes for incident and scattered radiation were covered by aluminium windows 1 mm thick. The pres- sure of the gas varied from 50 atm to 30 atm during these measurements_ The purity of the methane gas was 9997%, and the volume of the sample was deter- mined by the intersection of the solid angle of the radiation beam and the solid angle covered by the de- tector_ The cross-sectional diameters of the incoming and scattered beams were 6 mm and 10 mm, respec- tively, and the scattering angle was 1 SO“ -

The experimental, raw data is drawn in fig. 1 while

the deconvoluted, fmal result is given in fig. 2. The in- strumental function, which is obtained by convoluting the detector resolution function with the instrumental function due to the beam divergences, is drawn as an inset in fig_ 1. Since methane consists of very light atoms and since the value of the scattering vector is high, the cross section for elastic scattering is very low, as can be seen from fig_ l_ The background, which was measured by counting the scattering from lihe evacuat- ed pressure cell, was subtracted point by point from the spectrum shown in fig_ I_ The peak-to background ratio was 150 at the peak of the Compton profile. For further details concerning the experimental arrange- ment and the data processing the reader is referred to

earlier papers [7,8].

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Fig. 1. Experimental, raw data for Cb gas at 50 atm, and the instrumental resolution function relevant to the experiment.

Fig- 2. Compton profile a? C& gas at 50 atm.

3. Results and discussion

The results obtained from the above are given in table 1 together with previously reported experimental data as well as the theoretical data of Ahlenius et al. [6] _ The area under the present curve is equal to 4.99 electrons when integrated from 4 = 0 to 4 = 10 with

intervals of 0.1 au. For fair comparison of experiment with theory, the theoretical curve is convoluted with the residual instrumental function (RIF) relevant to the present experiment. The resulting values are given in column 6 of table 1_ Comparison shows that there still exist discrepancies which are greater than the es- timated experimental error (30) at low momenta (4 < 1 au). The deviation from the other theoretical calculations [4,5 J , not shown in table 1, is even great- er. The differences between the various experimental curves and the theory are further ilhrstrated in fig. 3, where it is clearly seen that all of the experimental re- sults deviate from the theory [63 by more than the estimated errors. Even at (I > 2 au the experimental results contain more high momentum values than are given by theory_ The area under the present experi- mental curve from 4 = 0 au to 9 = 2 au is 4.402 elec- trons compared with the theoretical results of 4.453 electrons.

In our experimental arrangement the position of the elastic line corresponds to about 15 au of momen- tum_ To get an indication of the values for the mo- ments which might be obtained from the present data, the kinetic energy ((p 2)) was calculated assuming linear behaviour from q = 5-au up to zero profile at-q = 15 au (cf. fig. 1). The resultingvalue,~@2) = 85, is ConsZder- ably higher than that obtained from electron spectros-

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Volume 53, number 2 CHEMICAL PHYSICS LETTERS 15 January 1978

Table 1 Theoretical and experimental Compton proffies, J(q), for CHq gas. J& is the theoretical profde calculated by Ahlenius and Lindner [6],

e- Jg: the experimental results obtaiqsd using X-rays [ 11, Jexp the experimental results obtained using electron scattering 121, J&*RIF

the th~o~~tid profile J$ convoluted with the residual instrumental function relevant to the present experiment and Jzq the

present results

4

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0

3.5 4.0 4.5 5.0 6.0 7.0 8.0 9.0

10.0

j-2 J(sh4

1:” J(q)dq

J(q)

Jk 5.024

JEM exp 4.986

Jeixp 5.02

Jr exp J; *RIF

4.899 i 0.05 5.013 4.979 4.841 4.604 4.270 3.857 3.395 2.920 2.465 2.052 1.694 l-145 0.786 0.562 0.423 0.337 0.225 0.167

4.930 4.769 4.503 4.173 3.772 3.335 2.891 2.455 2.051 1.685 L-114 0.765 0.575 0.473 0.386

4.94 4.85 4.51 4.18 3.71 3.25 2.82 2.39 2.00 1.63 1.13 0.78 0.55 0.41 0.33 0.21 0.15

4.959 4.802 4.550

- 4.219 3.829 3-403 2.963 2.529 2.124 L-758 1.167 0.78: 0.554 0.426 0.347 0.226 0.164

0.097 0.082

0.056 0.052

0.005

4.453

4.842 4.685 4.438 4.116 3.739 f 0.04 3.327 2.903 2.487 2.096 1.744 f 0.03 l-178 O-798 0.568 0.436 0.360 t 0.02 0.259 0.190

0.137 O-108 f 0.01 0.081 0.057 0.034 0.026 0.012 0.010 0.003

4.406 4.402

4.988

q J$-J& 0 ---I Jr4, *RIF -J& x J&-J&,,

-O.l!- I I I -4 1 2 3

q(aul Fig_ 3_ DifFerences between theoretical and experimental Coppton profdes, Ja - Jexp, for CHq gas. Kotations are given in the legend of table 1.

copy ((~2) = 71 -I 4) and also higher than the theoreti-

cal value of (p2> = 80.35 [6]. The determination of the values of higher moments from the experimental data is usually very sensitive to systematic errors and to the low statistical accuracy_ In this experiment, how- ever, the peak-to-background ratio is favourable and, in fact, the background itself could be measured and so subtracted without introducing systematic error. The high energy side of the spectrum is also free from parasitic components of radiation (for exampIe, escape peaks, etc.).

Granted that the results obtained from electron im- pact spectroscopy [2] agree with the theory at J(O),

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Volume 53, number 2 CHEMICAL PHYSICS LETTERS 15 Janu&$l978

nevertteless by around q = 0.6 au their deviaticn from thg theory is about three times the estimated error. Iu addition, they are normalized by m&ns‘of the Bethe sum rule and the area unddr the curve was about 2.6%. less than under the theoretical curve. It is important to note that results obtained from electron impact spec- troscopy can be compared with those obtained by photon Compton scattering or with those calculated -&I the impulse approknation, only if the binaj encoun- ter approximation is valid. It is suggested here that a more careful study of the significance of this approxi- mation might lead to an explanation for the discrepan- cies noted above.

References

[ 11 P. Eisenberger &d W-c. Marra, PhysI- Rev. ietters 2.7 (1971) 1413.

[2] R-W. Klapthot and J.S. Lee. C&m_ Phys. titters 45 (1977) 513.

[3] 1-R. Epstein, I. Chem. Phys. Si <19?0) 4425. 141 VIL Smith Jr_ and M.FL Whaugbo, Chem. Phys. 5 (1974)

234. [S] M-H. Whaxgbo, V.H. Smith and W. von Niessen, Chem.

Phys. 6 (1974) 282. [6] T. Ahlekius and P. Lindner, Chem. Phys. Letters 34

(1975) 123. 171 9. Paatero, S. Manninen and T. PaaIckari, Phil_ Mag. 30

(1974) 1281. [8] T- Paakkari and M. Merisalo, Cbem. Phys. Letters 33

(1975) 432.

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