Evaluation report for the elastic differential cross sections

　

Lin-Fan Zhu

　

All of the elastic differential cross sections (EDCS’s) have been measured by the traditional electron energy loss spectrometer, and most of them were normalized by referring to the absolute EDCS’s of helium (which is often used as a criteria) using the relative flow technique [1]. Because of the limitation of the experimental energy resolution, it is very difficult to resolve the pure rotational excitation from the elastic scattering peak. So the pure rotational excitations were included in the elastic peak. This time we have collected the EDCS’s for 12 molecules, and I will give this evaluation report according to different molecules.

 

I. EDCS’s for CO

The EDCS’s for CO up to 1983 have been reviewed by Trajmar et al. [1]. Subsequent to this review there have been measurements by Nickel et al. [2], Middleton et al. [3], Gote and Ehrhardt [4] and Gibson et al. [5]. These data were put on the absolute scale by the relative flow technique with helium as the standard gas and were reviewed by Brunger and Buckman [6]. Among these works, the data of Gote and Ehrhardt [4] and Gibson et al. [5] are most recent and extensive. In the first case, the energy range is very broad, covering the region between 5 and 200 eV and for the scattering angles between 10° and 160°. Gibson et al. [5] performed measurements at energies between 1–30 eV and the scattering angular range 15°–130°. So for the same incident electron energies the experimental data of Gote and Ehrhardt [4] and Gibson et al. [5] are recommended.

 

Ⅱ. EDCS’s for CO₂

Carbon dioxide has been studied by electron impact method for several decades covering various ranges of incident electron energies and scattering angles. Earlier, there have been a number of experimental and theoretical studies both for elastic and inelastic processes. Shyn, Sharp, and Carignan [7] measured elastic scattering and obtained the EDCS’s at incident energies of 3-90 eV. Register, Nishimura, and Trajmar [8] carried out a measurement of the absolute cross sections at 4, 10, 20, and 50 eV. Kanik, McCollum, and Nickel [9] obtained the differential cross sections in 20°-120° at 20-100 eV energies. Iga, Nogueira, and Lee [10] measured the absolute elastic cross sections at 500, 800, and 1000 eV.

After that, there are three measurements of EDCS’s published in the recent several years. One measurement made in Brazil [11] is in the energy range between 100 and 400 eV. The other two measurements were made in Japan [12] and Australia [13], these two measurements almost overlap to each other totally in the energy range and scattering angular range. We choose the data of Australia group where they overlap for three reasons. Firstly, Australia group made two independent measurements in two different laboratories to make sure the accuracy of their data. Secondly, their data agree better with the shape of the normalized cross section of Shyn et al. [7] than that of Japan group. Finally, their estimated uncertainty was generally smaller than that of Japan group (about 15%). So, in the energy range between 1.0 and 100 eV, we choose the data of these two groups at the energies they covered. At the energies they have not covered we choose the data of Kanik et al. [9], whose estimated uncertainty is no more than 27% (typically 16%). And in the energy range between 200 and 1000 eV, we choose the only published data made in Brazil [10,11], whose estimated uncertainties are 12-16% and 10.3% separately. All absolute values of elastic DCS’s we choose were obtained by the relative flow technique.

 

III. EDCS’s for H₂O

The EDCS’s for H₂O have been reported by Danjo and Nishimura [14], Shyn and Cho [15], Johnstone and Newell [16], Cho et al .[17], Shyn and Grafe [18], Katase et al. [19]. Among these works, Danjo and Nishimura [14] measured the EDCS’s in the energy range from 4 to 200 eV and in the angular range from 10° to 120° by a crossed beam method. Shyn and Cho [15] used a modulated crossed-beam method to measure the EDCS’s for the energy and angular ranges from 2.2 to 20 eV and from 15° to 150°, respectively. Johnstone and Newell [16] reported the EDCS’s in 10°-120° in the energy range 6–50 eV. Cho et al. [17] measured the EDCS’s at nine incident electron energies between 4 to 50 eV and over scattering angles between 10° and 180° using a crossed beam electron spectrometer. Shyn and Grafe [18] reported further cross section measurements in the energy range from 30 to 200 eV and the angular range from 12° to 156°. Katase et al. [19] reported the EDCS’s in 0°-180° and at incident energy range 100-1000 eV using the crossed beam method. Below 15 eV, the data of Danjo and Nishimura [14], Shyn and Cho [15], Johnstone and Newell [16] and Cho et al. [17] show general agreement. At energies between 20 and 50 eV the data of Danjo and Nishimura [14] are lower than other experimental ones. So below 50 eV for the same incident energies and scattering angles the recent data of Cho et al. [17] are recommended. Above 100 eV, the data of Katase et al. [19] are recommended. For other energies, the data of Refs. [15, 18] are recommended.

 

Ⅳ. EDCS’s for CH₄

The EDCS’s of CH₄ have been measured by Boesten et al. [20], Mapstone et al. [21], Iga et al. [22], Curry et al. [23], Sohn et al. [24], Tanaka et al. [25] and Vukovic et al.[26]. The theoretical calculation has been carried out by Ashok Jain [27].

Among these works, the calculated results by Ashok Jain [27] are largely different from those of Boesten et al. [20] and Vukovic et al. [26]. The EDCS’s of Tanaka et al. [25] were updated by themselves in Ref. [20]. The data were normalized point by point with the help of simultaneous measurements of the EDCS’s of He. This group has measured a large number of experimental EDCS’s for different molecules, and their results have been considered to be credible. So we recommend the experimental EDCS’s of this group for the same incident energies [20], and their experimental errors are about 15%. At the impact energies 12.5 and 17.5 eV in Ref. [23], the normalisation was achieved by interpolating between the values of known cross sections in Ref. [25] which are not so accurate comparing with the updated data in Ref. [20]. Since the data in Ref. [23] at those two impact energies were not carried by other group, they are also adopted. Since the incident energies of Refs. [21, 22, 24] are different from Refs. [20, 23], their EDCS’s which were measured by the relative flow technique are also used. The experimental errors in the Refs. [22,24] are about 10% and 10-15% , respectively.

 

Ⅴ. EDCS’s for C₂H₄

The EDCS’s for C₂H₄ have been measured experimentally by Mapstone and Newell [21], Fink et al. [28], Panajotovic et al. [29], Brescansin et al. [30], and Panajotovic et al. [31]. However, the results of Fink et al. [28] are relative and there is no data table available in the works of Panajotovic et al. [31]. Besides, the groups of Ref. [29] have carried out plenty of experimental measurements of EDCS’s and their results are considered to be credible. So at the same incident electron energies, we adopt the results of Panajotovic et al. [29].

The theoretical calculations have been carried out by Brescansin et al. [32]，Trevisan et al. [33], Winstead et al. [34] and Qiyan Sun et al. [35]. The results of these works are in general agreement with the experimental results [21, 29, 30].

Therefore, the experimental results of Refs. [21, 29, 30] are recommended.

 

Ⅵ. EDCS’s for C₃H₈

The EDCS’s for C₃H₈ have been measured by Boesten et al. [36], Tanaka et al. [37], and Merz and Linder [38]. The experimental errors in Ref. [36] and in Ref. [37] are (15-20) % and 15%, respectively. It is noticed that there is no data table available in Ref. [38] and the results are in agreement with that in Ref. [36]. The data table given in Ref. [37] are wrong by our analysis (which should be the result of C₃F₈). And we notice that the theoretical calculation [34] did not give the data table. So the experimental EDCS’s [36] are recommended.

 

Ⅶ. EDCS’s for C₆H₆

 The EDCS for C₆H₆ have been measured by Cho et al. [39], Boechat-Roberty et al. [40] and Gulley et al. [41]. The theoretical calculation has been carried out by Bettega et al. [42]. The data of Cho et al. [39] measured by the relative flow technique covers a large incident electron energy range, and they include the previous published data of the same group by Gulley et al. [41]. Boechat-Roberty et al.[40] measured the EDCS’s at 1keV impact energy which were determined from the elastic/inelastic ratio, while inelastic differential cross sections were determined from the generalized oscillator strenthg values which was normalized to the known optical oscillator strength. At the same incident electron energies, the experimental data are used. So the data of Refs. [39, 40] are recommended.

 

Ⅷ. EDCS’s for CF₄

To our knowledge, there are four measurements of the elastic differential cross sections of CF₄ covering various ranges of incident electron energies and scattering angles. Sakae et al. [43] measured the EDCS’s in 5°-135° at the incident energies of 75, 100, 150, 200, 300, 500, and 700 eV. The absolute EDCS’s were determined by using a gas chamber on the basis of the known absolute EDCS’s for He. The uncertainty in their data was estimated to be about 10%. But they have not provided the data tables. The Sophia University group in Japan made two measurements about the EDCS’s for CF₄ [44, 45]. The energy ranges and scattering angles in the two measurements are largely overlapped. The absolute EDCS’s were obtained by normalizing to a set of recommended elastic DCS’s of He and by the relative flow technique. The overall errors of their data were estimated to be 15-20% due to a combination of statistical, systematic and normalization errors in the experiments. We choose the recent data where they overlapped. Another measurement was that of Mann and Linder [46], their measurements were made at scattering angles between 10° and 105° and for electron energies from 0.5 to 20 eV. Their absolute values of EDCS’s were obtained by normaling the relative total cross section to the absolute one of Jones [47]. The absolute uncertainty of the measurements was estimated to be 20-30%. So we tabulate their data as supplement.

 

Ⅸ. EDCS’s for CF₃Cl

The EDCS’s for CF₃Cl have been measured by Sunohara et al. [48] and Mann and Linder [49]. The experimental errors in Ref. [48] and in Ref. [49] are 15-20% and 20-40% respectively. Because the data of Sunohara et al. [48] are the latest results and the groups of Ref. [48] have carried out plenty of experimental EDCS’s measurements and their results are considered to be credible, for the same incident electron energies, we adopt the experimental data of Ref. [48].

Besides, the theoretical calculations have been carried out by Natalense et al. [50, 51] and Bettega1 et al. [52]. But only the work [50] gives the data table, and their calculations are in agreement with the experimental results [48]. So we adopt the calculated results of Ref. [50] when the experimental result is absent.

So the EDCS’s of Refs. [48,49,50] are recommended.

 

Ⅹ. EDCS’s for CF₃I

Up to 2005, the only experimental EDCS’s were measured by Kitajima et al. [53] and the only theoretical EDCS’s were calculated by Bettega et al. [52]. Kitajima et al. [53] used the traditional electron energy loss method and their absolute results were obtained by referring to the absolute EDCS’s of helium. The experimental errors are about 15-20%. Bettega et al. [52] used the Schwinger multichannel method with pseudopotentials at the static exchange approximation. At the same energies of 6, 8, 10 and 20 eV, the results of Kitajima et al. [53] and Bettega et al. [52] are in good agreement. We recommend the experimental EDCS’s mentioned above.

 

Ⅺ. EDCS’s for C₄F₈

  The EDCS’s for C₄F₈ were measured by two groups using relative flow technique, and were reported by Ref. [54]. The data with less experimental errors at the same impact energy are chosen.

 

Ⅻ. EDCS’s for C₆F₆

To our knowledge, there is only one measurement of the EDCS’s of hexafluorobenzene [39]. The authors measured the EDCS’s for hexafluorobenzene between 10° and 130° at the energy range from 1.5 to 100 eV. Absolute differential cross sections were obtained by the relative flow technique. The estimated uncertainty in the data is 15%.

 

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