Valence-Shell Angle-Resolved Electron Energy Loss Spectra of SF 6

Espectros de perda de energia de elétrons foram obtidos para a molécula de hexafluoreto de enxofre na região da camada de valência (0 a 100 eV) com uma variação angular de 1.0° 15.0°. Os espectros foram medidos para uma energia de impacto de 1 keV. O estudo com variação angular sugere a presença de três transições proibidas na região de energia abaixo de 40 eV. Acima de 40 eV, estruturas interessantes aparecem para maiores ângulos de espalhamento podendo estar associadas a processos multieletrônicos proibidos. Uma nova estrutura foi observada em 76 eV. A seção de choque elástica absoluta foi obtida através de normalização dos dados relativos com valores experimentais encontrados na literatura. As seções de choque diferenciais inelásticas absolutas foram obtidas para as transições em 11,5 eV e 13,2 eV. A força do oscilador generalizada (FOG) foi determinada para a transição em 11,5 eV no intervalo de K entre 0,05 e 1,3 u.a.. O valor experimental da força do oscilador óptica (0,312) para o pico em 11,5 eV, obtido através de extrapolação da curva da FOG, mostra boa concordância com dados da literatura.


Introduction
Electron-energy-loss spectroscopy (EELS) has already proved to be a powerful technique in the study of valence and inner-shell electronic excitations.A great number of atoms and molecules have been studied using the electron impact technique at low and high-resolution conditions [1][2][3] .
Near zero scattering angle and at high incident electron energies the First Born Approximation (FBA) 4 is valid, and electrons behave like pseudophotons 5 .As a consequence, the electron energy loss spectra are similar to photoabsorption spectra.In fact, under these conditions the energy-loss spectrum shows the same excitation features, but with the relative intensities equal to the Eon-3 times the observed intensities in the optical spectrum, where Eon is the electron energy-loss (which corresponds to the photon excitation energy).This consequently means that although the observed features in both spectra will be the same, their relative intensities will be different.A small angle, high incident energy EELS spectrum will consequently furnish essential information on the photoabsorption processes of a given atomic or molecular target 4 .Moreover, it is also possible, using a single experimental set-up, to measure absorption data covering a broad energy range extending from the ultraviolet to the X-ray range.This is a very useful feature even when compared to synchrotron radiation measurements, which are usually plagued with harmonic contamination.Electron impact spectra obtained at nonzero scattering angles may additionally furnish invaluable spectroscopic information about dipole-forbidden electronic transitions in the valence as well as in the inner-shell excitation regions 6 .This is a major advantage of this technique over other conventional spectroscopic techniques.Despite the great spectroscopic potentiality of this technique, only a few groups have dedicated their efforts to the study of the angular dependence of valence and core excitations induced by electron impact.
In the present paper we address our attention to the SF6 molecule.Although this molecule has been the focus of many studies based on the use of photons [7][8][9][10] and electrons [11][12][13] , the first angle-resolved EELS measurements for this compound were published by Ying et al. 13 at an impact energy of 2.5 keV.In this work absolute absorption transition probabilities of valence-shell (7-70 eV) electronic transitions have been determined covering an angular range up to 8.5°.With the aim of exploring the valence and inner-valence excitation regions of the SF6 molecule and with the aim of elucidating the still controversial discussion about the assignment of the experimental features, its spectra have been studied using the angle-resolved electron impact technique at 1.0 keV incident energy.The energyloss range extends from zero to 100 eV and the angular range from 1.0° to 15.0°.Using the absolute elastic differential cross section, our data were normalized and the GOS-curves for the 11.5 eV and 13.2 eV transitions were determined.

Experimental
The experimental apparatus used for the present measurements has been described elsewhere in detail 14,15 .Basically it consists of a rotatable electron gun, a neutral gas beam, a Möllenstedt electron velocity analyser 16 fixed on the vacuum chamber wall and a conventional detection system.A crossed-beam geometry is used for the electrongas collision.The electron beam, produced by a triode-type electron gun, is used without prior energy selection.A typical beam current is 10 µA and the beam diameter, measured at the scattering region, is approximately 0.5 mm.The gas beam is produced by the expansion of a given sample inside the scattering chamber through a hypodermic needle with a 0.2 mm internal diameter.
The scattered electrons are velocity analyzed by the Möllenstedt analyzer and detected by an electron multiplier (Spiraltron, Galileo Electro Optics).The energy resolution of this system was set to 0.6 eV, as determined by the full width at half maximum (FWHM) of the elastic peak.The analyser viewing cone is determined by two parallel, circular apertures of 200 and 50 µm diameter, located, respectively, at 120 and 150 mm from the scattering center.The stray magnetic fields in the plane of the measurements have been reduced to less than 10 mG in all directions by three pairs of orthogonal Helmholtz coils.
The residual pressure is of the order of 10 -6 torr.When the gas sample is introduced into the scattering chamber the pressure is raised one order of magnitude.For each angle, the spectra are continuously recorded until a good signal to noise ratio is achieved.The background is corrected by subtracting another spectrum, obtained at the same experimental conditions, but with the gas sample introduced at a side flange, far from the scattering center.The energy-loss scale is calibrated by using the well-known transition 1s-2p of He at 21.22 eV.The scattering zero-degree angle was checked by measuring the elastic peak area over a 15° range on both the right-hand and left-hand sides with respect to the electron analyzer main geometrical axis.Although a precision mechanism allows the determination of the scattered angle with an accuracy of 0.02°, our angular resolution, defined by the set of apertures in front of the Möllenstedt analyzer, is limited to 1.0° in the present experiment.The experimental uncertainties are estimated in the following manner.The maximum statistical uncertainty was 1.5%.Fluctuations in the primary beam current and on the sample pressure were of the order of 1.0% and 0.5% respectively.The determination of the area of the peak is also subject to a 2% error.The elastic cross section which was used in the normalization procedure 24 has an associated uncertainty of 8%.The overall uncertainty δ, defined as δ = (Ε δi 2) 1/2 , is equal to 9%, including the error in the extrapolation of the GOS-curve, which was of 5%.
In the present work, the incident electron energy was 1000 eV and the electron energy-loss spectra have been obtained in the angular range of 1.0° -15.0° covering an energy range of 100 eV.
The angular dependence of the valence-shell spectra (2-50 eV) is shown in Fig. 2. The angular range is from 1.5°t o 5.5°.Several spectral changes can be observed as the scattering angle, θ, is increased, i.e., as the momentum transfer is increased.The intensity of features located at 11.5 eV, 16.0 eV, 17.0 eV, 19.5 eV and 23.0 eV clearly decreases with increasing scattering angle.On the other hand, features at 13.2 eV and 28.0 eV show an opposite behaviour i.e. they become more intense as the momentum transfer increases.This opposite behaviour demonstrates the different nature of the processes involved in these transitions.The decrease in the relative intensities of these features with momentum transfer suggests a dipole-allowed nature for these transitions, while the increase in the relative intensities with momentum transfer could suggest a nondipole nature associated to the transitions.
Recently Ying et al. 13 have measured angle-resolved valence-shell (7-70 eV) spectra of the SF6 molecule at an impact energy of 2.5 keV.Comparison to our data shows however some discrepancies concerning the nature of the transitions.Firstly the feature at 23.0 eV of Fig. 2, which shows, as mentioned before, an allowed behaviour, is considered by Ying et al. 13 to have nondipole character.It has been however assigned by Sze and Brion 12 as having a contribution from the [1t2u,5t1u] → 2t2g and 5a1g → 6t1u allowed transitions.A nondipole behavior is to be expected for the feature at 28.0 eV, which shows a prominent increase in intensity as the scattering angle approaches 5.5°( see Fig. 2).The 28.0 eV peak has been assigned to the 4t1u → 2t2g transition 12,13 .
In disagreement with the work of Ying et al. 13 , we observe a strong increase in intensity as the momentum transfer increases for the the 13.2 eV transition, indicating  a nondipole character.Trajmar and Chutjian 21 have also observed a forbidden transition at the same excitation energy, working at large scattering angles and very low impact energies.The experimental value of 12.8 eV measured by these authors has been assigned as the 1t1g → 7a1g forbidden transition 20 .Sze and Brion 12 have also observed a very weak structure at about 12.5 eV in their spectrum measured at 3.0 keV and 0°.They have suggested a forbidden character for this feature.The theoretical work of Hay 22 also predicts a nondipole transition to fall into this energy range.
Although many different studies have been performed on the valence-shell region of the SF6 molecule, most are however concentrated in the 10-40 eV energy range [8][9][10][11] , only a few extending to about 60 eV 12 or 70 eV as in the recent work of Ying et al. 13 .None of them, with exception of the work of Ying et al. 13 , has measured the angular dependence of the valence spectra.The region below 10 eV, has received little attention and has not been studied using angle-resolved EELS, shows the intensification of the band located at about 6 eV in Fig. 2 as the momentum transfer increases.This behaviour could suggest the existence of a dipole-forbidden transition.A feature located at 6.494 eV was observed as a very weak structure in the work of Sze and Brion 12 , although no possible assignment was suggested by these authors.
Another interesting region in the study of the valence excitations of the SF6 molecule is the region above 40 eV shown in Fig. 3.This is a very complex energy region because not only one-electron processes are allowed but also processes involving more than one electron.All double ionisation potentials lie in this region.A more detailed discussion of the excitation processes appearing in this high energy domain will be presented in a forthcoming publication 23 .
Figure 3 shows the valence-shell spectrum of the SF6 molecule at higher scattering angles and covering the energy range of 2-100 eV.Above 40 eV three new features can be observed.The fact that they are not observed at small angles could indicate a forbidden nature for these features.The band at about 44 eV was measured by Sze and Brion 12 and Ying et al. 13 , although its assignment is controversial.While a 3t1u → 2t2g transition was assigned by Sze and Brion 12 , a forbidden character (5a1g → 4eg) was suggested by Ying et al. 13 .Our data corroborate the nondipole character of this transition.The feature at about 60 eV was first observed by Ying et al. 13 and attributed to a nondipole many-body transition.Although very weak, it can be observed by higher θ in Fig. 3.The feature at about 76 eV in Fig. 3 was observed for the first time.It can be also related to nondipole processes although its assignment is very difficult without help from first principle calculations.
The relative experimental inelastic differential cross sections for the 11.5 eV and 13.2 eV peaks have been made absolute using the elastic differential cross section (EDCS), which was normalized to the absolute elastic differential cross section found in the literature 24 .In this procedure the interpolation was done using the absolute curve at the scattering angle of 10.5°.At this angle our cross section value was made equal to the absolute value obtaining thus the normalization factor.The experimental elastic differential cross section was measured over a 15° angular range and at an impact energy of 1 keV.Figure 4 shows the absolute elastic differential cross section for the SF6 molecule plotted together with the absolute curve.These results are also presented in Table 1 as a function of the scattering angle θ.From these values, it was possible to determine the absolute inelastic differential cross sections for the 11.5 eV and 13.2 eV transitions, which are shown as a function of the scattering angle θ in Fig. 5 and Table 2.
It is now possible to obtain the absolute generalized oscillator strength for both transitions in SF6.Within the First Born Approximation (FBA), the generalized oscillator strength, fon (K), is directly associated to the differential inelastic cross section (dσ/dΩ)on for the excitation of an atomic or molecular target from the ground state o to an excited state n through the expression 4 :     fon where Eon is the excitation energy, K is the momentum transfer, K = ki -kf, and ki and kf are respectively the initial and the final momentum vectors for the scattering electron.The GOS is independent of the incident energy at energies for which the FBA is valid.Lassettre and Skerbele 25 have additionally demonstrated that the GOS tends to the optical oscillator strength (OOS) in the K 2 = 0 (optical) limit.
As a first step in the determination of the GOS, the area of the 11.5 eV and 13.2 eV peaks were obtained through a standard deconvolution procedure 15 .The ratio between the areas of the inelastic and (absolute) elastic peak was determined in the 1.5° to 8.0° angular range.From these values it was possible to determine the GOS using Eq. 1.This method has been successfuly employed in the determination of the GOS values for several atoms and molecules 15 .A recent theoretical analysis, based on the use of an universal extrapolation formula for the GOS 26 , has shown, for example, that our experimental values extrapolate nicely to the optical oscillator strength for the C 1s transition in the CO2 molecule 27 .The absolute GOS results are presented in Fig. 6 and Table 3 as a function of K 2 .The GOS-curve as a function of K 2 was extrapolated to K 2 = 0 using the universal formula of Msezane and Sakmar 28 .A value of 0.312 was obtained for the optical oscillator strength from the data of Fig. 6 for the 11.5 eV transition.This result shows good agreement with the photoabsorption data of Blechschmidt et al. 7 (0.33) and Lee et al. 8 (0.20) and also with the EELS data of Hitchcock and van der Wiel 11 (0.21) and Ying et al. 13 (0.23).
In the 0.0 to 1.4 a.u.K 2 range, comparison with the experimental results of Ying et al. 13 shows a reasonable agreement only at K 2 = 0.0139 a.u.(θ = 0.5 o ) and K 2 = 1.13 a.u.(θ = 4.5 o ).At the moment no additional explanation can be furnished as to the observed disagreement at K 2 = 0.349 a.u.(θ = 2.5 o ) 29 .
In the case of the 13.2 eV curve (see Fig. 6), a different behavior is observed.Due to the absence of enough experimental points covering the K 2 range smaller than 0.2 a.u., it can not be definitively concluded that the GOS curve tends to zero as the scattering angle decreases.However, based on the experimental data of Figs. 2 and 3 and also on the discussion previously presented, it seems reasonable to reinforce the dipole-forbidden character of such a transition.

Conclusions
Angle-resolved EELS data have been measured for the valence-shell region (0-100 eV) of the SF6 molecule at an impact energy of 1.0 keV.At large scattering angles nondipole transitions have been identified, in agreement with previously published results.Particularly above 40 eV, three bands associated with forbidden processes involving many-body excitations were observed.A band at 76 eV has been observed for the first time.The absolute generalized oscillator strength for the 11.5 eV excitation has been determined in the K 2 range from 0.05 to 1.3 a.u. and a value of 0.312 for the optical oscillator strength was derived.The absolute elastic differential cross section has also been determined, through normalization of the relative data using the absolute data found in the literature.The absolute inelastic differential cross sections for the 11.5 eV and 13.2 eV transitions have been also determined.

Figure 2 .
Figure 2. Angle-resolved electron energy-loss spectra of the SF6 molecule measured at 1.0 keV and covering the angular range of 1.5° to 5.5°.

Figure 3 .
Figure 3. Angle-resolved electron energy-loss spectra of the SF6 molecule measured at different scattering angles covering an excitation energy range of 0 to 100 eV.

Figure 4 .
Figure 4. Absolute elastic differential cross section of SF6 as a function of the scattering angle θ.

Figure 5 .
Figure 5. Absolute inelastic differential cross section of SF6 for the 11.5 eV and 13.2 eV transitions as a function of the scattering angle θ.

Figure 6 .
Figure 6.Generalized oscillator strength (GOS) as a function of K 2 for the 11.5 eV and 13.2 eV transitions in SF6.The experimental data of Ying et al. 13 are also presented (see text).

Table 1 .
Elastic Differential Cross Section for the SF6 molecule.

Table 2 .
Absolute Inelastic Differential Cross Section for the 11.5 eV and 13.2 eV transitions in SF6.

Table 3 .
Generalized Oscillator Strength for the 11.5 eV transition in SF6.