THE JOURNAL OF CHEMICAL PHYSICS 139, 184301 (2013)

Electron impact excitation of the low-lying 3s[3/2]1 and 3s [1/2]1 levels in neon for incident energies between 20 and 300 eV M. Hoshino,1,a) H. Murai,1 H. Kato,1 M. J. Brunger,2,3 Y. Itikawa,4 and H. Tanaka1 1

Department of Physics, Sophia University, Chiyoda-ku, Tokyo 102-8554, Japan ARC Centre for Antimatter-Matter Studies, CaPS, Flinders University, GPO Box 2100, Adelaide, SA 5001, Australia 3 Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia 4 Institute of Space and Astronautical Science, Sagamihara, Kanagawa 252-5210, Japan 2

(Received 9 September 2013; accepted 23 October 2013; published online 8 November 2013) Absolute differential cross sections (DCSs) for electron impact of the two lower-lying 3s[3/2]1 (3 P0 ) and 3s [1/2]1 (1 P1 ) electronic states in neon (Ne) have been determined for eight incident electron energies in the range 20–300 eV. Comparisons between our results and previous measurements and calculations, where possible, are provided with best agreement being found with the recent largescale B-spline R-matrix computations [O. Zatsarinny and K. Bartschat, Phys. Rev. A 86, 022717 (2012)]. Based on these DCSs at 100, 200, and 300 eV, a generalised oscillator strength analysis enabled us to determine estimates for the optical oscillator strengths of the 3s[3/2]1 and 3s [1/2]1 levels. In this case, excellent agreement was found with a range of independent experiments and calculations, giving us some confidence in the validity of our measurement and analysis procedures. Integral cross sections, derived from the present DCSs, were presented graphically and discussed elsewhere [M. Hoshino, H. Murai, H. Kato, Y. Itikawa, M. J. Brunger, and H. Tanaka, Chem. Phys. Lett. 585, 33 (2013)], but are tabulated here for completeness. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4829056] I. INTRODUCTION

Electron scattering from neon is important in modeling applications in the lighting and laser industries,1, 2 plasma processing,3–5 and for the interpretation of astrophysical data.6, 7 In addition as neon is a relatively light target, with the ground state represented as a compact closed-shell system, it has also been a favoured target for developing and testing theoretical models, including for the 3s[3/2]1 and 3s [1/2]1 levels of this study. As a consequence, there have been extensive measurements and calculations of differential cross sections (DCSs) and integral cross sections (ICSs) for those levels. These investigations include work from Register et al.,8 for impact energies (E0 ) from 25 to 100 eV, Khakoo et al.,9 at E0 = 20, 30, 40, 50, and 100 eV and for scattered electron angles (θ ) between 1◦ and 130◦ and at higher energies (300, 400, and 500 eV) by Suzuki et al.10 New threshold data have also more recently been reported by Allan and colleagues.11, 12 Please note that other available experimental work, prior to 1984, has been well summarised in Register et al.8 and Khakoo et al.9 and so are not listed again here. Theoretical approaches applied to this problem include the first order many-body theory (FOMBT),13 a distorted wave Born approximation,14 and the R-matrix approach.13–19 Nonetheless, particularly at the differential cross section level, there still remain some quite serious discrepancies between the various experiments and theories and this latter observaa) Author to whom correspondence should be addressed. Electronic mail:

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tion forms a major rationale behind the present work. Note, however, that for the integral cross sections and for both the 3s[3/2]1 and 3s [1/2]1 levels, there is now excellent agreement between the measured data of Hoshino et al.20 and the largescale B-spline R-matrix (BSR) calculation of Zatsarinny and Bartschat,18 so that the discrepancies there have been largely resolved. There have also been numerous experimental and theoretical determinations for the optical oscillator strengths of the 3s[3/2]1 and 3s [1/2]1 levels. Some of the more important experimental data are due to Wiese et al.,21 Natali et al.,22 Aleksandrov et al.,23 Tsurubuchi et al.,24 Chan et al.,25 Suzuki et al.,10 Ligtenberg et al.,26 Curtis et al.,27 Gibson and Risley,28 and Zhong et al.29 Please note that while this list is by no means exhaustive, a more complete picture can be obtained from the references cited within those papers.10, 21–29 Corresponding theoretical calculations, again not complete but representative, are due to Gruzdev and Loginov,30 Albat and Gruen,31 Aleksandrov et al.,23 Hibbert et al.,32 and Avgoustoglou and Beck.33 Optical oscillator strengths (OOSs) play an important role as they provide a very sensitive test for the quality of the relevant target states used in the theory. In addition, here they also provide us with a useful self-consistency check on the validity of our measurement and analysis procedures. The structure of this paper is as follows. In Sec. II, we provide details of our experimental measurement and analysis procedures. Thereafter, in Sec. III, our results and a discussion of these results are presented. Finally, some conclusions from the present investigation are provided in Sec. IV.

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II. EXPERIMENTAL AND ANALYSIS DETAILS

The present measurements were performed at Sophia University using two crossed-beam spectrometers. In the first, for energies of 50 eV and below, the spectrometer consists of a standard hemispherical energy selector and analyser, a series of cylindrical lens elements for the electron gun and scattered electron optics, and a channeltron for the detection of the scattered electrons. The angular resolution of this spectrometer is ±2◦ and the typical angular range of its cross section measurements was 10◦ –130◦ . Full details on this apparatus can be found elsewhere.34–36 The second spectrometer contains many elements common to the first, with the exceptions of a double tandem-hemisphere configuration in the analyser and a physical aperture being placed between the analyser hemispheres to help eliminate primary beam interference at smaller scattered electron angles. This spectrometer was operated at energies of 100 eV and above, its angular resolution was ±1◦ and the typical angular range of its DCS measurements was 0.53◦ –15.6◦ (the actual range depended here on the incident electron energy in question). Both spectrometers employed single capillary nozzles (tubes of diameter 0.3 mm and length 5 mm), through which the target gas effuses to produce a well collimated beam of Ne atoms in the interaction region. The neon source was supplied from the Takachiho Chemical Company with a stated purity of better than 99.999%. A combination of 2 mm thick μ-metal shielding and Helmholtz coils around the top and bottom flanges of the vacuum chambers, rendered the earth’s magnetic field to less than a few mGauss in each spectrometer. The incident electron beam current, as measured in a Faraday Cup, was in the range 3–7 nA for the present measurements, while the overall energy resolution was about 28–40 meV (full-width-at-half-maximum, FWHM). As can clearly be seen from Fig. 1 that energy resolution was sufficient to largely resolve the four energy loss peaks (originating from excitation of the 3s[3/2]2 (16.619 eV), 3s[3/2]1 (16.671 eV), 3s [1/2]0 (16.716 eV), and 3s [1/2]1 (16.848 eV)37 electronic states) in the ∼15.5– 17.5 eV energy-loss range of our measurements (although a spectral deconvolution (fit) of those peaks was also

1.0

Ne E0 = 40 eV, θ = 30

Intensity (arb. untis)

0.8

ns'[1/2]

J=1

J=0 o

0

n=3

ΔE = 28 meV

0.6

0.4 J=2

0

n=3

0.2

0.0 16.4

ns[3/2]

J=1

16.5

16.6

16.7

16.8

16.9

17.0

17.1

Loss energy (eV)

FIG. 1. Typical energy loss spectrum from the present study. Here, the incident beam energy was 40 eV and the scattered electron angle was 30◦ .

performed to be sure – see Fig. 1). Note that the incident electron beam energy was calibrated against the 19.366 eV resonance in helium.38 In this investigation, the true zero degree scattering angle was determined by noting the symmetry of the elastic scattering and/or inelastic (21 P in He or 3s [1/2]1 state in neon) scattering intensities. Note that when assembling each spectrometer, the geometrical alignment for mounting both the selector and analyser to the centre of the beam-forming nozzle was checked as precisely as possible using a laser. With these precautions, we believe the accuracy of our angular calibration is better than ±0.5◦ . At each incident electron energy and scattered angle, the energy-loss spectra (Fig. 1) were measured. For the incident energies of interest (E0 = 20, 25, 30, 40, 50, 100, 200, and 300 eV) and the energy loss range of interest (E∼15.5– 17.5 eV), the ratio of the energy loss to the incident energy varies roughly in the range of 0.05 < E/E0 < 0.88. Thus, it is important to establish the transmission response of the analyser over this energy loss range. In the present case, all the lens voltages of the analyser optics have been calculated with an “in-house” developed computer program that traces electrons through the electric fields of the lenses, and minimises the sum of the squared deviations from user-specified parameters such as the image position and magnification, etc., by automatically adjusting, at any one time, three of the pertinent lens voltages. Note that the performance of our code has been benchmarked and verified against corresponding results obtained from the commercial Manchester University CPO code. After calculating a set of voltages, for the residual energies (Er = E0 −E) of the scattered electrons, of interest, we pass a cubic spline function through the data and then use the results of that spline fit to drive the analyser lenses by computer control. Such voltage sets have been calculated for all impact energies from 20 to 300 eV. In addition, we have explicitly checked our analyser response using the two experimental methods we now outline. In method 1, for the particular case of a scattered electron angle of 30◦ although our approach has been applied at many θ (consistent with the philosophy espoused in Allan39 ), we make use of the known absolute elastic DCS for electron–helium scattering40 and the elastic intensities that we measure with our apparatus as the incident beam energy is varied to cover the energy loss (or scattered electron energy) range of interest. The results of this process are given in Fig. 2, where we see that deviations from ideal response behaviour (i.e., a transmission efficiency = 1) are only important below 30 eV incident electron energy. Note that in all cases the incident electron beam current is carefully monitored in a Faraday Cup (placed at 10 mm from the collision centre with a 2 mm acceptance diameter), and that all the measured elastic intensities are normalised (if needed) to ensure unit incident current. In method 2, we make use of the known He elastic and 21 P excitation cross sections (see Ref. 41 and references therein) and the measured elastic and inelastic intensities in order to characterise the analyser transmission response. In this case, for E0 = 30 eV and 50 eV and again for θ = 30◦ , the results are also presented in Fig. 2. It is clear from Fig. 2 that the results we obtain with method 2, at those incident beam energies, are consistent with one another

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where ki and kf are the initial and final momenta of the incident and scattered electrons, E is the excitation energy for each electronic state, a0 is the Bohr radius (0.529 Å), R is the Rydberg energy (13.6 eV), Gexpt (K2 ) is the experimental generalised oscillator strength (GOS), and K2 is the momentum transfer squared defined by

4 o

θ = 30

Transmission efficiency

E0 = 20 eV E0 = 25 eV

3

E0 = 30 eV E0 = 50 eV

2

K 2 = (ki a0 )2 + (kf a0 )2 − 2(ki a0 )(kf a0 )cosθ.

1

0

0

3

6

9

12

15

18

21

24

Energy loss (eV) FIG. 2. Typical results for the present transmission calibration experiments at the scattered electron angle of 30◦ . Results using method 1 at E0 = 20 eV (—), 25 eV (- - -), 30 eV (- · · - · · -), and 50 eV (– · – · –), and method 2 at E0 = 30 eV (blue ●) and 50 eV (green ●) are shown. See text for details.

Vriens46 proposed the following formula to represent the GOS for a dipole-allowed excitation, based on analytic properties identified by Lassettre47 and Rau and Fano:48 ∞   fm x m 1 G(x) = , (3) (1 + x)6 m=0 (1 + x)m where x= and

and are very close to ideal analyser transmission behaviour. It is also clear from this figure that the analyser response functions from either method 1 or method 2 are consistent with one another. We are therefore confident that the sets of voltages we calculated, for incident energies of 30 eV and above, ensure (to an uncertainty ∼10%) uniform transmission response in the 30–300 eV range. However, at 20 eV and 25 eV some corrections to the measured DCS are required to account for their transmission response at those energies. Note that while our results using method 2 were specifically reported at θ = 30◦ , it has also been applied at many other values of θ with ideal transmission behaviour typically being found (for E0 = 30 eV and 50 eV and beyond). The peak intensities for the 3s[3/2]1 and 3s [1/2]1 , at each E0 and θ , and which are in relative units, are then converted into absolute DCSs by calibrating against the well known elastic DCS of helium40 by means of the established relative flow method.42, 43 That calibration requires equal Knudsen numbers for He and Ne in the interaction region, for which values of the hard sphere diameters of He (2.18 Å) and Ne (2.60 Å)44 were employed. With the correct implementation of our normalisation procedure, absolute DCSs for each of the 3s[3/2]1 and 3s [1/2]1 states and for each energy investigated were thus obtained. These results are listed in Tables I and II. The errors associated with the present data stem from an uncertainty in the He elastic DCS used in our normalisation (∼10%), an uncertainty in the transmission response of each analyser (∼10%) that we determined, statistical uncertainties associated with the measurements (