Measurement and analysis of blue shift on the helium 492.2 nm line in a liquid corona discharge
Introduction
Corona discharge experiments in liquid helium have been performed in the framework of electrical engineering studies [1]. The experimental setup consists of a point-plane electrode system, which is placed inside a helium cryostat. By applying high voltage across the electrodes, a streamer of either positively or negatively charged particles, ions and electrons is produced, which leads to the formation of localized plasma. As a rule, information on the medium can be inferred from passive spectroscopy. The emission lines due to excited helium atoms are subject to collisional (pressure-)broadening, which is determined by the density and the temperature of the perturbers. In this article, we report on the spectral analysis of the light emitted at 492.2 nm, corresponding to the 1s4d-1s2p transition of singlet helium. The spectrum presents a line which is strongly shifted to the blue direction. This shift is a feature of a potential energy difference having positive values at moderate internuclear distances, e.g. [2]. A blue shift has been observed on other lines visible in the same experiment and line shape fittings have been performed successfully, through the use of ab initio potential calculations [1] or with an analytical model [3]. Data on the helium 492.2 nm line shape in liquid are rather scarce. The investigation reported in [4] concerned the same line in the same experiment, but in gaseous helium. In liquid, a specific issue is that simultaneous collisions between an emitter and the perturbers occur. An accurate modeling requires a large number of nuclei to be accounted for, and the quasi-degeneracy of the upper level requires a large atomic base to be retained, which renders calculations prohibitive. We propose here a line shape model based on an empirical expression for the potential. Our approach is inspired by early investigations done using Lennard-Jones potentials, devoted to explain red shift and satellites on pressure-broadened lines [5], [6], [7]. We have adapted this model to the fitting of the experimental spectrum. The model involves three independent parameters. The article is organized as follows: in Section 2, we give an overview of spectra observed in the experiment; in Section 3, we present the line broadening model, to be used in the calculation of the 492.2 nm line; finally, we perform line shape fittings in Section 4 and we infer the maximum of the potential energy difference function. A discussion about the inferred parameter values is done.
Section snippets
Observation of the helium 492.2 nm line in liquid corona discharges
A series of corona discharges have been performed at a temperature of 4.2 K, for pressures ranging from 1 bar to 100 bars, with the aim of probing the dielectric properties of liquid helium. Details on the experiment can be found elsewhere, e.g. [1], [3]. Passive spectroscopy measurements carried out in the visible range have indicated the presence of intense lines (see Fig. 1). These lines are broadened due to the interactions between the excited helium atoms that contribute to the emission
Line broadening model
As a rule, the modeling of a spectral line shape involves the calculation of the Fourier transform of the emitter dipole autocorrelation function C(t), according towithHere, the trace Tr is performed over the whole space including the emitter and the perturbers surrounding it, and ρ and d are the density operator and the emitter dipole operator, respectively, expressed in the Heisenberg picture. Details on the formalism can be found in reviews, e.g.,
Fitting of the experimental line shape
While being shifted to the blue direction, the experimental profile of the helium 492.2 nm line has a red wing larger than the blue wing; this result is apparent on the plot in Fig. 2 and it was observed on all spectra recorded in the experiment. A model capable of reproducing this trend should involve positive values of Δu at moderate or large r, and negative values at smaller r. Based on the analysis done in the previous section, we have performed a line shape fitting using a Lennard-Jones
Conclusion
We have applied a line shape model to the fitting of an experimental spectrum of the helium 492.2 nm line observed in a liquid helium corona discharge. This line presents a significant shift towards the blue direction, indicating that the spectral profile is mainly sensitive to collisions with the atoms surrounding the emitters. Using an empirical model for the potential energy difference between an emitter and a perturber, we have performed a fitting of the line shape. The best-fit result is
Credit author statement
The authors contributed equally to this work.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work has been carried out within the framework of the IPMC “Réseau des plasmas froids” program.
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