Extended Analysis of Ar III and Ar IV M ó

A pulsed discharge light source was used to study the two and three times ionized argon (Ar II, Ar III) spectra in the 480–6218 Å region. A set of 129 transitions of Ar III and 112 transitions of Ar IV were classified for the first time. We extended the analysis of Ar III to five new energy levels belonging to 3s23p34d, 3s23p35s odd configurations. For Ar IV, 10 new energy levels of the 3s23p23d and 3s23p24p even and odd configurations, respectively, are presented. For the prediction of energy levels, line transitions, and transition probabilities, relativistic Hartree–Fock calculations were used.


Introduction
Spectral analysis of several ions of argon has implications in different fields.In astrophysics [1][2][3], argon spectral lines are important in determining the chemical abundance of elements and estimating radiative transfer through stellar plasmas.Argon plasma sources are also applied in various fields of industry and research [4][5][6][7].
A compilation of energy levels and observed spectral lines of all ionization stages of Ar was reported in [8].Many of the papers published on the spectra of two and three times ionized argon (Ar III, Ar IV) are cited in this work [8].The report by Hansen and Persson [9] that presented a revised and extended analysis of the optical spectrum of Ar III is noteworthy.They used hollow cathode and theta-pinch sources analyzing the 3s 2 3p 4 , 3s3p 5 , 3p 6 , 3s 2 3p 3 4s, 3s 2 3p 3 4p, and 3s 2 3p 3 3d configurations.Improved energy levels in this ion resulting from the best wavelengths in the literature in the range between 508 Å and 4183 Å were presented by Kaufman and Whaling [10].For Ar IV, Bredice et al. [11] reanalyzed the 3s 2 3p 3 , 3s3p 4 , 3s 2 3p 2 (3d + 4s) configurations to obtain new energy levels and classify new transitions.A more recent paper [12] presented an analysis of beam-foil and beam-gas excited spectrum of argon observed in the wavelength region 2965-3090 Å.New transitions in the spectrum of Ar III and Ar IV were also identified.
In the last few decades [13][14][15][16][17][18], there has been intense research on determining and compiling the transition probabilities of ionized argon.In the work of Burger et al. [19], transition probabilities were presented for 38 Ar III and 14 Ar IV spectral lines from the wavelength interval 2400-3080 Å.These were compared to other papers reporting theoretical values [15,17].In [15], Luna et al. used the Cowan code [20] carried out according to the relativistic Hartree-Fock (HF) approach.
Tables 1 and 2 show the new and calculated energy level values for these ions with the percentage composition in LS notation.We report three new energy levels belonging to 3s 2 3p 3 4d and two to 3s 2 3p 3 5s configurations of Ar III, and in Ar IV five new energy levels for 3s 2 3p 2 3d and five for 3s 2 3p 2 4p configurations.The calculated energy level values were obtained by least squares fit [20].Our calculations included all the energy levels experimentally known.Tables 3 and 4 show 23 and 53 new classified lines for Ar III and Ar IV, respectively, that were classified with the new levels presented in this work.We also present 106 and 59 new spectral lines for Ar III and Ar IV, respectively, corresponding to transitions with previously known levels.In these tables we also present gA transition probabilities to compare with the experimental intensity of the new observed lines.In the last columns of these tables we compare the values of gA with those of reference [16].The observed differences could be due to the fact that weighted values of the energy parameters were used in our work and the calculations presented in reference [16] are ab initio, therefore the composition percentages of the experimental levels are different; besides, the set of configurations used is not exactly the same and there are effects of cancellation factors in our calculations (Sections 14 and 15 in Reference [20]).The least squares calculation results are shown in Tables 5-8 for Ar III and Ar IV.In Tables 5  and 6, we show the radial parameters for the even and odd parity configurations of Ar III.In this calculation we also included the illegal-k effective-operator parameters F k (i,j) and G k (i,j) (Section 16-7 in Reference [20]).In the case of 3s 2 3p 3 3d configuration for the odd parity, we set free the G 2 (3p, 3d) parameter (there is no HF value for this parameter).The fitted value is in agreement with that published in [10].In these tables, all the adjusted parameters that were set free are in good agreement with the scaled HF values.The parameter α was left free in the calculation and then fixed to its optimized value.The strong configuration interactions for the even parity (Table 5) between 3s 2 3p 4 -3s3p 4 3d and 3s 2 3p 4 -3p 6 configurations were optimized and fixed at 90%, 85%, and 70% of their HF values, respectively.For the odd parity (Table 6), the interaction integrals between 3s3p 5 -3s 2 3p 3 3d and 3s 2 3p 3 3d-3s 2 3p 3 4d configurations were set free in the calculation.In the energy adjustment of Ar III, the standard deviation was 101 and 339 cm −1 for the even and odd parities, respectively.In Tables 7 and 8, we show the radial parameters for the odd and even parity configurations of Ar IV.The adjusted parameters in these tables are in accordance with the scaled HF values.The parameter α was left free in the calculation and then fixed to its optimized value, except for the 3s 2 3p 2 4s configuration, which was left fixed at the value of zero.The configuration interactions were set to 85% of their HF values.These values are omitted in Tables 7 and 8.For the even configurations, the integral of interaction between 3s3p 4 and 3s 2 3p 2 3d is significant, as it was seen in reference [11].The standard deviation was 266 and 242 cm −1 for the odd and even parities, respectively.
It should be mentioned that the accuracy in our calculations of the fitted values of the previously known energy levels are given according to the standard deviation for each of the parities in Ar III and Ar IV.

Conclusions
In this work we studied the Ar III and Ar IV spectra covering the wavelength range 480-6218 Å for the visible ultraviolet region using a pulsed electrical discharge.A set of 129 transitions of Ar III and 112 transitions of Ar IV were classified.Five new energy levels belonging to 3s 2 3p 3 4d, 3s 2 3p 3 5s and 10 new energy levels of 3s 2 3p 2 3d, 3s 2 3p 2 4p for Ar III and Ar IV, respectively, were presented.Relativistic Hartree-Fock calculations were used.We considered optimized values of the energy parameters using least squares technique where we adjusted the theoretical parameter values to fit the experimental levels.

Table 1 .
New Ar III energy levels.
a Calculated energy level values obtained using the fitted energy parameters.b Percentages below 5% have been omitted.

Table 2 .
New Ar IV energy levels.
a Calculated energy level values obtained using the fitted energy parameters.b Percentages below 5% have been omitted.

Table 3 .
New classified lines of Ar III.

Table 4 .
New classified lines of Ar IV.

Table 5 .
Energy parameters (cm −1 ) for the studied even parity configurations of Ar III.HF, Hartree-Fock.Parameters omitted from this table: direct and exchange integrals and spin-orbit ζ parameters set to 85% and 95% of their HF values, respectively; CI integrals were set to 85% of their HF values.The standard deviation for the energy adjustment was 101 cm −1 . a

Table 6 .
Energy parameters (cm −1 ) for the studied odd parity configurations of Ar III.
a Parameters omitted from this table: direct and exchange integrals, and spin-orbit ζ parameters set to 85% and 95% of their HFR values, respectively; CI integrals were set to 85% of their HFR values.The standard deviation for the energy adjustment was 339 cm −1 .

Table 7 .
Energy parameters (cm −1 ) for the studied odd parity configurations of Ar IV.Parameters omitted from this table: direct and exchange integrals, and spin-orbit ζ parameters set to 85% and 95% of their HF values, respectively; CI integrals were set to 85% of their HF values.The standard deviation for the energy adjustment was 266 cm −1 . a

Table 8 .
Energy parameters (cm −1 ) for the studied even parity configurations of Ar IV.Parameters omitted from this table: direct and exchange integrals, and spin-orbit ζ parameters set to 85% and 95% of their HF values, respectively; CI integrals were set to 85% of their HF values.The standard deviation for the energy adjustment was 242 cm −1 . a