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23 July 2021

New Transition and Energy Levels of Three-Times Ionized Krypton (Kr IV)

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,
,
and
1
Centro de Investigaciones Ópticas (CIOp), M.B. Gonnet, La Plata P.O. Box 3 (1897), Argentina
2
Institute of Physics “Gleb Wataghin”, University of Campinas (UNICAMP), Campinas 13083-970, SP, Brazil
3
School of Electrical and Computer Engineering, University of Campinas (UNICAMP), Campinas 13083-970, SP, Brazil
*
Author to whom correspondence should be addressed.
Atoms2021, 9(3), 48;https://doi.org/10.3390/atoms9030048
This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions
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Abstract

A capillary pulsed-discharge and a theta-pinch were used to record Kr spectra in the region of 330–4800 Å. A set of 168 transitions of these spectra were classified for the first time. We extended the analysis to twenty-five new energy levels belonging to 3s23p24d, 3s23p25d even configurations. We calculated weighted transition probabilities (gA) for all of the experimentally observed lines and lifetimes for new energy levels using a relativistic Hartree–Fock method, including core-polarization effects.

1. Introduction

Krypton that has been three-times ionized, Kr IV, belongs to the arsenic isoelectronic sequence. The most recent and complete compilation of the observed energy levels and transitions of the Kr IV ion was reported by Saloman [1]; that work used the extended analysis of our group (Reyna Almandos et al. [2]) for all but two Kr IV levels, 208,920 and 231,940 cm−1, which they took from Sugar and Musgrove [3]. The observed spectral lines of Kr IV were published by Saloman [1] from six sources: Boyce [4], Irwin et al. [5], Livingston [6], Fawcett and Bromage [7], Persson and Pettersson [8], and Bredice et al. [9]. The spectra of ions along the sequence of As I have been studied over many years [2] (references cited therein). These data and other recently published data on the arsenic isoelectronic sequence, for example, Rb V [10] and Y VII [11], were reported by NIST [12]. Reliable values of oscillator strengths, transition probabilities, and radiative lifetimes of energy levels are essential for the study of the ionized noble gases in Kr IV [9]; also, for astrophysical applications, for example, calculating Kr IV-VII oscillator strengths to consider radiative and collisional bound–bound transitions in detail in the non-LTE stellar–atmosphere models for the analysis of Kr lines that are exhibited in high resolution and high S/N ultraviolet (UV) observations of the hot white dwarf RE0503289 [13]. Recently energies and transition parameters have been reported for triply ionized Kr IV, Xe IV, and Rn IV using the general-purpose relativistic atomic structure package based on a fully relativistic multiconfiguration Dirac–Fock method [14]. In this article, we present an extension of the analysis of Kr IV from reference [2], including five energy levels of the configuration 3s23p24d and twenty levels of the 3s23p25d configuration. We interpreted this study using Hartree–Fock relativistic (HFR) calculations and parametric fits. We used the Cowan package [15] considering core polarization (CP) effects [16], which is the distortion of the internal cloud by the electric field of the outer electron orbital. For these energy levels, lifetimes were calculated using electron correlation effects. A set of 168 spectral lines of the Kr IV spectrum were classified for the first time; weighted transition probabilities (gA) were also reported for these transitions considering the CP effects.

2. Experiment

Krypton spectra covering the region from 330 to 4800 Å obtained from two different light sources (a capillary-pulsed discharge and a theta-pinch) were used. The discharge tube was built at Centro de Investigaciones Opticas (CIOp) in La Plata to study highly ionized gases [17], and the theta-pinch, used several years ago by A.G.T. and J.R.A. at the Lund Institute of Technology, Sweden, is described in Ref. [18]. Other experimental devices are detailed in reference [19]. A 3-m normal incidence vacuum spectrograph with a concave diffraction grating of 1200 lines/mm and a plate factor of 2.77 Å/mm in the first order was used in both experiments below 2000 Å. C, N, O, and available lines of krypton were recorded as internal standard lines. A wavelength range above 2000 Å was recorded in La Plata on a 3.4-m Ebert plane-grating spectrograph, with a plate factor of 5 Å/mm in the first diffraction order. The lines observed in this interval were measured by polynomial interpolation using reference lines from a thorium 232Th lamp, whose wavelengths were determined interferometrically [20]. The uncertainty in the wavelength values for lines that are not classified as w,d, or ul in Table 1 is ±0.01 Å in the measurements from Lund and ±0.01 Å and ±0.02 Å in the measurements from La Plata for the visible and the vacuum ultraviolet (VUV) regions, respectively. The intensity figures are visual estimates of photographic density and are only on a uniform scale within the limited wavelength ranges. To distinguish among different stages of ionization, we studied the behavior of the spectral line intensity as a function of pressure and discharge voltage. We used the LOPT [21] program to recalculate the energy levels from the observed wavelengths. In this adjustment, we considered the previously known lines [12] and included the new ones. The conversion between the air and vacuum wavelength used as the refraction index of the air was derived from the five-parameter formula given by E.R. Peck and K. Reeder [22].
Table 1. New classified lines of Kr IV.

3. Spectral Analysis and Theoretical Interpretation

To help in the spectral analysis, we calculated the level structures, the energy level lifetimes (τ), and weighted transition probabilities (gA) with the Hartree–Fock Cowan’s package [15] corrected by Kramida [23,24] and downloaded from the NIST website [25]. The programs that we used were modified as described by Pagan et al. [16] to include core polarization effects [26,27,28]. These methods demand knowledge of the polarizability and core cut radius. In this case, for Kr IV, a dipole polarizability αd = 0.20 a03 and a cut off radius rc = 0.55 a0 were taken from references [13,29], corresponding to a Kr8+ closed shell ionic core of the type 1s22s22p63s23p63d10, while the latter value was chosen as the mean value of ‹r› for the outer most core orbital (3d), as calculated by the HFR approach. We adjusted the values of the energy parameters to the experimental energy levels of this ion using a least squares calculation. With the adjusted values, we calculated the energy and composition of the levels as well as the gA and lifetimes of the energy levels [9,15]. The set of configurations for both of the parities used in our calculation was 4s24p3 + 4s24p25p + 4s24p26p + 4s24p24f + 4s24p25f + 4s24p26f + 4s4p34d + 4s4p35d + 4s4p36d + 4s4p35s + 4s4p36s + 4s24p4d2 + 4s24p4f2 + 4p5 + 4p44f (odd parity) and 4s4p4 + 4s24p24d + 4s24p25d + 4s24p26d + 4s24p25s + 4s24p26s + 4s24p27s + 4s4p34f + 4s4p35f + 4s4p36f + 4s4p35p + 4s4p36p + 4p44d + 4p45s + 4s4p24d2 (even parity). Intravalence correlations were considered in this calculation compared to previous work [2,9], where fewer configurations were taken into account. The introduction of the Rydberg series CI reduced the discrepancy between the observed and calculated levels values. Table 2 shows the new experimental and fitted energy level level values obtained by the least-squares fit with the percentage composition in LS notation. We extended the analysis of reference [2], presenting five and twenty new energy levels for the 4s24p24d and 4s24p25d configurations respectively. Additionally, the lifetimes of the energy levels calculated with HFR were reported by taking the fitted energy parameters and HFR + CP effects into account, as shown in the last two columns of this table. Table 1 shows 168 new classified lines of Kr IV that were classified using the new levels presented in this work, where the intensities of the lines given in the table were based on visual estimates of plate blackening. This table also reports the Ritz wavelength and its difference to observed values, calculated with the LOPT program [21]. The classification of the lower and the upper levels is presented. With the exception of transitions involving J = 9/2, it can be seen from this table that more than four spectral lines determine each experimental level. For example, in the best case, the level 4s24p2(3P)5d 2D3/2 in 303,713.2 cm−1 is determined by 17 transitions. The gA values in this table are from HFR and HFR + CP calculations, made with energy parameters adjusted by least-squares fitting. The label “*” in the last column refers to lines with cancellation factors [9] less than 0.05, as this fact may reflect errors in the estimation of gA values [15]. The least-squares calculation results are shown in Table 3 for even parity. The average energies (Eav) for the observed energy levels, the spin-orbit integrals (ζnl), and the single-configuration Slater integrals (Fk,Gk) were adjusted, keeping them free in the calculation except for the G1(4p,5s) of the 4s24p25s configuration, which was fixed at 85% at its HF value. The αd values for the 4s24p25d, 4s24p25s and 4s24p26s configurations were also fixed in the calculation. The configuration interactions 4s4p4-4s24p24d (R1(4p4p,4s4d)) and 4s4p4-4s24p25d (R1(4p4p,4s5d)) were kept free, but the CI integrals omitted in this table were set to 85% of their HFR values, and the direct and exchange integral, and spin- orbit ζ parameters were set to 85% and 95% of their HFR values. The standard deviation for the energy adjustment was 266 cm−1.
Table 2. New Kr IV energy levels.
Table 3. Energy parameters (cm−1) for the studied even parity configurations of Kr IV.

4. Conclusions

We studied the Kr IV spectrum covering the wavelength range 330–4800 Å using a capillary-pulsed discharge and a theta-pinch. We extended the analysis of this ion, including five energy levels of the configuration 3s23p24d and twenty levels of the 3s23p25d configuration. A total of 168 spectral lines were classified for the first time. Atomic HFR and HFR + CP calculation to determine weighted transition rates (gA) for all experimentally observed lines and lifetimes for new energy levels were used.

Author Contributions

Formal analysis, M.R., M.G., J.R.A. and C.J.B.P.; Investigation, M.R., M.G., J.R.A., A.G.T. and C.J.B.P.; Methodology, A.G.T.; Software, M.R. and C.J.B.P.; Supervision, J.R.A.; Writing—original draft, M.R. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by the Consejo Nacional de Investigaciones Científicas y Tecnicas (CONICET), Argentina, and by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil, Finance Code 001. The support from the Comision de Investigaciones Científicas de la Província de Buenos Aires (CIC), where M.R. and J.R.A. are researchers, is gratefully acknowledged.

Institutional Review Board Statement

Not applicable.

Data Availability Statement

All new data used in this study is contained within the article. Data from other sources are cited in the references.

Acknowledgments

We are very grateful to Fausto Bredice, who helped us in the preliminary discussions.

Conflicts of Interest

The authors declare no conflict of interest.

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