New energy levels of the 4s24p5s, 4s24p4d and 4s24p5p configurations of the Kr V spectrum

The spectrum of four-times-ionized krypton (Kr V) has been observed in the 240–2500 Å wavelength range. Three of the four possible levels of the 4s24p5s configuration and two of the three remaining energy level values for the 4s24p4d configurations were determined. Nine of the ten possible levels for the 4s24p5p configuration are also reported. The observed configurations were interpreted theoretically by means of Hartree–Fock relativistic calculations and a least-square fit of the energy parameters to the observed levels. 111 new classified lines are reported among the 4s24p2, 4s24p5p, 4s4p3, 4s24p5s, and 4s24p4d configurations.


Introduction
Energy levels of Kr I to Kr XXXVI were reviewed and compiled by Sugar and Musgrove (1991) and tables of the classified lines of Kr V to Kr XXXVI were compiled by Shirai et al (1995).
Four-times-ionized krypton, Kr V, belongs to the Ge I isoelectronic sequence and has the ground configuration 4s 2 4p 2 . The spectra of the first, second, third and fourth elements of this sequence were presented in the book Atomic Energy Levels (Moore 1971). The As II spectrum was reinvestigated by Li and Andrew (1971) and the Br IV spectrum was revised by Joshi and Budhiraja (1971).
The krypton isonuclear sequence has also been studied in different works by members of the Centro de Investigaciones Opticas Group, La Plata, Argentina and the Campinas Group, São Paulo, Brazil. Reyna  published new energy levels for Kr III and Kr IV. Pagan et al (1995) reported the study of the 4s4p4d and 4s4p5s configurations of Kr VI and Raineri et al (2000) presented the spectroscopic analysis of the 4p4d configuration of Kr VII. All these experiments were carried out using a discharge tube and a theta-pinch discharge. Trigueiros et al (1989Trigueiros et al ( , 1993, and references therein, studied the Kr V spectrum using different spectral sources. These authors presented new energy levels of the 4s 2 4p 2 , 4s4p 3 , 4s 2 4p4d and 4p 4 configurations. In this work we report an extended analysis of the four-times-ionized krypton (Kr V). We have established three new energy levels for the 4s 2 4p5s, two for the 4s 2 4p4d and nine for the 4s 2 4p5p configurations. 111 new lines were classified as combinations between levels of 4s 2 4p 2 , 4s 2 4p5p, 4s4p 3 , 4s 2 4p5s, and 4s 2 4p4d configurations. Analysis of the experimental data used Hartree-Fock calculation and parametric fit.
Configurations of the type ns 2 npn p have been studied by Kramida et al (1999) (n = 2, n = 3) and Gallardo et al (1999) (n = 5, n = 6) for elements of the same homologous sequence.
The interest in spectroscopic data for rare gases is due to applications in collision physics, laser physics, photo-electron spectroscopy and fusion diagnostics.

Experiment
The work is based on photographic recordings of the spectra of krypton between 240 and 2500 Å. We have used two different light sources in our experiment,a discharge tube and a thetapinch discharge. In both cases the energy is fed into the plasma using a capacitor bank, charged from a high-voltage power supply. The discharge tube was built at the Centro de Investigaciones Opticas (CIOp), La Plata, Argentina, to study highly ionized gases (Gallardo et al 1989). It is made with a Pyrex tube ending in a quartz window. The electrodes, 20 cm apart, were made of tungsten and covered with indium. The gas pressure was measured by a thermocouple vacuum gauge before and after exposures. The pressure range was varied between 20 and 300 mTorr. Gas excitation was produced by discharging through the tube a bank of lowinductance capacitors varying between 2.5 and 100 nF and charged up to 19 kV. A normalincidence vacuum spectrograph with a concave diffraction grating of 1200 lines mm −1 was used. The plate factor in the first order is 2.77 Å mm −1 . Kodak SWR plates were used to record the spectra. C III, N II and N III (Kelly 1987), O III (Pettersson 1982) and known lines of krypton (Kelly 1987, Shirai et al 1995 were recorded as internal standard lines. The other experimental data were obtained several years ago by two of the authors (JRA and AGT) at the Lund Institute of Technology, Sweden, using the theta pinch discharge. This consisted primarily of a cylindrical discharge tube, excited by an induction coil. The spark gap was pressurized with air. It was ignited by lowering the pressure in the spark chamber by means of a magnetic valve and triggered when the capacitor voltage reached a preset value. The theta pinch device had the following specifications: total capacitance 7.7 µF, total inductance 76 nH, period of damped oscillation 4.8 µs. Maximum current at 10 kV discharge voltage is about 100 kA. The repetition rate of the discharge was about 15 min −1 at a capacitor bank voltage of 10 kV. A 3 m normal-incidence vacuum spectrograph with a concave diffraction grating of 1200 lines mm −1 was used. The plate factor in the first order was 2.77 Å mm −1 . The spectra were exposed on Kodak SWR plates and the lines from C III, N II and N III (Kelly 1987), O III (Pettersson 1982) and known lines of krypton (Kelly 1987) were used as internal standards.
To distinguish between different states of ionization in both spectral sources, a number of experimental parameters, e.g., gas pressure, discharge voltage, capacitance and the number of discharges were varied (Gallardo et al 1989, Trigueiros et al 1989. The approximate total number of Kr lines for all stages observed over the pertinent wavelength range was 7500. The accuracy of the wavelength values is estimated to be ±0.01 and ±0.02 Å in the measurements of Lund and La Plata respectively.

Analysis
The line identifications were guided by theoretical predictions of the energy level structure and line strengths obtained from the Cowan (1981) computer code, using Hartree-Fock relativistic (HFR) wavefunctions.
The new Kr V classified lines observed in the present work are given in table 1. The intensities of the lines are based on visual estimates and the wavenumber values in the calculated column are derived from the experimental energy level values, which, in turn, were derived from the observed lines. The predicted wavelength and log g f values, shown in columns 3 and 4 of this table, were obtained considering the fitted values for the energy parameters, in the HF calculation. This kind of calculation was also used to obtain the values of weighted oscillator strengths for Kr III and Kr IV spectra , Bredice et al 2000.
The new energy level values derived from the observed lines belonging to the 4s 2 4p5p, 4s 2 4p4d and 4s 2 4p5s configurations are given in table 2. The energy level values were determined from the observed wavelengths. In our case the uncertainties of the adjusted experimental energy level values are generally less than 2 cm −1 . All level designations in table 2 are in L S notation, and in the same table we present the percentage composition of the levels that were taken from the least-squares fit.
(i) 4s 2 4 p4d. The 4s 2 4p4d configuration was studied by Trigueiros et al (1989). In this work we have extended the analysis reporting the new values 190 279 and 192 949 cm −1 for the 3 F 2 and 3 F 3 energy levels respectively. These levels were found by transitions with the new 4s 2 4p5p and ground configurations. The theoretical value for the remaining 3 F 4 energy level of the 4s 2 4p4d configuration obtained from the least-squares fit is 196 425 cm −1 . (ii) 4s 2 4 p5s. We propose three new energy level values of this configuration. For the 3 P 1 , 3 P 2 and 1 P 1 levels, the experimental values are 240926, 246 798 and 250 993 cm −1 respectively. These levels were also found by transitions with the new 4s 2 4p5p and ground configurations. The calculated value for the 3 P 0 energy level, obtained from the leastsquares fit, is 238 871 cm −1 . (iii) 4s 2 4 p5 p. Of the ten possible levels of this configuration, we found nine of them by transitions with the 4s4p 3 and 4s 2 4p4d configurations. Only the level 4s 2 4p5p 3 P 0 was not determined. The theoretical value for this level obtained from the least-squares fit is 284 942 cm −1 . From the percentage composition of table 1, we can observe that the 3 D 1 and 1 P 1 levels are very mixed. In this case the L S designation has very little physical significance.

Theoretical interpretation
The configurations were interpreted by fitting the theoretical energy expression to the observed energy levels using least-squares techniques. The adjusted parameter values for the odd and even configurations are compared with results from HFR calculations in tables 3 and 4 respectively. For the odd parity the matrix included the 4s4p 3 + 4s 2 4p4d + 4s 2 4p5s configurations. The fitted energy parameters were in accordance with scaled Hartree-Fock values. The effective electrostatic parameter α(4p, 4p) and the configuration interaction integral R 1 (4p4p, 4s4d) between 4s4p 3 and 4s 2 4p4d configurations were optimized and fixed in order to obtain better  results in the least-squares fit. The standard deviation was 124 cm −1 . If we compare this work with the report of Trigueiros et al (1989), we find that our electrostatic energy parameters are lower than those reported in that paper, except for the G 3 (4p4d) parameter of the 4s 2 4p4d configuration. The inclusion of the 3 F 2 and 3 F 3 levels of the 4s 2 4p4d configuration and the three new energy levels of the 4s 2 4p5s configuration affect this calculation, although the interaction integrals with the latter are not very significant. For the even parity the matrix included the 4s 2 4p 2 + 4s 2 4p5p + 4s4p 2 4d + 4p 4 + 4s 2 4p4f configurations. The configuration interaction integrals among these configurations are very strong except for those involving the 4s 2 4p5p because this has little influence on the calculation. The fitted average energy value of the 4s 2 4p 2 configuration is affected when we include the 4p 4 and 4s4p 2 4d configurations in the calculation. The fitted value is increased by 8022.74 cm −1 with respect to the experimental energy value. If we consider in the calculation only the 4s 2 4p 2 + 4s 2 4p5p configurations, the average energy value maintains its real value but the standard deviation increases substantially.
The levels belonging to the 4s4p 2 4d configuration are intermixed with the levels of the 4p 4 configuration. For this reason we did not fix E av for both configurations in the least-squares fit calculation. The energy parameters ζ nl , F k (nl, nl) and G k (nl, nl) for the 4s4p 2 4d configuration were fixed at 1.00, 0.85 and 0.85 of their Hartree-Fock values respectively.
From the 4s 2 4p 2 and 4p 4 we obtained two adjusted parameters (in addition to E av ), by linking together all Coulomb parameters F 2 (4p4p) in one group and the spin-orbit parameter ζ 4p in a second group. A similar procedure was adopted in the work of Cavalcanti et al (1996) for Ar V. These authors also include ns 2 nd 2 (n = 3) type configurations in the calculation, but in our case (n = 4) this was not necessary because the E av is so far from the other configurations. However, we included the same ns 2 np4f (n = 4) type configurations as Gallardo et al (1999) for Xe V (n = 5), as this reduces the standard deviation in our calculation. The energy parameters E av , ζ nl , F k (nl, nl) and G k (nl, nl) for the ns 2 np4f configuration were fixed at 1.00, 1.00, 0.85 and 0.85 of their Hartree-Fock values respectively.
All the configuration interaction integrals were held fixed in the calculation at 0.85 of their Hartree-Fock values, except for the direct radial integrals of the 4s 2 4p 2 -4p 4 , 4s4p 2 4d-4p 4 and 4s4p 2 4d-4s 2 4p4f that were fixed in the calculation to 0.75, 0.70 and 0.75 of their Hartree-Fock values respectively. In this way we achieved better results in the least-squares fit. The standard deviation was 82 cm −1 .