Spectrum of doubly ionized xenon (Xe III)

The spectrum of doubly ionized xenon has been investigated. The study is based on photographic recordings of xenon spectra in the 490-8900 Å range. The number of classified lines has been increased from about 300 to about 1400. The lines have been classified as transitions between 73 even levels belonging to the 5s25p4, 5s25p36p, 4f, 5f and 5s05p6 configurations, and 83 odd levels belonging to the 5s5p5, 5s25p36s, 7s, 5d and 6d configurations. In particular, the classifications include most of the Xe III laser lines. The experimentally observed level structures are compared with the results of Hartree-Fock calculations and least-squares fits. A comparison is also made between the results of the present analysis and the published data on the Xe N4,5 OO Auger spectrum.


Introduction
The doubly ionized xenon atom, Xe2+ ( Z = 54), is isoelectronic with neutral tellurium. The ground configuration in this sequence is 5?5p4. Although there has been a great demand, e.g., from laser and collision physics, for improved data on the Xe I11 spectrum and energy level system for many years, very little work has been reported since the 1930's when Boyce [l], Humphreys [2] and Humphreys et al. [3] undertook extensive studies of the spectrum. A few reports have appeared treating the lower levels of the spectrum [4-61 and the 5s' 5p6 ' So level [7, 81. A large number of strong xenon laser lines were reported some 20 years ago [9]. Primarily due to the work of the group in La Plata, the laser lines were classified as originating in doubly and trebly ionized xenon, but no further classifications were possible due to the lack of relevant spectroscopic data.
In the present investigation we have recorded xenon spectra photographically in the 490-6900 A range. When analysing the vast amount of experimental data we have made extensive use of Hartree-Fock calculations and parametric fits. Configuration-interaction (CI) effects, including Rydberg series CI, have been included in the calculations. The configurations studied are 5? 5p4, 5s5ps, 5s' 5p6, 5? 5p36p, 6s, 7s, 5d, 6d and 4J The lowest term of the 5fconfiguration has also been located. The number of classified lines has been increased from about 300 to, in all, 1400. These lines originate from transitions between 73 even-and 83 odd-parity levels.
As a consequence of the present analysis it has been possible to classify the majority of the laser lines ascribed to Xe 111. The extended analysis of the Xe I11 spectrum also has some consequences for the interpretation of the Auger spectrum following ionization in the 4d subshell of neutral xenon.

Experimental
The vacuum-ultraviolet part of the spectrum was recorded in Lund. Two different light sources were used: a direct-current hollow-cathode discharge [IO] and a theta-pinch discharge [ll]. The hollow-cathode source gives a Xe I11 spectrum of better quality as regards resolution and obtainable wavelength accuracy, while the theta-pinch exposures were of great value in the determination of the ionization stages of the observed lines. The spectrum was photographed on a 3 m normal-incidence spectrograph with a plate factor of 2.77 Ajmm in the first diffraction order [12]. The wavelength range above 2000A was recorded on a 3.4m Ebert planegrating spectrograph in La Plata. This instrument has a plate factor of 5 A/mm in the first diffraction order. The results of the wavelength measurements in air have been discussed previously [ 131. The spectrum was excited in a laser-tube-like source (without end-mirrors) about 1 m in length and with an inner diameter of 3". The tube has inner electrodes and was viewed end-on [14].
The wavelengths and intensities of all classified Xe I11 lines are given in Table I. In the long-wavelength end of the spectrum, outside the range covered by the present recording, a few lines have been included from an unpublished xenon line-list by Humphreys [15]. The quality of the recorded spectra does not permit very accurate wavelength determination. Most lines are fairly wide. The overall wavelength accuracy is estimated to be 0.05 A in the air region and 0.02 A in the vacuum-ultraviolet wavelength region.
The intensity figures are visual estimates of photographic density, and are on a uniform scale only within limited wavelength ranges. For the lines quoted from Humphreys' list the intensities are on a completely different scale.
All the experimentally established Xe I11 levels are given in Tables I1 and. 111. The level values were determined by a least-squares procedure in which the appropriately weighted wave numbers of the identified lines were used as input. All level designations are in LS notation. In most cases the names given to the levels were taken from least-squares fits of the theoretical energy expressions to the experimentally observed level values. In general, the calculated purities of the states  (Tables I1 and 111) are low, showing that the coupling conditions in the configurations investigated are intermediate.

Analysis
When performing the analysis of the experimental data we were guided by theoretical predictions of the level structures. Such predictions were obtained by diagonalization of the appropriate energy matrices, including CI matrix elements. The radial parts of the matrix elements were determined in Hartree-Fock calculations. Approximate scaling factors were determined from comparisons with calculations for similar structures. Figure 1 shows the relative positions and extensions of the configurations studied. The levels in 52 5p4, 5s5p5 and 5s' 5p6 were known from earlier investigations, though the designation of one level, 5s5p5 'PI has been revised. The 5s25p3nl configurations can be considered as being built on the ground configuration of Xe IV, 5sz5p3, with the addition of an outer electron. The parent configuration gives three terms, namely 4S, 2D and 2P. Almost all levels of the 5?5p36p, 6s and 5d configurations have been experimentally established or verified in this work. In the 4f configuration, five of the levels based on the 2P parent term are missing and in the 5s?5p37s and 6d configurations only levels based on the 4S and ' 0 parent terms have been located. In the Sfconfiguration, only the levels belonging to the lowest term, (4S)5F, have been located with certainty. Figure 1 shows that there is severe overlapping of configurations of the same parity. This leads to heavy mixing of states belonging to different configurations, even if the matrix elements connecting the states are small. Such mixing occurs between 6s and 5d, 7s and 6d and between 6p and 4f states.

3.1, Even configurations
When interpreting the observed energy-level structure of the even-parity configurations, the total energy matrix for the 5?5p4 + 5?5p3(6p + 4f + 5f) + 5s5p45d + 5s05p6 configurations was diagonalized. The calculated energy-level values were fitted to the observed ones by least-squares fits in which some of the energy parameters were treated as free parameters (Tables IV and V).
Physica Scripta 38 As is evident from Fig. 1, there are large energy separations between the levels of the ground configuration and the excited configurations. In cases like this, it is customary to diagonalize the energy matrix and to perform a least-squares fit for the ground configuration separately. However, it was found that a least-squares fit to the levels of the ground configuration, omitting the effective configuration-interaction parameter a, gives a large discrepancy between the observed and the calculated positions of the 5s25p4 ID, level. The radial integral in the CI matrix element between the s2p4 and sop6 configurations is very large ( -67 000 cm-] ). A simple perturbation calculation indicates that this interaction gives rise to a large shift (-8000cm-') of the 'So level of the ground configuration. In a similar way, it was found that the interaction between the ground configuration and a "pure" 5s5p4 5d configuration gives rise to large shifts (-4000cm-I) of the 3P and ID levels, but not to the 'So level. Evidently, large specific level shifts may occur from these interactions between distant configurations. It was also found that the 5s05p6 'So state interacts strongly with the 'So state of the 5s5p45d configuration and a substantial mixing of these two states occurs.
In the light of the above discussion we decided to include the ground configuration and the high-lying 5s5p45d configuration in the energy matrix of the even configurations. CI effects between all the configurations were taken into account. In particular, it was found that the large specific deviation of the p4 ID2 level was removed in this way, even with the configuration interaction parameters fixed at their H F values. As none of the levels belonging to the 5s5p45d configuration has been established experimentally, the energy parameters of this configuration were held fixed at their H F values during the fitting process (except the F2(5p, 5p) integral which was scaled to 0.8 times the H F value.) The level structure of the 5?5p36p and 4fconfigurations is given in Fig. 2. The positions of the observed levels of the lowest term of the Sfconfiguration are also indicated. It turns out that 4fis almost as low a configuration as 6p. This reflects the fact that Xe I11 is close to the lanthanides and 4f is no longer hydrogenic. All levels are given in LSnotation. Generally the designations given represent the largest contribution to the eigenvector. However, for many levels the purities are very low, the largest component amounting to only about 30% in some cases. In one case we have used the second largest eigenvector component to name the level. Thus the LS designations often have very little physical significance.

Odd conjigurations
The odd-parity configurations were also interpreted by means of energy matrix diagonalizations and parametric least-squares fits to the energy levels. The energy matrix included the 5s5p5 + 5sz5p3(6s + 7s + 5d + 6 d ) configurations (Tables VI and VII).
The detailed structure of the 5s5p5 and the 5s?5p3(5d + 6s) configurations is shown in Fig. 3. The experimentally established part of the 5$5p3(6d + 7s) configurations is shown in Fig. 4. As can be seen from the figures, there are a number of fortuitous coincidences between 6s and 5d levels, and between 7s and 6d levels causing severe mixing of the corresponding states.
All levels are given in LS notation, but, as for the evenparity levels, the designations often have very little physical significance because of the severe mixing of states with There is also strong mixing between 5s5p5 and 5s25p3 5d states. Primarily this mixing is not caused by close level coincidences, but rather by large matrix elements connecting the states. The mixing is most pronounced for the singlets. In fact, there is no level having 5s5p5 'P as its largest eigenvector component. On the other hand, there are five levels having a substantial 5s5p5 'P contribution to their eigenvectors. As will be discussed below, this mixing has some consequences 3 4 5 6 J drawn lines, 4flevels by dashed and 5flevels by broken lines with dots in the centre. All levels are given in the LS coupling scheme.
for the Auger spectrum following ionization of an inner 4d electron.
A general observation regarding p3d configurations seems to be that the 3S term of the lowest d configuration is predicted far below its observed position. crepancy is of the order of 3000 cm-' . The discrepancy is also present in lighter elements, for instance in the 2p33d configuration of Ne I11 [20]. It was shown in Refs [17] and [18] that, to a large extent, the discrepancy in the 4p34d configurations of Sr V and Rb IV could be accounted for by the introduction of Rydberg-series configuration interactions, in 5p' levels are indicated by broken lines with dots in the centre, 6s levels by dashed and 5d by fully drawn lines. All levels are given in the LS coupling scheme. particular the 4d t , 5d interaction, in the theoretical predictions of the level structure.
In Xe I11 the deviation between the observed and the calculated positions of the 5p35d 3S, level is 700cm-', even when using fitted values of the energy parameters. When introducing the Rydbergseries configuration interaction the Physica Scripta 38 deviation decreases to 170 cm-' . At the same time the overall mean error of the fit decreases by approximately 20%. The 5d H 6d R3 CI integral could not be treated as an adjustable parameter at the same time as the R' and R2 CI integrals. The R3 integral was therefore optimized in a series of separate calculations and kept fixed in the final calculation.
In general there is good agreement between the g, factors determined in the least-square fit and those obtained experimentally by Humphreys et al. [3] (Table VI). We have no reasonable explanation for the small observed g, factors of the two J = 1 levels at 133 234 and 138 145cm-'.

Discussion
Recently, much effort has been devoted to the construction of VUV lasers. One recently observed [21] VUV laser transition is the transition at 1089 A in Xe2+ connecting the odd level at 119 026 cm-I above the ground state, and the even-parity 5s05p6 ISo state at 210857cm-'. The lower state, previously designated as 5s5ps 'PI, is considered to decay rapidly to the ground state while the upper state can be populated by Auger processes.
As already pointed out, there is considerable mixing between the 5s5ps and the 5? 5p35d states, and in the present analysis the lower level has been designated 5?5p3(*D)5d ' P I . The purity of the state is only 44% and the 5s5p5 'PI contribution is 28%. The 5s5ps 'PI state is mixed into a number of different 5d states and this opens many different decay modes for the upper 5s05p6 'So state. This fact probably has to be taken into account when discussing the possible efficiency of the laser action of this particular transition.
The present analysis, in particular as regards the mixing between the 5s5ps and the 5?5p35d states, also has consequences for the intrepretation of the Auger spectrum of xenon following the ionization of a 4d electron, the N4,,00 spectrum (Fig. 5). The spectrum shown was recorded by Werme et al. [22], but has also been extensively studied by Southworth er al. [23], and Aksela et al. [24].
The spectrum consists of lines corresponding to the Xe2+ ion being left in different final states. There are two lines possible for each final state, corresponding to the fine structure of the initial hole in the 4d shell. One group of strong lines corresponds to the ion being left in the 52 5p4 configuration, another group to the 5s5ps final states and a third group corresponds to the ion being left with an empty 5s shell, i.e., the configuration 5s05p6. The additional strong lines are satellites and are mainly caused by final-state configuration interaction, i.e., in the terminology of the present study, by the mixing between the 5s5ps and the 52 5p3 5d (and possibly 6s) states.
A detailed comparison between the Auger data and the present optical data is given in Table VIII. The energy of the 5s25p4 3P2 ground level is set to zero. The agreement in relative energies is very good; the deviation never exceeding the estimated uncertainties in the Auger values (z 0.05 eV). The largest discrepancy is found for the (2P)6s ' P I level. However, the identification of this state in the Auger spectrum is tentative as it is based on a single line. Moreover, this line is doubly classified. It can also be seen that those 5d levels which have a significant 5s5p5 contribution to the eigenvector give rise to strong satellite lines in the Auger spectrum.
The new classifications for the Xe2+ laser lines are sum- marized in Table IX. The laser data are taken from the compilation by Beck et al. [9]. Table IX includes all laser lines ascribed with certainty or with some doubt to Xe2+. Only very few lines remain unclassified. We have also included a laser line at 3349A, which, with a question mark, has been ascribed to Xe3+, but in the present analysis has been classified as a Xe2+ line. Based on a revised analysis and isoelectronic comparisons, Gallardo et al. [5] determined the value of 250400 & 300cm-' (31.05 & 0.04eV) for the ionization energy of Xe2+. Their value, which was about 9000 cm-' lower than the previously accepted value [25], is in fairly good agreement with the later value by Dutil and Marmet [26]. Using electronimpact ionization of xenon they arrived at the value of 31.24 k O.lOeV. The present analysis does not indicate any need for revising the value of the ionization energy.
.45 (,Dj5d 'PI -(*0)6p ID,                                                 Energy parameters (in c m -' ) for the 5s5p5 + 5?5p3(5d + 6d + 6s + 7s) conjgurations of The values in parentheses are a measure of the amount of cancellation which occurred in forming the integral. These numbers are the ratio of the true Rk value to an Rk value calculated using the absolute value of each wavefunction.