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 A 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.

The doubly ionized xenon atom, Xe2+ (Z = 54), is isoelectronic with neutral tellurium.The ground configuration in this sequence is 5s*5pA.Although there has been a great demand, e.g., from laser and collision physics, for improved data on the Xe I I I spectrum and energy level system for many years, very little work has been reported since the 1930's when Boyce [1], 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 [4-6] and the 5/5/?6 'So level [7,8].
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 classifica tions 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 para metric fits.Configuration-interaction (Cl) effects, including Rydberg series Cl, have been included in the calculations.The configurations studied are 5s1 Sp*, SsSp5, 5^° 5pb, 5s15pi 6p, 6s, 7s, 5d, 6d and 4/.The lowest term of the 5/ configuration 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.A s a consequence of the present analysis it has been possible to classify the majority of the laser lines ascribed to Xe III.

The extended analysis of the Xe I I I spectrum also has
Physica Scripta 38 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 C l 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 5s25p*, 5s5p5 and 5sP5p6 were known from earlier investigations, though the designation of one level, 5s5ps X P X has been revised.The 5s15pi n l configurations can be considered as being built on the ground configuration of Xe IV, 5s? 5p3, with the addition of an outer electron.The parent configur ation gives three terms, namely 4 S', 2D and 2P .Almost all levels of the 5s25pi 6p, 6s and 5d configurations have been experimentally established or verified in this work.In the 4/ configuration, five of the levels based on the 2P parent term are missing and in the 5s2 5p* 7s and configurations only levels based on the 4S and 2D parent terms have been located.In the 5/configuration, only the levels belonging to the lowest term, C S )SF, have been located with certainty.Figure 1 shows that there is severe overlapping of con figurations 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 6 5 and 5d, 7s and 6 d and between 6 p and 4/ states.

Even configurations
When interpreting the observed energy-level structure of the even-parity configurations, the total energy matrix for the 5s2 5p4 + 5si25p3(6p + 4f + 5 f) + 5s5p*5d -I-5j° 5p6 con figurations 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).
As is evident from Fig. 1, there are large energy separ ations 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 5s? 5p* 'D 2 level.The radial integral in the C l matrix element between the s2p 4 and s°p6 configurations is very large ( ~ 67000cm-1).A simple per turbation calculation indicates that this interaction gives rise to a large shift (~ 8000 cm-1) of the 'S0 level of the ground configuration.In a similar way, it was found that the interac tion between the ground configuration and a "pure" 5s5p45d configuration gives rise to large shifts ( ~ 4000 cm" 1 ) of the 3P and lD levels, but not to the 'S 0 level.Evidently, large specific level shifts may occur from these interactions between distant configurations.It was also found that the 5s°5p6 'S0 state interacts strongly with the 'S 0 state of the 5s5p45d configur ation 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 con figuration in the energy matrix of the even configurations.C l effects between all the configurations were taken into account.In particular, it was found that the large specific deviation of the p 4 X D 2 level was removed in this way, even with the configuration interaction parameters fixed at their H F values.A s 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 F 2(5p, 5p) integral which was scaled to 0.8 times the H F value.) The level structure of the 5s?5p*6p and 4/configurations is given in Fig. 2. The positions of the observed levels of the lowest term of the 5/configuration are also indicated.It turns out that 4/is almost as low a configuration as 6 p .This reflects the fact that Xe I I I is close to the lanthanides and 4f is no longer hydrogenic.A ll levels are given in L S notation.Gener ally 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 L S designations often have very little physical significance.

O dd configurations
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 5s5ps + 5s25pi (6s + 7s + 5d + 6 d ) configur ations (Tables V I and VII).
The detailed structure of the 5s5ps and the 5s25p3(5d + 6s) configurations is shown in Fig. 3.The experimentally estab lished part of the 5s25pi (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 5 d levels, and between 7s and 6 d levels causing severe mixing of the corresponding states.
All levels are given in L S 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 5s5ps and 5s*5p*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 5s5ps lP as its largest eigenvector component.On the other hand, there are five levels having a substantial 5s5ps lP contribution to their eigenvectors.As will be discussed below, this mixing has some consequences for the Auger spectrum following ionization of an inner 4d electron.
A general observation regarding p*d configurations seems to be that the 3S term of the lowest d configuration is predic ted far below its observed position.In the  Recently, much effort has been devoted to the construction of V U V lasers.One recently observed [21] V U V laser transition is the transition at 1089Â in Xe2+ connecting the odd level at 119026 cm-1 above the ground state, and the even-parity 5s?5p6 lS 0 state at 210857cm-1.The lower state, previously designated as 5s5ps lP t , 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 5s5p5 and the 5s*5p35d states, and in the present analysis the lower level has been designated 5s2 5p3(*D)5d 'P x.The purity of the state is only 44% and the 5s5ps 'P, contri bution is 28%.The 5s5ps 'P, state is mixed into a number of different 5d states and this opens many different decay modes for the upper 5s°5p6 lS 0 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 5s25p35d states, also has conse quences for the intrepretation of the Auger spectrum of xenon following the ionization of a 4d electron, the N 4 50 0 spectrum (Fig. 5).The spectrum shown was recorded by Werme et al. [22], but has also been extensively studied by South worth et 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 struc ture of the initial hole in the 4d shell.One group of strong lines corresponds to the ion being left in the 5s2 5/?4 configur ation, 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 5s°5pb.The additional strong lines are satellites and are mainly caused by final-state con figuration interaction, i.e., in the terminology of the present study, by the mixing between the 5s5ps and the Ss^/r^Si/iand possibly 6j) states.In general there is good agreement between the g j factors determined in the least-square fit and those obtained exper imentally by Humphreys et al. [3] (Table VI).We have no reasonable explanation for the small observed g j factors of the two J = 1 levels at 133234 and 138 145cm"1.

Physica Scripta 38
particular the 4d 5d interaction, in the theoretical predic tions of the level structure.
In Xe I I I the deviation between the observed and the calculated positions of the 5pi 5 d 3S i level is 700 cm-1, even when using fitted values of the energy parameters.When introducing the Rydbergseries configuration interaction the         O bserved [ 3 ] and calculated g j fa c to rs are listed I and III) are low, showing that the coupling con ditions in the configurations investigated are intermediate.

Fig. 1 .
Fig. 1.Gross structure of the observed Xe III configurations.Broken lines indicate that not all levels o f the configuration have been located.

Fig. 2 .
Fig. 2. Structure o f the 5s*5py(6p + 4 /) configurations o f Xe III.The drawn lines, 4/"levels by dashed and 5/levels by broken lines with dots in the position o f the lowest 5/'term is also indicated.6p levels are indicated by fully centre.All levels are given in the LS coupling scheme.
4py4 d configuration of Kr I I I [16], Rb IV [17], Sr V [18], and Y V I [19] the dis crepancy is of the order of 3000 cm -1.The discrepancy is also present in lighter elements, for instance in the 2py?>d con figuration of Ne I I I [20].It was shown in Refs [17] and [18] that, to a large extent, the discrepancy in the 4py\ d configur ations of Sr V and Rb IV could be accounted for by the introduction of Rydberg-series configuration interactions, in

Fig. 3 .Fig. 4 .
Fig. 3. Structure o f the 5s5ps + 5r5p'(5d + 6r) configurations of Xe III.5p5 levels are indicated by broken lines with dots in the centre, 6r levels by dashed and 5d by fully drawn lines.AH levels are given in the LS coupling scheme.

Table V III. The energy of the Sir 5p4 3P 2 ground level is set to zero. The agreement in rela tive energies is very good; the deviation never exceeding the estimated uncertainties in the Auger values ( « 0.05 eV). The largest discrepancy is found for the (2P)6j 'R, 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 5i/levels which have a significant 5s5ps contribution to the eigenvector give rise to strong satellite lines in the Auger spectrum. The new classifications for the Xe2+ laser lines are sum- 44 350 4. Discussion deviation decreases to 170 cm . At the same time the overall mean error of the fit decreases by approximately 20%. The 5
d <-» 6d R 3 C l

Table I .
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4 8 Table I .
C ontinued T able I. Continued

Table I .
C ontinued

Table I .
C ontinued a (cm ')

Table I .
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Table I .
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Table III .
Continued

* No levels o f 5s5p*5d have been established experimentally bat the configuration is included in the theoretical treatment of the even configurations (see Section 3.1). Physica Scripta 38 60 T ab le IV . ContinuedTable VI .
Comparison between observed and calculated energy-level values ( in cm~x) and calculated percentage compositions fo r the 5s5ps + 5s*5p3 (6s + 7s + 5 d + 6d ) configurations o f X e III.Eigenvector com ponents larger than 5 % are given.