1s4p and 1s4s excitations

After the removal of the exponential ansatz the prominent spectral feature in the interval between 10 and 50 eV above the K edge is disclosed as a resonance and an edge in close succession and a compound edge further out (inset in Fig 5b). The energies are in rough agreement with DF estimates for [1s4p] and [1s4s] states. In Rb, the resonance (A) is considerably wider than in Kr, more than expected from the slight increase of the K vacancy lifetime width (2.75 eV in Kr, 2.99 eV in Rb [44]). Conversely, the adjacent edge (B) is higher in Kr. The compound [1s4s] edge (C) appears similar in both elements.

The picture becomes considerably clearer in the deconvoluted spectrum of Kr (Fig 6a) where the striking similarity with Ar is demonstrated. The same series of channels can be followed in both elements: a Fano resonance (a0), a sharp resonance (a1,2) and a subsequent edge (a3), a [1s4s] resonance (b1) and the edge (b2) with superposed diffuse structure.

Fig. 6. Details of 1s4p and 1s4s MPE groups in Kr and Rb (below). Note the similarity of the deconvoluted spectra (middle) with the respective Ar and K 1s3p groups (above). Corrected HF excitation energies (see text) and labels in Table 3. The Ar and K data are shifted by 3.2 and 3.8 eV, respectively.

In Rb (Fig 6b), only a part of the natural width may be removed by deconvolution due to a higher level of noise: so most of the detail remains hidden. The wide [1s4p] resonance reveals a composite structure, comparable to that in the homologue K. The strength of the resonant channel is larger than in Kr by a factor of 1.4: this value is close to the corresponding factor of 1.5 for the 1s 5p single-electron resonances at the K edge. The subsequent [1s4p] edge is smaller in Rb for a factor of 1.7.

The energy markers (a-c) in Fig 6(a,b) are obtained in a combined HF-DF calculation where average multiplet energies from HF [45] are corrected for the CI shifts from DF. The complete analogy with Ar and K provides the candidate coupling scheme and CI in the initial and final states [16,17,27]. The prominent resonance is a combination of [1s4p]5p^2 and [1s4p]4d^2 states (a1 and a2, respectively), the latter accessible from the admixture of the [4p^2]4d^2 ground state by a single electron transition 1s 4p. In Kr, the two mixing multiplets occupy the same narrow energy interval and form a sharp resonant peak. In Rb, the HF center of gravity for 5p^2 lies almost 2 eV higher, and the resulting compound resonance is accordingly wider. The subsequent edge (a3) is predominantly of [1s4p]5p character - it is the Rydberg limit of the[1s4p]5p^2 component of the mixed (a1,a2) resonance. The other component has a Rydberg daughter [1s4p^2]4d^2 5p at c1 and the continuum limit [1s4p^2]4d^2 at (c2).

The Fano resonance a0 at the low-energy side of the feature is a fingerprint of the interaction of the Rydberg d series and continuum d states admixed to the 4d orbital in the weak [1s4p]5s4d transition.

In explanation of the [1s4s] resonance (b1), the agreement between the experiment and the DF estimates is obtained after admixing of appropriate [1s4p^2] excitations, as already demonstrated by Dyall [46] for the case of Ar [1s3s] feature. There, the mixing provided the necessary -5 eV shift of the 1s3s resonant state. In Kr and Rb, the calculation of the analogous mixing of [1s4s]5p5s and [1s4p^2]5s5p4d states does not converge: the extrapolation of results from a series of atoms with augmented Z values gives a shift of -4.5 eV. The mixing ratio 2:1 is roughly the same as the 68:32 ratio reported for Ar. With a similar calculation, the subsequent edge is recognized as a mixed [1s4s]5s + [1s4p^2]5s4d state (b2), i.e. the promotion of the 1s electron to a continuum p state, with the same coexcitation(s) as in the resonance.

The definite presence of the 5s4d combination precludes the attractive idea that the strong b1 peak and the subsequent b2 edge result from another instance of a direct excitation from the ground state admixture [4p^2]4d^2, namely by a single electron transition 1s 5p or 1s ep. As already mentioned, their fingerprints are the resonance (c1) and the edge (c2) which lie considerably higher and do not mix with the [1s4s]5p5s or [1s4s]5s state. However, the double vacancy [4p^2] in the ground-state admixture [4p^2]4d^2 as well as in the triple excitation [1s4p^2]5s4d np is , and so are both promoted pairs 4d^2 and 5s4d, respectively.

Table 3. Corrected HF energies (see text) of 4p and 4s coexcitations in Kr and Rb.

[1s3d] excitations

The relatively strong [1s3d] MPE group shows, on a finer scale, a lot of detail modifying the basic shake profile (Fig. 7). The profile includes a distinct shake-off component recognizable by its slow saturation. Its total amplitude is approximately equal to the shake-up edge amplitude, although the latter saturates in the span of the natural width (a few eV) and the former in the range of the order of MPE excitation energy, i.e. the binding energy of the coexcited 3d electron (50 and 60 eV in our shake-off model, for Kr and Rb, respectively).

Fig. 7. 3d coexcitations in Rb and Kr. The origin of energy scale is shifted to the position of the leading1s3d peak. The position of triple 1s3d4p excitation is indicated.

The leading resonance in the d coexcitation has been shown to maintain a fixed ratio to the K-edge resonance: the relation has been followed in the 4d MPE features from xenon far into the lanthanide series [22,24,25]. The 1s3d resonances in Kr and Rb in Fig.7 also seem to keep the relation of the respective resonant 1s 5p excitations at the K-edge. The observation is supported by the absorption spectrum of Rb+ ion in an aqueous solution of RbNO3 [31,47]. There, the 3d peak is stronger and wider than the 3d peak in the Rb vapor spectrum, in the same way as the prominent 1s 5p white line in the ion spectrum is stronger and wider than the Rb vapor 1s 5p resonance. The empirical finding may have a simple explanation: if the core excitation (1s np) and the coexcitation (d d) do not involve the same orbitals, the transition matrix element factorizes (to a good approximation) so that the strength of the coexcitation follows the strength of the single-electron excitation at the edge.

The Rb spectrum provides an additional puzzle: the 1s3d resonance is recognizably split. The splitting of 6 eV, however, does not readily suggest what states might be involved: the splitting is much smaller. The analysis of the [1s3d]5p4d multiplet with the total spread of 9.1 eV shows a dense group between 0 and 4.5 eV, and two separate levels, at 7.2 and 9.1 eV in almost pure LS coupling of [3d]4d . The direct promotion of the d electron may give these levels a larger cross section, so that they show up in comparable strength to the large group below 4.5 eV where all levels involve d promotion with a nonzero change of angular momentum.

In Kr, the spread of the multiplet is only one half that of Rb, with the two direct-promotion levels at 4.6 and 4.7 eV. The effective width of the group is thus below 3.5 eV, forming a single peak in the 3 eV natural width spectrum. The observed difference in the widths of the multiplet between the two elements can thus be ascribed to the imminent collapse of the 4d orbital: Rb[1s3d] with two core vacancies is already on the other side of the collapse threshold. The shake-up multiplets [1s3d]4d show analogous splitting as the respective resonant multiplets. In the shake-off multiplets [1s3d], which involve no 4d orbital, there is a single tight group of levels.

Fig. 8. Model components of the Kr and Rb 1s3d group: resonant (dots), shake-up (dashes) and shake-off (dash-dots) two-electron channels. The residual (below) indicates the presence of tri- and perhaps even four-electron excitations. DF multiplets and HF levels are shown. Note the similarity of the residuals to the respective 1s4p structures in Fig. 4.

The flat rise of the cross section above the resonance in both elements is a superposition of the shake-off profile and a small hump 25 eV above the 3d threshold. In Kr, the hump has been ascribed to a triple vacancy state [7] without identification of reaction channels. Fig. 8 shows the sum of two-electron excitation components of our model: the residual in Kr resembles the profile of the 1s4p/4s group. It comprises a resonance and an edge, with energies close to the [1s3d4p]4d^3 and [1s3d4p]4d^2, respectively, and possibly a shake-off component. The similarity with the 1s4p/4s group is apparent also in Rb, in spite of larger noise level. The unusual strength of the triple excitation can again be explained as a transition from the [4p^2]4d^2 component of the ground state whence two electrons are promoted: 1s 4p accompanied by either 3d 4d or 3d ed. In the sharper Kr spectrum, the removal of the double-vacancy components from the 1s3d feature even reveals a tiny Rydberg daughter 1s 5p belonging, formally, to a quadruple vacancy state [1s3d4p^2]!

[1s3p] and [1s3s] excitations

The 1s3p feature is recognized as a distinct break of slope 240 and 270 eV above the K edge of Kr and Rb, respectively, close to the DF energy estimates. Pure contribution of the [1s3p] channels is revealed after a careful elimination of the [1s3d] shake-off upon which it is superposed. The long saturation profile points to a predominant shake-off character. Yet the vestiges of a structure immediately above the threshold reliably define also a resonant and a shake-up contribution, both in a doublet with a splitting of approximately 8.5 and 10 eV for Kr and Rb, respectively (Fig. 9). The splitting is induced by the subshell structure which remains the main feature of the multiplets in spite of coupling with 1s and excitation orbitals.

Fig. 9. Model components of the 1s3p and 1s3s group in Kr and Rb. Channels of the 1s3p group are subtracted to show the 1s3s group as a residual. It is only decomposed into a single shake-up and shake-off component due to the large noise.

A small [1s3s] feature can be resolved in the residue after subtraction of the [1s3p] model components from the experimental spectrum. The feature in Kr is revealed as a small and broad absorption edge close to the energy of the Dirac-Fock estimate. A similar edge is recognized in Rb in spite of larger noise. This is the deepest MPE observed so far. As in the case of [1s3p], the feature is a combination of a [1s3s] shake-up and shake-off channel. The large width is partly due to the 6 eV singlet-triplet splitting of the [1s3s] vacancy pair, and partly due to the intrinsic lifetime width, the sum of the [1s] and [3s] widths. The model amplitude of the shake-off transition is strongly coupled with the parameters of the [1s3p] shake-off upon which the feature is superposed.

Among earlier discussions of Kr MPE spectrum, Deutsch &Hart [3,4] identified all subshell groups and their main features. The [1s3s] feature in their report [3] appears within 5 eV of ours. The estimated amplitudes of the shake-up and shake-off exceed ours by a factor of 2.




Last change: 28-Jun-2006