Shakeup calculations

When the nuclear charge changes due to radioactive decay and/or an inner-shell vacancy is produced, the bound electrons in the same atom or molecule experience the sudden change in the central potential and have a small but finite probability to be excited to an unoccupied bound state (shakeup) or ejected to the continuum (shakeoff). We calculated the shakeup-plu.s-shakeoff probabilities accompanying PI and EC using the method of Carlson and Nestor [45]. 

The calculated shakeup-plus-shakeoff probabilities for V and Cr following PI and EC are listed in Table 13. It is clear that the probabilities for EC are negligibly small and those for PI are about 5% for 3p electrons and about 10% for 3d electrons. Using the values of Table 13, we obtained the effective numbers of 3p, 3d, and 4s electrons after EC and PI and calculated the Kjd/Ka ratios for atoms. There is no influence of the shake process on the Kf3/Ka... 

It should be noted, however, that in actual situations the final states of the shakeup process are molecular Rydberg states and should be described by the MO wave functions. We estimated the contributions from the shakeup probabilities for atoms accompanying A -shell PI to the total (shakeup-plus-shakeoff) probabilities. The shakeup probabilities were calculated with the HS wave functions as the overlap integrals by the method used in our previous work [47]. The shakeup probabilities in PI were found to be about 30 40% of the total probabilities for 3p electrons and about 40 50% for 3d electrons. These large shakeup probabilities suggest that the chemical effect on the shakeup process would be large if the shakeup probabilities are calculated with the MO wave functions and the contributions of the shake process in PI to the Kf3/Ka ratios for 3d elements would be appreciable. 

Synchrotron-radiation and x-ray photoemission studies of the valence states of condensed phase-pure Cm showed seventeen distinct molecular features extending 23 cV below the highest occupied molecular states with intensity variations due to matrix-element effects involving both cluster and free-electron-like final states. Pseudopotential calculations established the origin of these features, and comparison with experiment was excellent. The sharp C Is main line indicated a single species, and the nine satellite structures were due to shakeup and plasmon features. The 1.9-eV feature reflected transitions to the lowest unoccupied molecular level of the excited state. 

In the present work we tried to interpret the satellite peaks which accompany the CO Cls spectrum as a shakeup process. The values we calculated are used to assign the experimental spectrum. The results are also compared with assignments by other calculation methods. 

Next, we describe how we calculate the satellite peak energies which are observed for the shakeup transition in XPS. The energy of the shakeup peaks observed in XPS can be represented by the wave functions ... 

Next, we describe how we calculate the shakeup transition energy for two electrons. When these two electrons are excited to the same orbital, the energy can be expressed as... 

In Fig.l, the theoretical shakeup energies are compared with the experimental spectrum reported by Schirmer et al. (4). The main peak for the Cl s photoemission is set to OeV. Schirmer et al. pointed out that peaks B, C and a small part of peak 1 arise from inelastic scattering of photoelectrons by other molecules. The observed peak positions are marked 1-6 and connected by thin lines to the calculated ones in the present and previous works. The present estimates reproduce all the sharp peaks 1-6 and agree well with the experimental... 

Cls photoemission shakeup satellites for the CO molecule were calculated with the spin-polarized discrete variational Xa method. The transition state method was applied to the estimation of multiplet peak positions for the shakeup transitions and the results are in reasonable agreement with the experimental values. 

A pair of molecular orbitals involved in the shakeup process produces two states and all the sharp peaks in the experimental spectrum can be assigned to the calculated states. The present and previously reported assignments agree with each other for the first two shakeup excitations due to the Ijt — 2n transition, however the other assignments depend on the theoretical model. The present multiplet calculations are basically performed in the same way as the SW-Xcx method but are in better agreement with the experimental results. One of the improvements was analyzed by considering the exchange Interaction and the atomic constituents of the molecular orbitals concerned. 

Using the total shake (shakeoff plus shakeup) probabilities in Table IV, we modified the the number of 2>p, 3d, and 4s electrons and calculated the K/3IKa ratios after PI. Comparing the K(3IKa ratios for PI with and without the shake processes, the increase in the IKa ratio due to the shake processes is found to be less than 0.5% for V and less than 0.4% for Cr. This fact indicates that the shakeoff and shakeup processes increase the K/3 IK a ratios for PI, but play a minor role in the difference between EC and PI. 

However, for 3p and 3d electrons the final excited states in the shakeup process should be expressed as MO s, while the calculations in Table IV were made for AO s. In order to estimate the contributions of the shakeup process to the total shake probability in Table IV, we calculated the shakeup probabilities accompanying K -shell PI by the use of the method similar to that used in our previous work (36). The shakeup probabilities in PI were obtained to be about 30-40% of the total probability in Table IV for 3p electrons and about 40-50% for 3d electrons. In the shakeup probabilities, the dominant contributions come from the 3p-4p and 3dAd transitions. For V, the former transition amounts to 27% of the total 3p shake probability and the latter is 35% of the total shake probability of 3d... 

The present results suggest that large difference in the K/3 IKa ratios observed in earlier experiments can be ascribed to the combination of the effect of the excess 3d electron in EC and the chemical effect in the samples used in two difference excitation modes. Since in the shakeup process the final excited states should be expressed as a molecular wave functions, it is interesting to calculate the shakeup probabilities by the use of MO s. 

NR2 calculations confirmed the one-electron picture of ionization for the first two cationic states of H2P. The PSs are smaller than those obtained with the P3 method. Although the absolute IE values are lower than the P3 results (which is normal for the basis set and the active orbital space used), the energy gap is consistent with the experimental and relative positions of the states. No shakeup states with significant PSs are predicted for these two transitions. 

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