Theory ofKLLAuger Energies Including Static Relaxation

A previously overlooked relaxation energy $R$ is introduced into the intermediate-coupling formulas of Asaad and Burhop to calculate the $\mathrm{KLL}$ Auger energies of the elements from $Z=10\mathrm{} \mathrm{to} 100$. By employing the concept of equivalent cores, together with the work of Hedin and Johansson on polarization energies of electron holes, a method was developed to estimate $R$ accurately from ground-state two-electron integrals calculated by Mann. These integrals were also used in the intermediate-coupling calculation. Agreement with experiment is excellent. A table of $\mathrm{KLL}$ Auger energies based on this work is given. These energies appear to be preferable to the older semiempirical values because they are comparable in accuracy and they have a sound theoretical basis. Their adoption for analysis of Auger spectra is suggested. The semiempirical values were based on two sets of parameters for light and heavy elements. They gave good fits only by using unrealistic values of the two-electron integrals in the intermediate-coupling equations, because the relaxation energy was omitted. In addition to predicting $\mathrm{KLL}$ Auger energies accurately, this work shows that the spin-orbit coupling constant $\zeta$ for $2p$ electrons in two-hole states is essentially the same as in one-hole states. The success of the intermediate-coupling calculations also shows that two-electron integrals in these two-hole states are accurately equal to those calculated for neutral atoms. The relaxation-energy concept can be applied to other problems.