X-ray shifts for additional atomic vacancies

The simple analytical model of Burch et al. for the calculation of $K$ x-ray and Auger energy shifts resulting from an additional vacancy in the $2p$ orbital is extended to arbitrary defect configurations. The energy shifts for $K$, $L$, and $M$ x-ray series of ${}_{}{}^{86}{}_{}{}^{}\mathrm{Rn}$ are calculated for vacancies in $1s$, $2p$, $3d$, and $4f$ orbitals. The relative importance of inner- and outer-shell vacancies in producing the x-ray shifts is discussed.