Interatomic Auger rates for the sodium fluoride crystal

Abstract

Interatomic Auger rates for the NaF crystal are calculated for initial 1s, 2s, and 2p holes in the ${\mathrm{Na}}^{+}$ ion. The crystal is simulated by a (${\mathrm{NaF}}_6$ ${)}^{5\mathrm{-}}$ cluster embedded in a large number of point ions, and the one-electron orbitals are obtained from restricted Hartree-Fock calculations of the initial state. The continuum-electron orbital is obtained from the Coulomb potential for a spherically averaged superposition of atomic charge densities for the initial state, and exchange is treated by the method of Riley and Truhlar. The continuum orbital is orthogonalized to the occupied molecular orbitals. The calculated Na(KLL) rate is about 20% greater than the experimental value. The calculated interatomic Auger widths for the transitions Na(1s)Na(2p)F(2p), Na(2s)Na(2p)F(2p), and Na(2p)F(2p)F(2p)’ [following the notation of J. A. D. Matthew and Y. Komninos, Surf. Sci. 53, 716 (1975)] are 0.001 73, 0.641, and 0.153 eV, respectively. For comparison, the width of the Na(KLL) Auger transition is close to 0.26 eV. All three interatomic transitions have been identified by Citrin, Rowe, and Christman. Widths for the transitions Na(1s)Na(2p)F(2p) and Na(2p)F(2p)F(2p)’ can be inferred from experimental data. Theory and experiment agree to within 50%. This represents a considerable improvement over previous theoretical treatments.