Interatomic radiative transition rates for the sodium fluoride crystal

Abstract

Interatomic electric-dipole radiative transition 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 molecular orbitals are obtained from open-shell restricted-Hartree-Fock calculations of the initial state and final states. This allows the transition matrix element to be calculated in the self-consistent-field (ΔSCF) formalism where both initial- and final-state determinantal wave functions are used, and the nonorthogonality of the two sets of molecular orbitals is taken into account. One interatomic radiative transition, the K${\beta }_1$ satellite line, has been observed as a high-energy satellite of the Na K${\alpha }_1$ ${\alpha }_2$ line. The measured intensity ratio ${\beta }_1$/${\alpha }_1$ ${\alpha }_2$ is 1.2×${10}^{\mathrm{-}2}$; our theoretical ratio is 1.13×${10}^{\mathrm{-}2}$. This level of agreement between theory and experiment is similar to, but somewhat better than, that recently obtained by us for interatomic Auger transitions in NaF, using molecular orbitals from the same calculations. The other interatomic radiative transitions in NaF have considerably smaller transition energies and unobservably small transition rates. The sensitivity of the rates to the choice of Hartree-Fock Gaussian basis set is explored. Rates based on a single determinantal wave function are compared with the ΔSCF rates. The one-center approximation for the K${\beta }_1$ rate was found to account for 82% of the rate.