K-shell binding energy of Be and its fluorescence yield

Abstract

The smallness of Be and its valence structure are attractive characteristics for the rigorous application and testing of the flexibility and utility of many-body theories. Recently, a number of results of many-electron calculations have been published on the $1s$ binding energy (BE) and the Auger width ($\ensuremath{\Gamma}$) of the hole state. They show considerable dispersion. We have studied these properties and the fluorescence yield (${\ensuremath{\omega}}_{K}$) of ${\mathrm{Be}}^{+} 1s2{s}^{2}^{2}S$ by applying a general theory of autoionizing states which is based on projected function spaces and justifies the variational calculation of localized relativistic or nonrelativistic correlation and the subsequent inclusion of the continuum. Two computational methods have been employed: The first method (A) aims at the accurate calculation of the total energy of initial and final states. In the case of Be, its ground-state energy is known accurately. The excited-state energy is computed in this work variationally and includes the effect of the continuum. The resulting correlated square-integrable wave function ${\ensuremath{\Psi}}_{0}$ of the hole state is then employed for the calculation of the Auger width and the radiative transition probabilities to the lower discrete states $1{s}^{2}2p$ and $1{s}^{2}3p^{2}P^{o}$. We find that the angular correlation increases the decay rates whereas inclusion of radial and spin-polarization correlation eventually decreases them by a factor of 2 from the Hartree-Fock (HF) value. Nonorthonormality (NON) is taken into account explicitly; we show that radiative decay does not arise only from correlation effects. The second method (B) is based on the consistent analysis of electronic structure and aims at the calculation of only those one- and two-subshell correlations which contribute to the BE the most. The validity and generality of the second method---which has been applied before to a number of atoms in the periodic table---is demonstrated once again. Our results are, with method A, a BE of 123.732 eV, $\ensuremath{\Gamma}=0.023$ eV, and ${\ensuremath{\omega}}_{K}=1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ and, with method B, a BE of 123.82 eV. The BE's include an empirical relativistic correction of 0.027 eV. An Auger-spectroscopy measurement has yielded a BE of 123.6\ifmmode\pm\else\textpm\fi{}0.1 eV. Our value for ${\ensuremath{\omega}}_{K}$ is closer to the available experimental values from the solid state (\ensuremath{\cong}3.3\ensuremath{\sim}${10}^{\ensuremath{-}4}$) than a previous many-electron calculation, by a factor of 5.