Many-Body Theory of the Magnetic Hyperfine Interaction in the Excited State (1s22s2pP3) of the Beryllium Atom

Abstract

The hyperfine interaction in the ($1{s}^{2}2s2p^{3}P_{2}$) excited state of the beryllium atom is of interest since it is the lowest excited state in which hyperfine effects can occur, the ground state being a singlet. In the present work the magnetic hyperfine interaction for ${\mathrm{Be}}^{9}$ is studied theoretically using the linked cluster many-body perturbation theory including up to second order in the electron-electron interaction, certain classes of ladder diagrams, and selected third-order diagrams. Our theoretical value of $A$ in $A\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$ is composed of - 107.41 MHz from the zero-order valence $2s$ and $2p$ electrons and - 16.80 MHz from higher-order diagrams the total value - 124.21 MHz being in good agreement with the experimental result of - 124.5368\ifmmode\pm\else\textpm\fi{}0.0017 MHz. The contributions from various diagrams are interpreted in terms of physical effects such as exchange core-polarization and correlation effects, the influence of $2s2p$ interactions being significant in influencing the hyperfine constant.