Relativistic all-order calculations of energies and matrix elements for Li and Be+

Abstract

Valence removal energies, hyperfine constants, and E1 transition amplitudes are calculated for the 2${s}_{1/2}$, 2${p}_{1/2}$, 2${p}_{3/2}$, and 3${s}_{1/2}$ states of Li and ${\mathrm{Be}}^{+}$. This calculation is an extension of earlier second- and third-order many-body perturbation theory (MBPT) calculations, in which now an infinite subset of MBPT terms is evaluated using all-order methods. Agreement with experiment at the 0.01% level for energies, and at the 0.1% level for matrix elements, is found. Issues involved with those higher-order terms omitted by the technique are discussed.