Abstract
Rules for obtaining transition amplitudes that are equal in length form and velocity form, order-by-order in relativistic many-body perturbation theory are presented. Explicit formulas are derived for first-, second-, and third-order amplitudes for transitions between valence states in alkali-metal atoms. Numerical codes are developed to evaluate amplitudes through third order and applied to $3s\ensuremath{-}{3p}_{1/2}$ and $3s\ensuremath{-}{3p}_{3/2}$ transitions in sodium and sodiumlike ions. The present calculations for sodiumlike ions are compared with other accurate theoretical calculations.
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