Gauge-invariant approach to the calculation of transition probabilities for many-electron atoms

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Abstract
Based on field theory, we use a Green’s-function formalism to derive an order-by-order approximation to the transition probability of many-electron atoms. The nth-order approximation is obtained by cutting the kernel in the Dyson equation at the nth order of the electron-electron interaction. From the perturbative point of view, each order of approximation is equivalent to the sum of an infinite subset of Feynmann diagrams. The transition probability in each order of approximation is shown analytically to be gauge invariant. Numerical calculations have been done for several atoms. The results of the second-order approximation are, in addition to being gauge invariant, in good agreement with experiment.