Extension of the Siegert theorem for photon emission

When the long-wavelength approximation is not performed, extensions of the Siegert theorem can take various forms. An alternative expression is derived for the electric multipole fields, which is inspired by earlier works on photonuclear reactions. It is applied to the Siegert transformation of electric transition operators for single photon emission. In the particular case of isospin forbidden $E1$ transitions, which can be useful for some important radiative capture reactions, an approximation of this electric transition operator is established and discussed.

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