Nonvanishing J=1↔0 equal-frequency two-photon decay: E1M2 decay of the He-like 2 ³S₁ state

The selection rule which forbids J=1↔0 two-photon decay when the energies of the two photons are equal is shown to apply only when the multipolarities of the two photons are the same (i.e., 2E1, 2M1, etc.) and does not generally apply to mixed multipolarity amplitudes such as E1M2. A calculation of the two-photon decay rate for He-like ions in the 2 ³S₁ state including both 2E1 and E1M2 two-photon decay amplitudes is presented. It shows a significant contribution for the case of equal-energy photons. The ratio of the E1M2 contribution to the 2E1 contribution is found to be surprisingly large. For example, it is 0.27 for two-photon decay of the 2 ³S₁state in He-like uranium.