The effect of an external magnetic field on the determination of E1M1 two-photon decay rates in Be-like ions

In this work we report on ab initio theoretical results for the magnetic field induced 2s2p ^3P_0 - 2s^2 ^1S_0 E1 transition for ions in the beryllium isoelectronic sequence between Z=5 and 92. It has been proposed that the rate of the E1M1 two-photon transition 2s2p ^3P_0 - 2s^2 ^1S_0 can be extracted from the lifetime of the ^3P_0 state in Be-like ions with zero nuclear spin by employing resonant recombination in a storage-ring. This experimental approach involves a perturbing external magnetic field. The effect of this field needs to be evaluated in order to properly extract the two-photon rate from the measured decay curves. The magnetic field induced transition rates are carefully evaluated and it is shown that, with a typical storage-ring field strength, it is dominant or of the same order as the E1M1 rate for low- and mid-Z ions. Results for several field strengths and ions are presented and we also give a simple Z-dependent formula for the rate. We estimate the uncertainties of our model to be within 5% for low- and mid-Z ions, and slightly larger for more highly charged ions. Furthermore we evaluate the importance of including both perturber states, ^3P_1 and ^1P_1, and it is shown that excluding the influence of the ^1P_1 perturber overestimates the rate by up to 26% for the mid-Z ions.