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

Abstract

In this work we report on ab initio theoretical results for the magnetic-field-induced $2s\phantom{\rule{0.16em}{0ex}}2p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}\ensuremath{\rightarrow}2{s}^{2\phantom{\rule{0.16em}{0ex}}1}{S}_{0}$ 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 $2s\phantom{\rule{0.16em}{0ex}}2p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}\ensuremath{\rightarrow}2{s}^{2\phantom{\rule{0.16em}{0ex}}1}{S}_{0}$ can be extracted from the lifetime of the ${}^{3}{P}_{0}$ 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, ${}^{3}{P}_{1}$ and ${}^{1}{P}_{1}$, and it is shown that excluding the influence of the ${}^{1}{P}_{1}$ perturber overestimates the rate by up to $26%$ for the mid-$Z$ ions.