Resolving a discrepancy between experimental and theoretical lifetimes in atomic negative ions

Recently the lifetime of the excited $^{2}P_{1/2}$-state of S$^-$ was measured to be $503\pm 54$ s (B\"ackstr\"om et al. Phys. Rev. Lett. 114, 143003 (2015)). The earlier theoretical lifetime of $436$ s was clearly outside the experimental error bars. To investigate this discrepancy we have performed systematic and large-scale multiconfiguration Dirac-Hartree-Fock calculations for this system. After including a careful treatment of correlation and relativistic effects, we predict a well-converged value of $492$ s for this lifetime, with an uncertainty considerably less than 1%, thereby removing the apparent conflict between theory and experiment. We also show that this result corresponds to the non-relativistic limit in the $LS$-approximation for the M1 transition within this $^2P$ term. We also demonstrate the usefulness of the latter approach for $^2P$ transitions in O$^-$, Se$^-$ and Te$^-$, as well as for analogous M1 transitions within $^2D$ terms in Ni$^-$ and Pt$^-$ ions.