Relativistic nuclear recoil, electron correlation and QED effects in highly charged Ar ions

We have performed extensive theoretical studies on the 1s$^{2}$2s$^{2}$2p$^{2}$P$_{3/2}$ -- $^{2}$P$_{1/2}$ M1 transition in Ar${}^{13+}$ ions. Accurate radiative lifetimes are sensitive to QED corrections like the electron anomalous magnetic moment and to relativistic electron correlation effects. The lifetime of the P$_{3/2}$ metastable state was determined to be 9.573(4)(5) ms (stat)(syst) [1] using the Heidelberg electron beam ion trap. Theoretical predictions cluster around a value that is significantly shorter than this high-precision experimental result. This discrepancy is presently unexplained. The wavelengths of the above transition in Ar$^{13+}$ and the 1s$^{2}$2s2p $^{3}$P$_{1}$ -- $^{3}$P$_{2}$ M1 transition in Ar$^{14+}$ were compared for the isotopes $^{36}$Ar and $^{40}$Ar [2]. The observed mass shift has confirmed the relativistic theory of nuclear recoil effects in many-body systems. Our calculations, based on the fully relativistic recoil operator, are in excellent agreement with the measured results. [1] A. Lapierre, U.D. Jentschura, J.R. Crespo L\'{o}pez-Urrutia {\it et al.}, Phys. Rev. Lett. 95, 183001 (2005); [2] R. Soria Orts, Z. Harman, J.R. Crespo L\'{o}pez-Urrutia {\it et al.}, Phys. Rev. Lett. 97, 103002 (2006)